Posts Tagged 'Keynes'

Nick Rowe Goes Bonkers over Milton Friedman

Nick Rowe, usually a very cool guy, recently wrote a gushing post about the awesomeness of Milton Friedman. How uncool of him. As followers of this blog may know, even though I like free markets, am skeptical of big government programs, believe that the business cycle is largely a monetary phenomenon, I am not a fan of Milton Friedman. So I am going to offer some comments about Nick’s panegyric to Friedman.

I can’t think of any economist living today who has had as much influence on economics and economic policy as Milton Friedman had, and still has. Neither on the right, nor on the left.

Bob Lucas and Ned Prescott have not had as much influence on modern macroeconomics as Milton Friedman? I am less of a fan of  Lucas and Prescott than I am of Friedman, but surely Nick can’t be serious.

If you had a time machine, went back to (say) 1985, picked up Milton Friedman, brought him forward to 2015, and showed him the current debate over macroeconomic policy, he could immediately join right in. Is there anything important that would be really new to him?

We are all Friedman’s children and grandchildren. The way that New Keynesians approach macroeconomics owes more to Friedman than to Keynes: the permanent income hypothesis; the expectations-augmented Phillips Curve; the idea that the central bank is responsible for inflation and should follow a transparent rule. The first two Friedman invented; the third pre-dates Friedman, but he persuaded us it was right. Using the nominal interest rate as the monetary policy instrument is non-Friedmanite, but the new-fangled “Quantitative Easing” is just a silly new name for Friedmanite base-control.

Certainly Friedman looms large, and New Keynesianism is indeed a way of rationalizing the price and wage stickiness that Friedman, like so many others, relied on to account for the correlation between downward cyclical movements in nominal GDP, or in its rate of growth, and real GDP. To be sure the permanent-income hypothesis was a great achievement, for it wasn’t just Friedman’s, but the expectations-augmented Phillips Curve was anticipated by far too many people (including David Hume) for Friedman to be given very much credit. He certainly gave an influential statement of the reasoning behind the expectations-augmented Phillips Curve, but that hardly counts as a breakthrough. So of the three key elements of New Keynesianism for which Nick credits Friedman only one was (co-)invented by Friedman; the other two were promoted by Friedman, and he certainly influenced the profession, but they were ideas already out there, when he picked them up. And just what does Nick mean by “Friedmanite base-control?” That Friedman invented open-market operations? Good grief!

Then Nick waxes nostalgic:

We easily forget how daft the 1970’s really were, and some ideas were much worse than pet rocks. (Marxism was by far the worst, of course, and had a lot of support amongst university intellectuals, though not much in economics departments.) When inflation was too high, and we wanted to bring inflation down, many (most?) macroeconomists advocated direct controls on prices and wages.

And governments in Canada, the US, the UK (there must have been more) actually implemented direct controls on prices and wages to bring inflation down. Milton Friedman actually had to argue against price and wage controls and against the prevailing wisdom that inflation was caused by monopoly power, monopoly unions, a grab-bag of sociological factors, and had nothing to do with monetary policy.

Many economists unfortunately either supported, or did not forthrightly oppose, wage and price controls when they were imposed successively in the US, UK and Canada in the early 1970s. And Friedman was certainly right to oppose them, and deserves credit for speaking out eloquently against them. But their failure became palpable to most economists, and it is not as if Friedman required any special insight to see the underlying fallacy that Nick nicely articulates. He was just straightforwardly applying Econ 101.

Imagine if I argued today: “Inflation is dangerously low. In order to increase inflation, governments should pass a law saying that all firms must raise all prices and wages by a minimum of 2% a year, unless they apply for and get special permission from the Prices and Incomes Board to raise them by less.” What are the chances my policy proposal would be accepted?

I hope zero, but are we indebted to Friedman for any argument against wage and price controls that was not understood by economists long before Friedman appeared on the scene?

Friedman had a mountain to move, and he moved it. And because he already moved it, we simply cannot have a Friedman today.

Great men like Friedman require a great job to do, or else they can’t become great men. They also require an aristocracy, oligarchy, or monarchy, where only a few voices can get heard, or else they can’t become one of the few voices. The internet actually makes it harder to create great public intellectuals, which is probably a good thing, simply because it’s harder to stand out as great, when there’s lots of competition.

The right won the economics debate; left and right are just haggling over details. The big debate is no longer about economics (sadly for me); and it won’t be held on the pages of the New York Times or in the economics journals.

Actually I agree with Nick that Friedman was a great man and a great economist. He did make a difference, but the difference was not mainly the result of any important theoretical discoveries or contributions, his theory of the consumption function being his main theoretical contribution. Otherwise, he was a great applied and empirical economist, specializing in US monetary history, but his knowledge of the history of monetary theory was sketchy, causing him to make huge blunders in describing the quantity theory of money as a theory of the demand for money, and in suggesting that his 1956 restatement of the quantity theory was inspired by an imagined Chicago oral tradition, when, in fact, his restatement was a reworking of the Cambridge theory of the demand for money that Keynes had turned into his theory of liquidity preference. He hardly cited the work of earlier monetary theorists, aside from Keynes and Irving Fisher, completely ignoring the monetary theory of Hawtrey and Hawtrey’s monetary explanation of the Great Depression, which preceded Friedman’s by some 30 years. Friedman also wrote a famous paper repackaging a slightly dumbed down version of Karl Popper’s philosophy of science as the methodology of positive economics, without acknowledging Popper, an omission that he seems never to have been called on. But his industriousness and diligence were epic, he had a fine intellect and a true mastery of microeconomic theory, coupled with great empirical and statistical insight when applying theory. His ability to express himself cogently and forcefully in writing and in speech was remarkable, and he had a gift for strategic simplification, which unfortunately often led him to convenient oversimplification. Nor do I doubt that he was sincerely motivated by an idealistic dedication to his conception of free-market principles, which he expounded and defended tirelessly.

Nick seems to believe that because hardly any younger economists recognize then name J. K. Galbraith, and because no one any longer advocates imposing wage and price controls to control or speed up inflation, it is obvious that the right won the economics debate. I don’t entirely disagree with that, but I do think it is more complicated than that, the terms right and left being far too limited to portray a complex reality. Galbraith believed that the book he published in 1967 The New Industrial State was going to demonstrate the market economics was a snare and a delusion, because both the Soviet Union and the US were moving toward an economic system dominated by huge enterprises that engaged in long-term planning and were able to impose their plans on unwilling consumers and workers. The most devastating review of Galbraith’s book was published in the June 1968 edition of The Economic Journal by James Meade, an eminent British economist who had been a close disciple of Keynes at Cambridge, and was a kind of market socialist, or a self-described LibLaberal. The entire essay is worth reading, but I just want to highlight a few excerpts from it.

