Archive for the 'Hayek' Category

Aggregate Demand and Coordination Failures

Regular readers of this blog may have noticed that I have been writing less about monetary policy and more about theory and methodology than when I started blogging a little over three years ago. Now one reason for that is that I’ve already said what I want to say about policy, and, since I get bored easily, I look for new things to write about. Another reason is that, at least in the US, the economy seems to have reached a sustainable growth path that seems likely to continue for the near to intermediate term. I think that monetary policy could be doing more to promote recovery, and I wish that it would, but unfortunately, the policy is what it is, and it will continue more or less in the way that Janet Yellen has been saying it will. Falling oil prices, because of increasing US oil output, suggest that growth may speed up slightly even as inflation stays low, possibly even falling to one percent or less. At least in the short-term, the fall in inflation does not seem like a cause for concern. A third reason for writing less about monetary policy is that I have been giving a lot of thought to what it is that I dislike about the current state of macroeconomics, and as I have been thinking about it, I have been writing about it.

In thinking about what I think is wrong with modern macroeconomics, I have been coming back again and again, though usually without explicit attribution, to an idea that was impressed upon me as an undergrad and grad student by Axel Leijonhufvud: that the main concern of macroeconomics ought to be with failures of coordination. A Swede, trained in the tradition of the Wicksellian Stockholm School, Leijonhufvud immersed himself in the study of the economics of Keynes and Keynesian economics, while also mastering the Austrian literature, and becoming an admirer of Hayek, especially Hayek’s seminal 1937 paper, “Economics and Knowledge.”

In discussing Keynes, Leijonhufvud focused on two kinds of coordination failures.

First, there is a problem in the labor market. If there is unemployment because the real wage is too high, an individual worker can’t solve the problem by offering to accept a reduced nominal wage. Suppose the price of output is $1 a unit and the wage is $10 a day, but the real wage consistent with full employment is $9 a day, meaning that producers choose to produce less output than they would produce if the real wage were lower, thus hiring fewer workers than they would if the real wage were lower than it is. If an individual worker offers to accept a wage of $9 a day, but other workers continue to hold out for $10 a day, it’s not clear that an employer would want to hire the worker who offers to work for $9 a day. If employers are not hiring additional workers because they can’t cover the cost of the additional output produced with the incremental revenue generated by the added output, the willingness of one worker to work for $9 a day is not likely to make a difference to the employer’s output and hiring decisions. It is not obvious what sequence of transactions would result in an increase in output and employment when the real wage is above the equilibrium level. There are complex feedback effects from a change, so that the net effect of making those changes in a piecemeal fashion is unpredictable, even though there is a possible full-employment equilibrium with a real wage of $9 a day. If the problem is that real wages in general are too high for full employment, the willingness of an individual worker to accept a reduced wage from a single employer does not fix the problem.

In the standard competitive model, there is a perfect market for every commodity in which every transactor is assumed to be able to buy and sell as much as he wants. But the standard competitive model has very little to say about the process by which those equilibrium prices are arrived at. And a typical worker is never faced with that kind of choice posited in the competitive model: an impersonal uniform wage at which he can decide how many hours a day or week or year he wants to work at that uniform wage. Under those circumstances, Keynes argued that the willingness of some workers to accept wage cuts in order to gain employment would not significantly increase employment, and might actually have destabilizing side-effects. Keynes tried to make this argument in the framework of an equilibrium model, though the nature of the argument, as Don Patinkin among others observed, was really better suited to a disequilibrium framework. Unfortunately, Keynes’s argument was subsequently dumbed down to a simple assertion that wages and prices are sticky (especially downward).

Second, there is an intertemporal problem, because the interest rate may be stuck at a rate too high to allow enough current investment to generate the full-employment level of spending given the current level of the money wage. In this scenario, unemployment isn’t caused by a real wage that is too high, so trying to fix it by wage adjustment would be a mistake. Since the source of the problem is the rate of interest, the way to fix the problem would be to reduce the rate of interest. But depending on the circumstances, there may be a coordination failure: bear speculators, expecting the rate of interest to rise when it falls to abnormally low levels, prevent the rate of interest from falling enough to induce enough investment to support full employment. Keynes put too much weight on bear speculators as the source of the intertemporal problem; Hawtrey’s notion of a credit deadlock would actually have been a better way to go, and nowadays, when people speak about a Keynesian liquidity trap, what they really have in mind is something closer to Hawtreyan credit deadlock than to the Keynesian liquidity trap.