This argument for a national indicative plan is strangely overlooked by Professor Galbraith. Indeed, there is a great hiatus in his analysis of the economic system as a whole or, perhaps more accurately, in his implied analysis of what the economic system as a whole would be like when virtually the whole of it was controlled by large modern corporations. Professor Galbraith asserts that each modern corporation plans ahead the quantities of the various products which it will produce and the prices at which it will sell them; he assumes we will discuss this assumption later that as a general rule each corporation through its advertising and other sales activi-ties can so mould consumers’ demands that these planned quantities are actually sold at these planned prices. But he never explains why and by what mechanism these individual plans can be expected to build up into a coherent whole. . . .

In short, if all individual plans are to be simultaneously fulfilled they must in the first instance be consistent. But Professor Galbraith never considers this problem. It is a strange oversight in a modern professional economist-to overlook the problem of general, as contrasted with particular, equilibrium. (pp. 377-78)

Professor Galbraith writes always as if planning meant deciding in advance what should be produced and sold, in what quantities, at what cost and at what prices, and then taking effective steps to ensure that quantities and prices of inputs and outputs developed in precisely this way, and as if the market mechanism meant taking no thought for the morrow, taking no initiative in planning ahead the introduction of new products and processes, but just waiting for consumers to come to the firm and order a new car of such-and-such a bespoke design. It is by silly contrasts of this kind that Professor Galbraith pokes fun at his professional colleagues. (p. 382)

In the modern complex economy there are two major forces at work. One of these is that which Professor Galbraith rightly emphasises, namely the increased need for careful forward planning in a system which involves the commitment of large resources to inflexible uses over long periods of time.

But there is a second and equally important trend, which he entirely neglects: namely, the increased need in the modern industrial economy for a price mechanism, that is to say for reliance on a system of prices as a signaling device to indicate to producers and consumers what is and what is not scarce. This increased need for a price mechanism arises because in the modern industrial system input-output relationships have become so complex and the differentiation between products (many of which are the technically sophisticated inputs of other productive processes) has become so manifold that simple quantitative planning without a price or market mechanism becomes increasingly clumsy and inefficient. Moreover, this increased need for a signaling system through prices is occurring at a time when advances in mathematical economics and in the electronic and other technologies for measuring and metering have made a great extension of the price mechanism possible. Public authorities begin to make serious quantitative cost-benefit studies where previously pure hunches would have had to serve; and we nowadays seriously consider as, for example, in electronic metering devices for charging for the use of road space by motor vehicles-extensions of the use of pricing which would previously have been considered technologically impossible.

The particular brand of conventional wisdom which Professor Galbraith promotes in his recent book overlooks all these increased needs and opportunities for the use of the price mechanism. But many of the planned socialist societies are not falling into this error. Experiments which they are making in such devices as setting the maximisation of profit as the success criterion for the managers of socialised plants, in the direct use of the free market as in Yugoslavia, and generally in an increased reliance on price-mechanism indicators for many decentralised decisions constitute an undoubtedly significant development. The use of the price mechanism is, of course, not the same thing as the use of a market mechanism. A completely planned socialist economy could theoretically be run without any markets at all but with a complete system of “shadow prices” to measure relative scarcities and to be used as the decisive indicators for the adjustments to be made in the economy’s quantitative planned inputs and outputs. But in many, though not of course in all, cases an actual market mechanism will be found to be institutionally the best way of operating a price mechanism. There are many degrees and forms of such extensions of the market; for example, in some cases the prices at which transactions take place might be centrally controlled and adjusted, while in others they might be freely determined by supply and demand in the market. But in one form or an-other increased reliance on a price mechanism does imply increased reliance at least on something closely analogous to a market mechanism.

Professor Galbraith expressly denies that recent developments in the socialist countries have any significant connections with the use of the market as a controlling device. This denial would, by the uncouth, be called drivel-if I may be permitted to use Professor Galbraith’s own expression. But he has to hold this view simply because the socialist countries continue to plan while he, drawing no distinction between the price mechanism and a market mechanism, believes that one can have either planning or a market-price mechanism but not both. In fact, “planning and the price mechanism” not “planning or the price mechanism” should be a central theme of every modern economist’s work. (pp. 391-92)

In his 1977 Nobel Lecture, as Marcus Nunes informed us a few days ago, Meade explicitly advocated targeting nominal GDP writing as follows:

I have told this particular story simply to make the point that the choice between fiscal action and monetary action must often depend upon basic policy issues which should certainly be the responsibility of the government rather than of any independent monetary authority. Perhaps the best compromise is an independent monetary authority charged so to manage the money supply and the market rate of interest as to maintain the growth of total money income on its 5-per-cent-per-annum target path, after taking into account whatever fiscal policies the government may adopt.

So let me ask Nick the following: Was Meade right or left? And was he on the winning side or the losing side?

Hicks on IS-LM and Temporary Equilibrium

Jan, commenting on my recent post about Krugman, Minsky and IS-LM, quoted the penultimate paragraph of J. R. Hicks’s 1980 paper on IS-LM in the Journal of Post-Keynesian Economics, a brand of economics not particularly sympathetic to Hicks’s invention. Hicks explained that in the mid-1930s he had been thinking along lines similar to Keynes’s even before the General Theory was published, and had the basic idea of IS-LM in his mind even before he had read the General Theory, while also acknowledging that his enthusiasm for the IS-LM construct had waned considerably over the years.

Hicks discussed both the similarities and the differences between his model and IS-LM. But as the discussion proceeds, it becomes clear that what he is thinking of as his model is what became his model of temporary equilibrium in Value and Capital. So it really is important to understand what Hicks felt were the similarities as well as the key differences between the temporary- equilibrium model, and the IS-LM model. Here is how Hicks put it:

I recognized immediately, as soon as I read The General Theory, that my model and Keynes’ had some things in common. Both of us fixed our attention on the behavior of an economy during a period—a period that had a past, which nothing that was done during the period could alter, and a future, which during the period was unknown. Expectations of the future would nevertheless affect what happened during the period. Neither of us made any assumption about “rational expectations” ; expectations, in our models, were strictly exogenous.3 (Keynes made much more fuss over that than I did, but there is the same implication in my model also.) Subject to these data— the given equipment carried over from the past, the production possibilities within the period, the preference schedules, and the given expectations— the actual performance of the economy within the period was supposed to be determined, or determinable. It would be determined as an equilibrium performance, with respect to these data.

There was all this in common between my model and Keynes'; it was enough to make me recognize, as soon as I saw The General Theory, that his model was a relation of mine and, as such, one which I could warmly welcome. There were, however, two differences, on which (as we shall see) much depends. The more obvious difference was that mine was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model. I shall have much to say about this difference, but I may as well note, at the start, that I do not think it matters much. I did not think, even in 1936, that it mattered much. IS-LM was in fact a translation of Keynes’ nonflexprice model into my terms. It seemed to me already that that could be done; but how it is done requires explanation.

The other difference is more fundamental; it concerns the length of the period. Keynes’ (he said) was a “short-period,” a term with connotations derived from Marshall; we shall not go far wrong if we think of it as a year. Mine was an “ultra-short-period” ; I called it a week. Much more can happen in a year than in a week; Keynes has to allow for quite a lot of things to happen. I wanted to avoid so much happening, so that my (flexprice) markets could reflect propensities (and expectations) as they are at a moment. So it was that I made my markets open only on a Monday; what actually happened during the ensuing week was not to affect them. This was a very artificial device, not (I would think now) much to be recommended. But the point of it was to exclude the things which might happen, and must disturb the markets, during a period of finite length; and this, as we shall see, is a very real trouble in Keynes. (pp. 139-40)

Hicks then explained how the specific idea of the IS-LM model came to him as a result of working on a three-good Walrasian system in which the solution could be described in terms of equilibrium in two markets, the third market necessarily being in equilibrium if the other two were in equilibrium. That’s an interesting historical tidbit, but the point that I want to discuss is what I think is Hicks’s failure to fully understand the significance of his own model, whose importance, regrettably, he consistently underestimated in later work (e.g., in Capital and Growth and in this paper).

The point that I want to focus on is in the second paragraph quoted above where Hicks says “mine [i.e. temporary equilibrium] was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model.” This, it seems to me, is all wrong, because Hicks, is taking a very naïve and misguided view of what perfect competition and flexible prices mean. Those terms are often mistakenly assumed to meant that if prices are simply allowed to adjust freely, all  markets will clear and all resources will be utilized.

I think that is a total misconception, and the significance of the temporary-equilibrium construct is in helping us understand why an economy can operate sub-optimally with idle resources even when there is perfect competition and markets “clear.” What prevents optimality and allows resources to remain idle despite freely adjustming prices and perfect competition is that the expectations held by agents are not consistent. If expectations are not consistent, the plans based on those expectations are not consistent. If plans are not consistent, then how can one expect resources to be used optimally or even at all? Thus, for Hicks to assert, casually without explicit qualification, that his temporary-equilibrium model was a full-employment model, indicates to me that Hicks was unaware of the deeper significance of his own model.

If we take a full equilibrium as our benchmark, and look at how one of the markets in that full equilibrium clears, we can imagine the equilibrium as the intersection of a supply curve and a demand curve, whose positions in the standard price/quantity space depend on the price expectations of suppliers and of demanders. Different, i.e, inconsistent, price expectations would imply shifts in both the demand and supply curves from those corresponding to full intertemporal equilibrium. Overall, the price expectations consistent with a full intertemporal equilibrium will in some sense maximize total output and employment, so when price expectations are inconsistent with full intertemporal equilibrium, the shifts of the demand and supply curves will be such that they will intersect at points corresponding to less output and less employment than would have been the case in full intertemporal equilibrium. In fact, it is possible to imagine that expectations on the supply side and the demand side are so inconsistent that the point of intersection between the demand and supply curves corresponds to an output (and hence employment) that is way less than it would have been in full intertemporal equilibrium. The problem is not that the price in the market doesn’t allow the market to clear. Rather, given the positions of the demand and supply curves, their point of intersection implies a low output, because inconsistent price expectations are such that potentially advantageous trading opportunities are not being recognized.

So for Hicks to assert that his flexprice temporary-equilibrium model was (in Keynes’s terms) a full-employment model without noting the possibility of a significant contraction of output (and employment) in a perfectly competitive flexprice temporary-equilibrium model when there are significant inconsistencies in expectations suggests strongly that Hicks somehow did not fully comprehend what his own creation was all about. His failure to comprehend his own model also explains why he felt the need to abandon the flexprice temporary-equilibrium model in his later work for a fixprice model.

There is, of course, a lot more to be said about all this, and Hicks’s comments concerning the choice of a length of the period are also of interest, but the clear (or so it seems to me) misunderstanding by Hicks of what is entailed by a flexprice temporary equilibrium is an important point to recognize in evaluating both Hicks’s work and his commentary on that work and its relation to Keynes.

Temporary Equilibrium One More Time

It’s always nice to be noticed, especially by Paul Krugman. So I am not upset, but in his response to my previous post, I don’t think that Krugman quite understood what I was trying to convey. I will try to be clearer this time. It will be easiest if I just quote from his post and insert my comments or explanations.

Glasner is right to say that the Hicksian IS-LM analysis comes most directly not out of Keynes but out of Hicks’s own Value and Capital, which introduced the concept of “temporary equilibrium”.

Actually, that’s not what I was trying to say. I wasn’t making any explicit connection between Hicks’s temporary-equilibrium concept from Value and Capital and the IS-LM model that he introduced two years earlier in his paper on Keynes and the Classics. Of course that doesn’t mean that the temporary equilibrium method isn’t connected to the IS-LM model; one would need to do a more in-depth study than I have done of Hicks’s intellectual development to determine how much IS-LM was influenced by Hicks’s interest in intertemporal equilibrium and in the method of temporary equilibrium as a way of analyzing intertemporal issues.

This involves using quasi-static methods to analyze a dynamic economy, not because you don’t realize that it’s dynamic, but simply as a tool. In particular, V&C discussed at some length a temporary equilibrium in a three-sector economy, with goods, bonds, and money; that’s essentially full-employment IS-LM, which becomes the 1937 version with some price stickiness. I wrote about that a long time ago.

Now I do think that it’s fair to say that the IS-LM model was very much in the spirit of Value and Capital, in which Hicks deployed an explicit general-equilibrium model to analyze an economy at a Keynesian level of aggregation: goods, bonds, and money. But the temporary-equilibrium aspect of Value and Capital went beyond the Keynesian analysis, because the temporary equilibrium analysis was explicitly intertemporal, all agents formulating plans based on explicit future price expectations, and the inconsistency between expected prices and actual prices was explicitly noted, while in the General Theory, and in IS-LM, price expectations were kept in the background, making an appearance only in the discussion of the marginal efficiency of capital.

So is IS-LM really Keynesian? I think yes — there is a lot of temporary equilibrium in The General Theory, even if there’s other stuff too. As I wrote in the last post, one key thing that distinguished TGT from earlier business cycle theorizing was precisely that it stopped trying to tell a dynamic story — no more periods, forced saving, boom and bust, instead a focus on how economies can stay depressed. Anyway, does it matter? The real question is whether the method of temporary equilibrium is useful.

That is precisely where I think Krugman’s grasp on the concept of temporary equilibrium is slipping. Temporary equilibrium is indeed about periods, and it is explicitly dynamic. In my previous post I referred to Hicks’s discussion in Capital and Growth, about 25 years after writing Value and Capital, in which he wrote

The Temporary Equilibrium model of Value and Capital, also, is “quasi-static” [like the Keynes theory] – in just the same sense. The reason why I was contented with such a model was because I had my eyes fixed on Keynes.

As I read this passage now — and it really bothered me when I read it as I was writing my previous post — I realize that what Hicks was saying was that his desire to conform to the Keynesian paradigm led him to compromise the integrity of the temporary equilibrium model, by forcing it to be “quasi-static” when it really was essentially dynamic. The challenge has been to convert a “quasi-static” IS-LM model into something closer to the temporary-equilibrium method that Hicks introduced, but did not fully execute in Value and Capital.