Keynes surely deserves credit for identifying and explaining two possible sources of coordination failures, failures affecting the macroeconomy, because interest rates and wages, though they actually come in many different shapes and sizes, affect all markets and are true macroeconomic variables. But Keynes’s analysis of those coordination failures was far from being fully satisfactory, which is not surprising; a theoretical pioneer rarely provides a fully satisfactory analysis, leaving lots of work for successors.

But I think that Keynes’s theoretical paradigm actually did lead macroeconomics in the wrong direction, in the direction of a highly aggregated model with a single output, a bond, a medium of exchange, and a labor market, with no explicit characterization of the production technology. (I.e., is there one factor or two, and if two how is the price of the second factor determined? See, here, here, here, and here my discussion of Earl Thompson’s “A Reformulation of Macroeconomic Theory,” which I hope at some point to revisit and continue.)

Why was it the wrong direction? Because, the Keynesian model (both Keynes’s own version and the Hicksian IS-LM version of his model) ruled out the sort of coordination problems that might arise in a multi-product, multi-factor, intertemporal model in which total output depends in a meaningful way on the meshing of the interdependent plans, independently formulated by decentralized decision-makers, contingent on possibly inconsistent expectations of the future. In the over-simplified and over-aggregated Keynesian model, the essence of the coordination problem has been assumed away, leaving only a residue of the actual problem to be addressed by the model. The focus of the model is on aggregate expenditure, income, and output flows, with no attention paid to the truly daunting task of achieving sufficient coordination among the independent decision makers to allow total output and income to closely approximate the maximum sustainable output and income that the system could generate in a perfectly coordinated state, aka full intertemporal equilibrium.

This way of thinking about macroeconomics led to the merging of macroeconomics with neoclassical growth theory and to the routine and unthinking incorporation of aggregate production functions in macroeconomic models, a practice that is strictly justified only in a single-output, two-factor model in which the value of capital is independent of the rate of interest, so that the havoc-producing effects of reswitching and capital-reversal can be avoided. Eventually, these models were taken over by modern real-business-cycle theorists, who dogmatically rule out any consideration of coordination problems, while attributing all observed output and employment fluctuations to random productivity shocks. If one thinks of macroeconomics as an attempt to understand coordination failures, the RBC explanation of output and employment fluctuations is totally backwards; productivity fluctuations, like fluctuations in output and employment, are the not the results of unexplained random disturbances, they are the symptoms of coordination failures. That’s it, eureka! Solve the problem by assuming that it does not exist.

If you are thinking that this seems like an Austrian critique of the Keynesian model or the Keynesian approach, you are right; it is an Austrian critique. But it has nothing to do with stereotypical Austrian policy negativism; it is a critique of the oversimplified structure of the Keynesian model, which foreshadowed the reduction ad absurdum or modern real-business-cycle theory, which has nearly banished the idea of coordination failures from modern macroeconomics. The critique is not about the lack of a roundabout capital structure; it is about the narrow scope for inconsistencies in production and consumption plans.

I think that Leijonhufvud almost 40 years ago was getting at this point when he wrote the following paragraph near toward end of his book on Keynes.

The unclear mix of statics and dynamics [in the General Theory] would seem to be main reason for later muddles. One cannot assume that what went wrong was simply that Keynes slipped up here and there in his adaptation of standard tools, and that consequently, if we go back and tinker a little more with the Marshallian toolbox his purposes will be realized. What is required, I believe, is a systematic investigation from the standpoint of the information problems stressed in this study, of what elements of the static theory of resource allocation can without further ado be utilized in the analysis of dynamic and historical systems. This, of course, would be merely a first step: the gap yawns very wide between the systematic and rigorous modern analysis of the stability of simple, “featureless,” pure exchange systems and Keynes’ inspired sketch of the income-constrained process in a monetary exchange-cum production system. But even for such a first step, the prescription cannot be to “go back to Keynes.” If one must retrace some step of past developments in order to get on the right track – and that is probably advisable – my own preference is to go back to Hayek. Hayek’s Gestalt-conception of what happens during business cycles, it has been generally agreed, was much less sound that Keynes’. As an unhappy consequence, his far superior work on the fundamentals of the problem has not received the attention it deserves. (pp. 401-02)

I don’t think that we actually need to go back to Hayek, though “Economics and Knowledge” should certainly be read by every macroeconomist, but we do need to get a clearer understanding of the potential for breakdowns in economic activity to be caused by inconsistent expectations, especially when expectations are themselves mutually dependent and reinforcing. Because expectations are mutually interdependent, they are highly susceptible to network effects. Network effects produce tipping points, tipping points can lead to catastrophic outcomes. Just wanted to share that with you. Have a nice day.