What are the alternatives? One — which took over much of macro — is to do intertemporal equilibrium all the way, with consumers making lifetime consumption plans, prices set with the future rationally expected, and so on. That’s DSGE — and I think Glasner and I agree that this hasn’t worked out too well. In fact, economists who never learned temporary-equiibrium-style modeling have had a strong tendency to reinvent pre-Keynesian fallacies (cough-Say’s Law-cough), because they don’t know how to think out of the forever-equilibrium straitjacket.

Yes, I agree! Rational expectations, full-equilibrium models have turned out to be a regression, not an advance. But the way I would make the point is that the temporary-equilibrium method provides a sort of a middle way to do intertemporal dynamics without presuming that consumption plans and investment plans are always optimal.

What about disequilibrium dynamics all the way? Basically, I have never seen anyone pull this off. Like the forever-equilibrium types, constant-disequilibrium theorists have a remarkable tendency to make elementary conceptual mistakes.

Again, I agree. We can’t work without some sort of equilibrium conditions, but temporary equilibrium provides a way to keep the discipline of equilibrium without assuming (nearly) full optimality.

Still, Glasner says that temporary equilibrium must involve disappointed expectations, and fails to take account of the dynamics that must result as expectations are revised.

Perhaps I was unclear, but I thought I was saying just the opposite. It’s the “quasi-static” IS-LM model, not temporary equilibrium, that fails to take account of the dynamics produced by revised expectations.

I guess I’d say two things. First, I’m not sure that this is always true. Hicks did indeed assume static expectations — the future will be like the present; but in Keynes’s vision of an economy stuck in sustained depression, such static expectations will be more or less right.

Again, I agree. There may be self-fulfilling expectations of a low-income, low-employment equilibrium. But I don’t think that that is the only explanation for such a situation, and certainly not for the downturn that can lead to such an equilibrium.

Second, those of us who use temporary equilibrium often do think in terms of dynamics as expectations adjust. In fact, you could say that the textbook story of how the short-run aggregate supply curve adjusts over time, eventually restoring full employment, is just that kind of thing. It’s not a great story, but it is the kind of dynamics Glasner wants — and it’s Econ 101 stuff.

Again, I agree. It’s not a great story, but, like it or not, the story is not a Keynesian story.

So where does this leave us? I’m not sure, but my impression is that Krugman, in his admiration for the IS-LM model, is trying too hard to identify IS-LM with the temporary-equilibrium approach, which I think represented a major conceptual advance over both the Keynesian model and the IS-LM representation of the Keynesian model. Temporary equilibrium and IS-LM are not necessarily inconsistent, but I mainly wanted to point out that the two aren’t the same, and shouldn’t be conflated.

Krugman on Minsky, IS-LM and Temporary Equilibrium

Catching up on my blog reading, I found this one from Paul Krugman from almost two weeks ago defending the IS-LM model against Hyman Minsky’s criticism (channeled by his student Lars Syll) that IS-LM misrepresented the message of Keynes’s General Theory. That is an old debate, and it’s a debate that will never be resolved because IS-LM is a nice way of incorporating monetary effects into the pure income-expenditure model that was the basis of Keynes’s multiplier analysis and his policy prescriptions. On the other hand, the model leaves out much of what most interesting and insightful in the General Theory – precisely the stuff that could not easily be distilled into a simple analytic model.

Here’s Krugman:

Lars Syll approvingly quotes Hyman Minsky denouncing IS-LM analysis as an “obfuscation” of Keynes; Brad DeLong disagrees. As you might guess, so do I.

There are really two questions here. The less important is whether something like IS-LM — a static, equilibrium analysis of output and employment that takes expectations and financial conditions as given — does violence to the spirit of Keynes. Why isn’t this all that important? Because Keynes was a smart guy, not a prophet. The General Theory is interesting and inspiring, but not holy writ.

It’s also a protean work that contains a lot of different ideas, not necessarily consistent with each other. Still, when I read Minsky putting into Keynes’s mouth the claim that

Only a theory that was explicitly cyclical and overtly financial was capable of being useful

I have to wonder whether he really read the book! As I read the General Theory — and I’ve read it carefully — one of Keynes’s central insights was precisely that you wanted to step back from thinking about the business cycle. Previous thinkers had focused all their energy on trying to explain booms and busts; Keynes argued that the real thing that needed explanation was the way the economy seemed to spend prolonged periods in a state of underemployment:

[I]t is an outstanding characteristic of the economic system in which we live that, whilst it is subject to severe fluctuations in respect of output and employment, it is not violently unstable. Indeed it seems capable of remaining in a chronic condition of subnormal activity for a considerable period without any marked tendency either towards recovery or towards complete collapse.

So Keynes started with a, yes, equilibrium model of a depressed economy. He then went on to offer thoughts about how changes in animal spirits could alter this equilibrium; but he waited until Chapter 22 (!) to sketch out a story about the business cycle, and made it clear that this was not the centerpiece of his theory. Yes, I know that he later wrote an article claiming that it was all about the instability of expectations, but the book is what changed economics, and that’s not what it says.

This all seems pretty sensible to me. Nevertheless, there is so much in the General Theory — both good and bad – that isn’t reflected in IS-LM, that to reduce the General Theory to IS-LM is a kind of misrepresentation. And to be fair, Hicks himself acknowledged that IS-LM was merely a way of representing one critical difference in the assumptions underlying the Keynesian and the “Classical” analyses of macroeconomic equilibrium.

But I would take issue with the following assertion by Krugman.

The point is that Keynes very much made use of the method of temporary equilibrium — interpreting the state of the economy in the short run as if it were a static equilibrium with a lot of stuff taken provisionally as given — as a way to clarify thought. And the larger point is that he was right to do this.

When people like me use something like IS-LM, we’re not imagining that the IS curve is fixed in position for ever after. It’s a ceteris paribus thing, just like supply and demand. Assuming short-run equilibrium in some things — in this case interest rates and output — doesn’t mean that you’ve forgotten that things change, it’s just a way to clarify your thought. And the truth is that people who try to think in terms of everything being dynamic all at once almost always end up either confused or engaging in a lot of implicit theorizing they don’t even realize they’re doing.

When I think of a temporary equilibrium, the most important – indeed the defining — characteristic of that temporary equilibrium is that expectations of at least some agents have been disappointed. The disappointment of expectations is likely to, but does not strictly require, a revision of disappointed expectations and of the plans conditioned on those expectations. The revision of expectations and plans as a result of expectations being disappointed is what gives rise to a dynamic adjustment process. But that is precisely what is excluded from – or at least not explicitly taken into account by – the IS-LM model. There is nothing in the IS-LM model that provides any direct insight into the process by which expectations are revised as a result of being disappointed. That Keynes could so easily think in terms of a depressed economy being in equilibrium suggests to me that he was missing what I regard as the key insight of the temporary-equilibrium method.

Of course, there are those who argue, perhaps most notably Roger Farmer, that economies have multiple equilibria, each with different levels of output and employment corresponding to different expectational parameters. That seems to me a more Keynesian approach, an approach recognizing that expectations can be self-fulfilling, than the temporary-equilibrium approach in which the focus is on mistaken and conflicting expectations, not their self-fulfillment.

Now to be fair, I have to admit that Hicks, himself, who introduced the temporary-equilibrium approach in Value and Capital (1939) later (1965) suggested in Capital and Growth (p. 65) that both the Keynes in the General Theory and the temporary-equilibrium approach of Value and Capital were “quasi-static.” The analysis of the General Theory “is not the analysis of a process; no means has been provided by which we can pass from one Keynesian period to the next. . . . The Temporary Equilibrium model of Value and Capital, also, is quasi-static in just the same sense. The reason why I was contented with such a model was because I had my eyes fixed on Keynes.

Despite Hicks’s identification of the temporary-equilibrium method with Keynes’s method in the General Theory, I think that Hicks was overly modest in assessing his own contribution in Value and Capital, failing to appreciate the full significance of the method he had introduced. Which, I suppose, just goes to show that you can’t assume that the person who invents a concept or an idea is necessarily the one who has the best, or most comprehensive, understanding of what the concept means of what its significance is.

Explaining Post-Traumatic-Inflation Stress Disorder

Paul Krugman and Steve Waldman having been puzzling of late about why inflation is so viscerally opposed by the dreaded one percent (even more so by the ultra-dreaded 0.01 percent). Here’s how Krugman phrased the conundrum.

One thought I’ve had and written about is that the one percent (or actually the 0.01 percent) like hard money because they’re rentiers. But you can argue that this is foolish — that they have much more to gain from asset appreciation than they have to lose from the small chance of runaway inflation. . . .

But maybe the 1% doesn’t make the connection?

Steve Waldman, however, doesn’t take the one percent — and certainly not the 0.01 percent — for the misguided dunces that Krugman suggests they are. Waldman sees them as the cunning, calculating villains that we all (notwithstanding his politically correct disclaimer that the rich aren’t bad people) know they really are.

Soft money types — I’ve heard the sentiment from Scott Sumner, Brad DeLong, Kevin Drum, and now Paul Krugman — really want to see the bias towards hard money and fiscal austerity as some kind of mistake. I wish that were true. It just isn’t. Aggregate wealth is held by risk averse individuals who don’t individually experience aggregate outcomes. Prospective outcomes have to be extremely good and nearly certain to offset the insecurity soft money policy induces among individuals at the top of the distribution, people who have much more to lose than they are likely to gain.

That’s all very interesting. Are the rich opposed to inflation because they are stupid, or because they are clever? Krugman thinks it’s the former, Waldman the latter. And I agree; it is a puzzle.

But what about the poor and the middle class? Has anyone seen any demonstrations lately by the 99 percent demanding that the Fed increase its inflation target? Did even one Democrat in the Senate – not even that self-proclaimed socialist Bernie Sanders — threaten to vote against confirmation of Janet Yellen unless she promised to raise the Fed’s inflation target? Well, maybe that just shows that the Democrats are as beholden to the one percent as the Republicans, but I suspect that the real reason is because the 99 percent hate inflation just as much as the one percent do. I mean, don’t the 99 percent realize that inflation would increase total output and employment, thereby benefitting ordinary workers generally?

Oh, you say, workers must be afraid that inflation would reduce their real wages. That’s a widely believed factoid about inflation — that inflation is biased against workers, because wages adjust more slowly than other prices to changes in demand. Well, that factoid is not necessarily true, either in theory or in practice. That doesn’t mean that inflation might not be associated with reduced real wages, but if it is, it would mean that inflation is facilitating a market adjustment in real wages that would tend to increase total output and total employment, thereby increasing aggregate wages paid to workers. That is just the sort of tradeoff between a prospective upside from growth-inducing inflation and a perceived downside from inflation redistribution. In other words, the attitudes of the one percent and of the 99 percent toward inflation don’t seem all that different.

And aside from the potential direct output-expanding effect of inflation, there is also the redistributional effect from creditors to debtors. A lot of underwater homeowners could have sold their homes if a 10- or 20-percent increase in the overall price level had kept nominal home prices from falling below nominal mortgage indebtedness. Inflation would have been the simplest and easiest way to avoid a foreclosure crisis and getting stuck in a balance-sheet recession. Why weren’t underwater homeowners out their clamoring for some inflationary relief?

I have not done a historical study, but I cannot think of any successful political movement or campaign that has ever been carried out on a platform of increasing inflation. Even FDR, who saved the country from ruin by taking the US off the gold standard in 1933, did not say that he would do so when running for office.

Nor has anyone ever stated the case against inflation more eloquently than John Maynard Keynes, hardly a spokesman for the interests of rentiers.

Lenin is said to have declared that the best way to destroy the capitalist system was to debauch the currency. By a continuing process of inflation, governments can confiscate, secretly and unobserved, an important part of the wealth of their citizens. By this method they not only confiscate, but they confiscate arbitrarily; and, while the process impoverishes many, it actually enriches some. The sight of this arbitrary rearrangement of riches strikes not only at security but [also] at confidence in the equity of the existing distribution of wealth.

Those to whom the system brings windfalls, beyond their deserts and even beyond their expectations or desires, become “profiteers,” who are the object of the hatred of the bourgeoisie, whom the inflationism has impoverished, not less than of the proletariat. As the inflation proceeds and the real value of the currency fluctuates wildly from month to month, all permanent relations between debtors and creditors, which form the ultimate foundation of capitalism, become so utterly disordered as to be almost meaningless; and the process of wealth-getting degenerates into a gamble and a lottery.

Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of society than to debauch the currency. The process engages all the hidden forces of economic law on the side of destruction, and does it in a manner which not one man in a million is able to diagnose. (Economic Consequences of the Peace)

One might say that when Keynes wrote this he was still very much of an orthodox Marshallian economist, who only later outgrew his orthodox prejudices when he finally saw the light and wrote the General Theory. But Keynes was actually quite explicit in the General Theory that he favored a monetary policy aiming at price-level stabilization. If Keynes favored inflation it was only in the context of counteracting a massive deflation. Similarly, Ralph Hawtrey, who famously likened opposition to monetary stimulus, out of fear of inflation, during the Great Depression to crying “fire, fire” during Noah’s Flood, favored a monetary regime aiming at stable money wages, a regime that over the long term would generate a gradually falling output price level. So I fail to see why anyone should be surprised that a pro-inflationary policy would be a tough sell even when unemployment is high.

But, in thinking about all this, I believe it may help to distinguish between two types of post-traumatic-inflation stress disorder. One is a kind of instinctual aversion to inflation, which I think is widely shared by people from all kinds of backgrounds, beliefs, and economic status. After arguing and pleading for higher inflation for over three years on this blog, I am a little bit embarrassed to make this admission, but I suffer from this type of post-traumatic-inflation stress disorder myself. I know that it’s weird, but every month when the CPI is announced, and the monthly change is less than 2%, I just get a warm fuzzy feeling inside of me. I know (or at least believe) that people will suffer because inflation is not higher than a measly 2%, but I can’t help getting that feeling of comfort and well-being when I hear that inflation is low. That just seems to be the natural order of things. And I don’t think that I am the only one who feels that way, though I probably suffer more guilt than most for not being able to suppress the feeling.

But there is another kind of post-traumatic-inflation stress disorder. This is a purely intellectual disorder brought on by excessive exposure to extreme libertarian dogmas associated with pop-Austrianism and reading too many (i.e., more than zero) novels by Ayn Rand. Unfortunately, one of the two major political parties seems to have been captured this group of ideologues, and anti-inflationary dogma has become an article of faith rather than a mere disposition. It is one thing to have a disposition or a bias in favor of low inflation; it is altogether different to make anti-inflationism a moral or ideological crusade. I think most people, whether they are in the one percent or the 99 percent are biased in favor of low inflation, but most of them don’t oppose inflation as a moral or ideological imperative. Now it’s true that that the attachment of a great many people to the gold standard before World War I was akin to a moral precept, but at least since the collapse of the gold standard in the Great Depression, most people no longer think about inflation in moral and ideological terms.

Before anti-inflationism became a moral crusade, it was possible for people like Richard Nixon and Ronald Reagan, who were disposed to favor low inflation, to accommodate themselves fairly easily to an annual rate of inflation of 4 percent. Indeed, it was largely because of pressure from Democrats to fight inflation by wage and price controls that Nixon did the unthinkable and imposed wage and price controls on August 15, 1971. Reagan, who had no interest in repeating that colossal blunder, instead fought against Paul Volcker’s desire to bring inflation down below 4 percent for most of his two terms. Of course, one doesn’t know to what extent the current moral and ideological crusade against inflation would survive an accession to power by a Republican administration. It is always easier to proclaim one’s ideological principles when one doesn’t have any responsibility to implement them. But given the current ideological commitment to anti-inflationism, there was never any chance for a pragmatic accommodation that might have used increased inflation as a means of alleviating economic distress.

The Trouble with IS-LM (and its Successors)

Lately, I have been reading a paper by Roger Backhouse and David Laidler, “What Was Lost with IS-LM” (an earlier version is available here) which was part of a very interesting symposium of 11 papers on the IS-LM model published as a supplement to the 2004 volume of History of Political Economy. The main thesis of the paper is that the IS-LM model, like the General Theory of which it is a partial and imperfect distillation, aborted a number of promising developments in the rapidly developing, but still nascent, field of macroeconomics in the 1920 and 1930s, developments that just might, had they not been elbowed aside by the IS-LM model, have evolved into a more useful and relevant theory of macroeconomic fluctuations and policy than we now possess. Even though I have occasionally sparred with Scott Sumner about IS-LM – with me pushing back a bit at Scott’s attacks on IS-LM — I have a lot of sympathy for the Backhouse-Laidler thesis.

The Backhouse-Laidler paper is too long to summarize, but I will just note that there are four types of loss that they attribute to IS-LM, which are all, more or less, derivative of the static equilibrium character of Keynes’s analytic method in both the General Theory and the IS-LM construction.

1 The loss of dynamic analysis. IS-LM is a single-period model.

2 The loss of intertemporal choice and expectations. Intertemporal choice and expectations are excluded a priori in a single-period model.

3 The loss of policy regimes. In a single-period model, policy is a one-time affair. The problem of setting up a regime that leads to optimal results over time doesn’t arise.

4 The loss of intertemporal coordination failures. Another concept that is irrelevant in a one-period model.

There was one particular passage that I found especially impressive. Commenting on the lack of any systematic dynamic analysis in the GT, Backhouse and Laidler observe,

[A]lthough [Keynes] made many remarks that could be (and in some cases were later) turned into dynamic models, the emphasis of the General Theory was nevertheless on unemployment as an equilibrium phenomenon.

Dynamic accounts of how money wages might affect employment were only a little more integrated into Keynes’s formal analysis than they were later into IS-LM. Far more significant for the development in Keynes’s thought is how Keynes himself systematically neglected dynamic factors that had been discussed in previous explanations of unemployment. This was a feature of the General Theory remarked on by Bertil Ohlin (1937, 235-36):

Keynes’s theoretical system . . . is equally “old-fashioned” in the second respect which characterizes recent economic theory – namely, the attempt to break away from an explanation of economic events by means of orthodox equilibrium constructions. No other analysis of trade fluctuations in recent years – with the possible exception of the Mises-Hayek school – follows such conservative lines in this respect. In fact, Keynes is much more of an “equilibrium theorist” than such economists as Cassel and, I think, Marshall.

Backhouse and Laidler go on to cite the Stockholm School (of which Ohlin was a leading figure) as an example of explicitly dynamic analysis.

As Bjorn Hansson (1982) has shown, this group developed an explicit method, using the idea of a succession of “unit periods,” in which each period began with agents having plans based on newly formed expectations about the outcome of executing them, and ended with the economy in some new situation that was the outcome of executing them, and ended with the economy in some new situation that was the outcome of market processes set in motion by the incompatibility of those plans, and in which expectations had been reformulated, too, in the light of experience. They applied this method to the construction of a wide variety of what they called “model sequences,” many of which involved downward spirals in economic activity at whose very heart lay rising unemployment. This is not the place to discuss the vexed question of the extent to which some of this work anticipated the Keynesian multiplier process, but it should be noted that, in IS-LM, it is the limit to which such processes move, rather than the time path they follow to get there, that is emphasized.

The Stockholm method seems to me exactly the right way to explain business-cycle downturns. In normal times, there is a rough – certainly not perfect, but good enough — correspondence of expectations among agents. That correspondence of expectations implies that the individual plans contingent on those expectations will be more or less compatible with one another. Surprises happen; here and there people are disappointed and regret past decisions, but, on the whole, they are able to adjust as needed to muddle through. There is usually enough flexibility in a system to allow most people to adjust their plans in response to unforeseen circumstances, so that the disappointment of some expectations doesn’t become contagious, causing a systemic crisis.

But when there is some sort of major shock – and it can only be a shock if it is unforeseen – the system may not be able to adjust. Instead, the disappointment of expectations becomes contagious. If my customers aren’t able to sell their products, I may not be able to sell mine. Expectations are like networks. If there is a breakdown at some point in the network, the whole network may collapse or malfunction. Because expectations and plans fit together in interlocking networks, it is possible that even a disturbance at one point in the network can cascade over an increasingly wide group of agents, leading to something like a system-wide breakdown, a financial crisis or a depression.

But the “problem” with the Stockholm method was that it was open-ended. It could offer only “a wide variety” of “model sequences,” without specifying a determinate solution. It was just this gap in the Stockholm approach that Keynes was able to fill. He provided a determinate equilibrium, “the limit to which the Stockholm model sequences would move, rather than the time path they follow to get there.” A messy, but insightful, approach to explaining the phenomenon of downward spirals in economic activity coupled with rising unemployment was cast aside in favor of the neater, simpler approach of Keynes. No wonder Ohlin sounds annoyed in his comment, quoted by Backhouse and Laidler, about Keynes. Tractability trumped insight.

Unfortunately, that is still the case today. Open-ended models of the sort that the Stockholm School tried to develop still cannot compete with the RBC and DSGE models that have displaced IS-LM and now dominate modern macroeconomics. The basic idea that modern economies form networks, and that networks have properties that are not reducible to just the nodes forming them has yet to penetrate the trained intuition of modern macroeconomists. Otherwise, how would it have been possible to imagine that a macroeconomic model could consist of a single representative agent? And just because modern macroeconomists have expanded their models to include more than a single representative agent doesn’t mean that the intellectual gap evidenced by the introduction of representative-agent models into macroeconomic discourse has been closed.

How to Think about Own Rates of Interest, Version 2.0

In my previous post, I tried to explain how to think about own rates of interest. Unfortunately, I made a careless error in calculating the own rate of interest in the simple example I constructed to capture the essence of Sraffa’s own-rate argument against Hayek’s notion of the natural rate of interest. But sometimes these little slip-ups can be educational, so I am going to try to turn my conceptual misstep to advantage in working through and amplifying the example I presented last time.

But before I reproduce the passage from Sraffa’s review that will serve as our basic text in this post as it did in the previous post, I want to clarify another point. The own rate of interest for a commodity may be calculated in terms of any standard of value. If I borrow wheat and promise to repay in wheat, the wheat own rate of interest may be calculated in terms of wheat or in terms of any other standard; all of those rates are own rates, but each is expressed in terms of a different standard.

Lend me 100 bushels of wheat today, and I will pay you back 102 bushels next year. The own rate of interest for wheat in terms of wheat would be 2%. Alternatively, I could borrow $100 of wheat today and promise to pay back $102 of wheat next year. The own rate of interest for wheat in terms of wheat and the own rate of interest for wheat in terms of dollars would be equal if and only if the forward dollar price of wheat is the same as the current dollar price of wheat. The commodity or asset in terms of which a price is quoted or in terms of which we measure the own rate is known as the numeraire. (If all that Sraffa was trying to say in criticizing Hayek was that there are many equivalent ways of expressing own interest rates, he was making a trivial point. Perhaps Hayek didn’t understand that trivial point, in which case the rough treatment he got from Sraffa was not undeserved. But it seems clear that Sraffa was trying — unsuccessfully — to make a more substantive point than that.)

In principle, there is a separate own rate of interest for every commodity and for every numeraire. If there are n commodities, there are n potential numeraires, and n own rates can be expressed in terms of each numeraire. So there are n-squared own rates. Each own rate can be thought of as equilibrating the demand for loans made in terms of a given commodity and a given numeraire. But arbitrage constraints tightly link all these separate own rates together. If it were cheaper to borrow in terms of one commodity than another, or in terms of one numeraire than another, borrowers would switch to the commodity and numeraire with the lowest cost of borrowing, and if it were more profitable to lend in terms of one commodity, or in terms of one numeraire, than another, lenders would switch to lending in terms of the commodity or numeraire with the highest return.

Thus, competition tends to equalize own rates across all commodities and across all numeraires. Of course, perfect arbitrage requires the existence of forward markets in which to contract today for the purchase or sale of a commodity at a future date. When forward markets don’t exist, some traders may anticipate advantages to borrowing or lending in terms of particular commodities based on their expectations of future prices for those commodities. The arbitrage constraint on the variation of interest rates was discovered and explained by Irving Fisher in his great work Appreciation and Interest.

It is clear that if the unit of length were changed and its change were foreknown, contracts would be modified accordingly. Suppose a yard were defined (as once it probably was) to be the length of the king’s girdle, and suppose the king to be a child. Everybody would then know that the “yard” would increase with age and a merchant who should agree to deliver 1000 “yards” ten years hence, would make his terms correspond to his expectations. To alter the mode of measurement does not alter the actual quantities involved but merely the numbers by which they are represented. (p. 1)

We thus see that the farmer who contracts a mortgage in gold is, if the interest is properly adjusted, no worse and no better off than if his contract were in a “wheat” standard or a “multiple” standard. (p. 16)

I pause to make a subtle, but, I think, an important, point. Although the relationship between the spot and the forward price of any commodity tightly constrains the own rate for that commodity, the spot/forward relationship does not determine the own rate of interest for that commodity. There is always some “real” rate reflecting a rate of intertemporal exchange that is consistent with intertemporal equilibrium. Given such an intertemporal rate of exchange — a real rate of interest — the spot/forward relationship for a commodity in terms of a numeraire pins down the own rate for that commodity in terms of that numeraire.

OK with that introduction out of the way, let’s go back to my previous post in which I wrote the following:

Sraffa correctly noted that arbitrage would force the terms of such a loan (i.e., the own rate of interest) to equal the ratio of the current forward price of the commodity to its current spot price, buying spot and selling forward being essentially equivalent to borrowing and repaying.

That statement now seems quite wrong to me. Sraffa did not assert that arbitrage would force the own rate of interest to equal the ratio of the spot and forward prices. He merely noted that in a stationary equilibrium with equality between all spot and forward prices, all own interest rates would be equal. I criticized him for failing to note that in a stationary equilibrium all own rates would be zero. The conclusion that all own rates would be zero in a stationary equilibrium might in fact be valid, but if it is, it is not as obviously valid as I suggested, and my criticism of Sraffa and Ludwig von Mises for not drawing what seemed to me an obvious inference was not justified. To conclude that own rates are zero in a stationary equilibrium, you would, at a minimum, have to show that there is at least one commodity which could be carried from one period to the next at a non-negative profit. Sraffa may have come close to suggesting such an assumption in the passage in which he explains how borrowing to buy cotton spot and immediately selling cotton forward can be viewed as the equivalent of contracting a loan in terms of cotton, but he did not make that assumption explicitly. In any event, I mistakenly interpreted him to be saying that the ratio of the spot and forward prices is the same as the own interest rate, which is neither true nor what Sraffa meant.

And now let’s finally go back to the key quotation of Sraffa’s that I tried unsuccessfully to parse in my previous post.

Suppose there is a change in the distribution of demand between various commodities; immediately some will rise in price, and others will fall; the market will expect that, after a certain time, the supply of the former will increase, and the supply of the latter fall, and accordingly the forward price, for the date on which equilibrium is expected to be restored, will be below the spot price in the case of the former and above it in the case of the latter; in other words, the rate of interest on the former will be higher than on the latter. (“Dr. Hayek on Money and Capital,” p. 50)

In my previous post I tried to flesh out Sraffa’s example by supposing that, in the stationary equilibrium before the demand shift, tomatoes and cucumbers were both selling for a dollar each. In a stationary equilibrium, tomato and cucumber prices would remain, indefinitely into the future, at a dollar each. A shift in demand from tomatoes to cucumbers upsets the equilibrium, causing the price of tomatoes to fall to, say, $.90 and the price of cucumbers to rise to, say, $1.10. But Sraffa also argued that the prices of tomatoes and cucumbers would diverge only temporarily from their equilibrium values, implicitly assuming that the long-run supply curves of both tomatoes and cucumbers are horizontal at a price of $1 per unit.

I misunderstood Sraffa to be saying that the ratio of the future price and the spot price of tomatoes equals one plus the own rate on tomatoes. I therefore incorrectly calculated the own rate on tomatoes as 1/.9 minus one or 11.1%. There were two mistakes. First, I incorrectly inferred that equality of all spot and forward prices implies that the real rate must be zero, and second, as Nick Edmunds pointed out in his comment, a forward price exceeding the spot price would actually be reflected in an own rate less than the zero real rate that I had been posited. To calculate the own rate on tomatoes, I ought to have taken the ratio of spot price to the forward price — (.9/1) — and subtracted one plus the real rate. If the real rate is zero, then the implied own rate is .9 minus 1, or -10%.

To see where this comes from, we can take the simple algebra from Fisher (pp. 8-9). Let i be the interest rate calculated in terms of one commodity and one numeraire, and j be the rate of interest calculated in terms of a different commodity in that numeraire. Further, let a be the rate at which the second commodity appreciates relative to the first commodity. We have the following relationship derived from the arbitrage condition.

(1 + i) = (1 + j)(1 + a)

Now in our case, we are trying to calculate the own rate on tomatoes given that tomatoes are expected (an expectation reflected in the forward price of tomatoes) to appreciate by 10% from $.90 to $1.00 over the term of the loan. To keep the analysis simple, assume that i is zero. Although I concede that a positive real rate may be consistent with the stationary equilibrium that I, following Sraffa, have assumed, a zero real rate is certainly not an implausible assumption, and no important conclusions of this discussion hinge on assuming that i is zero.

To apply Fisher’s framework to Sraffa’s example, we need only substitute the ratio of the forward price of tomatoes to the spot price — [p(fwd)/p(spot)] — for the appreciation factor (1 + a).

So, in place of the previous equation, I can now substitute the following equivalent equation:

(1 + i) = (1 + j) [p(fwd)/p(spot)].

Rearranging, we get:

[p(spot)/p(fwd)] (1 + i) = (1 + j).

If i = 0, the following equation results:

[p(spot)/p(fwd)] = (1 + j).

In other words:

j = [p(spot)/p(fwd)] – 1.

If the ratio of the spot to the forward price is .9, then the own rate on tomatoes, j, equals -10%.

My assertion in the previous post that the own rate on cucumbers would be negative by the amount of expected depreciation (from $1.10 to $1) in the next period was also backwards. The own rate on cucumbers would have to exceed the zero equilibrium real rate by as much as cucumbers would depreciate at the time of repayment. So, for cucumbers, j would equal 11%.

Just to elaborate further, let’s assume that there is a third commodity, onions, and that, in the initial equilibrium, the unit prices of onions, tomatoes and cucumbers are equal. If the demand shift from tomatoes to cucumbers does not affect the demand for onions, then, even after the shift in demand, the price of onions will remain one dollar per onion.

The table below shows prices and own rates for tomatoes, cucumbers and onions for each possible choice of numeraire. If prices are quoted in tomatoes, the price of tomatoes is fixed at 1. Given a zero real rate, the own rate on tomatoes in period is zero. What about the own rate on cucumbers? In period 0, with no change in prices expected, the own rate on cucumbers is also zero. However in period 1, after the price of cucumbers has risen to 1.22 tomatoes, the own rate on cucumbers must reflect the expected reduction in the price of a cucumber in terms of tomatoes from 1.22 tomatoes in period 1 to 1 tomato in period 2, a price reduction of 22% percent in terms of tomatoes, implying a cucumber own rate of 22% in terms of tomatoes. Similarly, the onion own rate in terms of tomatoes would be 11% percent reflecting a forward price for onions in terms of tomatoes 11% below the spot price for onions in terms of tomatoes. If prices were quoted in terms of cucumbers, the cucumber own rate would be zero, and because the prices of tomatoes and onions would be expected to rise in terms of cucumbers, the tomato and onion own rates would be negative (-18.2% for tomatoes and -10% for onions). And if prices were quoted in terms of onions, the onion own rate would be zero, while the tomato own rate, given the expected appreciation of tomatoes in terms of onions, would be negative (-10%), and the cucumber own rate, given the expected depreciation of cucumbers in terms of onions, would be positive (10%).


The next table, summarizing the first one, is a 3 by 3 matrix showing each of the nine possible combinations of numeraires and corresponding own rates.


Thus, although the own rates of the different commodities differ, and although the commodity own rates differ depending on the choice of numeraire, the cost of borrowing (and the return to lending) is equal regardless of which commodity and which numeraire is chosen. As I stated in my previous post, Sraffa believed that, by showing that own rates can diverge, he showed that Hayek’s concept of a natural rate of interest was a nonsense notion. However, the differences in own rates, as Fisher had already showed 36 years earlier, are purely nominal. The underlying real rate, under Sraffa’s own analysis, is independent of the own rates.

Moreover, as I pointed out in my previous post, though the point was made in the context of a confused exposition of own rates,  whenever the own rate for a commodity is negative, there is an incentive to hold it now for sale in the next period at a higher price it would fetch in the current period. It is therefore only possible to observe negative own rates on commodities that are costly to store. Only if the cost of holding a commodity is greater than its expected appreciation would it not be profitable to withhold the commodity from sale this period and to sell instead in the following period. The rate of appreciation of a commodity cannot exceed the cost of storing it (as a percentage of its price).

What do I conclude from all this? That neither Sraffa nor Hayek adequately understood Fisher. Sraffa seems to have argued that there would be multiple real own rates of interest in disequilibrium — or at least his discussion of own rates seem to suggest that that is what he thought — while Hayek failed to see that there could be multiple nominal own rates. Fisher provided a definitive exposition of the distinction between real and nominal rates that encompasses both own rates and money rates of interest.

A. C. Pigou, the great and devoted student of Alfred Marshall, and ultimately his successor at Cambridge, is supposed to have said “It’s all in Marshall.” Well, one could also say “it’s all in Fisher.” Keynes, despite going out of his way in Chapter 12 of the General Theory to criticize Fisher’s distinction between the real and nominal rates of interest, actually vindicated Fisher’s distinction in his exposition of own rates in Chapter 17 of the GT, providing a valuable extension of Fisher’s analysis, but apparently failing to see the connection between his discussion and Fisher’s, and instead crediting Sraffa for introducing the own-rate analysis, even as he undermined Sraffa’s ambiguous suggestion that real own rates could differ. Go figure.

About Me

David Glasner
Washington, DC

I am an economist at the Federal Trade Commission. Nothing that you read on this blog necessarily reflects the views of the FTC or the individual commissioners. Although I work at the FTC as an antitrust economist, most of my research and writing has been on monetary economics and policy and the history of monetary theory. 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.

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