Nick Rowe on Money and Coordination Failures

Via Brad Delong, I have been reading a month-old post by Nick Rowe in which Nick argues that every coordination failure is attributable to an excess demand for money. I think money is very important, but I am afraid that Nick goes a bit overboard in attempting to attribute every failure of macroeconomic coordination to a monetary source, where “monetary” means an excess demand for money. So let me try to see where I think Nick has gotten off track, or perhaps where I have gotten off track.

His post is quite a long one – over 3000 words, all his own – so I won’t try to summarize it, but the main message is that what characterizes money economies – economies in which there is a single asset that serves as the medium of exchange – is that money is involved in almost every transaction. And when a coordination failure occurs in such an economy, there being lots of unsold good and unemployed workers, the proper way to think about what is happening is that it is hard to buy money. Another way of saying that it is hard to buy money is that there is an excess demand for money.

Nick tries to frame his discussion in terms of Walras’s Law. Walras’s Law is a property of a general-equilibrium system in which there are n goods (and services). Some of these goods are produced and sold in the current period; others exist either as gifts of nature (e.g., land and other privately owned natural resources), as legacies of past production). Walras’s Law tells us that in a competitive system in which all transactors can trade at competitive prices, it must be the case that planned sales and purchases (including asset accumulation) for each individual and for all individuals collectively must cancel out. The value of my planned purchases must equal the value of my planned sales. This is a direct implication of the assumption that prices for each good are uniform for all individuals, and the assumption that goods and services may be transferred between individuals only via market transactions (no theft or robbery). Walras’s Law holds even if there is no equilibrium, but only in the notional sense that value of planned purchases and planned sales would exactly cancel each other out. In general-equilibrium models, no trading is allowed except at the equilibrium price vector.

Walras’ Law says that if you have a $1 billion excess supply of newly-produced goods, you must have a $1 billion excess demand for something else. And that something else could be anything. It could be money, or it could be bonds, or it could be land, or it could be safe assets, or it could be….anything other than newly-produced goods. The excess demand that offsets that excess supply for newly-produced goods could pop up anywhere. Daniel Kuehn called this the “Whack-a-mole theory of business cycles”.

If Walras’ Law were right, recessions could be caused by an excess demand for unobtanium, which has zero supply, but a big demand, and the government stupidly passed a law setting a finite maximum price per kilogram for something that doesn’t even exist, thereby causing a recession and mass unemployment.

People might want to buy $1 billion of unobtanium per year, but that does not cause an excess supply of newly-produced goods. It does not cause an excess supply of anything. Because they cannot buy $1 billion of unobtanium. That excess demand for unobtanium does not affect anything anywhere in the economy. Yes, if 1 billion kgs of unobtanium were discovered, and offered for sale at $1 per kg, that would affect things. But it is the supply of unobtanium that would affect things, not the elimination of the excess demand. If instead you eliminated the excess demand by convincing people that unobtanium wasn’t worth buying, absolutely nothing would change.

An excess demand for unobtanium has absolutely zero effect on the economy. And that is true regardless of the properties of unobtanium. In particular, it makes absolutely no difference whether unobtanium is or is not a close substitute for money.

What is true for unobtanium is also true for any good for which there is excess demand. Except money. If you want to buy 10 bonds, or 10 acres of land, or 10 safe assets, but can only buy 6, because only 6 are offered for sale, those extra 4 bonds might as well be unobtanium. You want to buy 4 extra bonds, but you can’t, so you don’t. Just like you want to buy unobtanium, but you can’t, so you don’t. You can’t do anything so you don’t do anything.

Walras’ Law is wrong. Walras’ Law only works in an economy with one centralised market where all goods can be traded against each other at once. If the Walrasian auctioneer announced a finite price for unobtanium, there would be an excess demand for unobtanium and an excess supply of other goods. People would offer to sell $1 billion of some other goods to finance their offers to buy $1 billion of unobtanium. The only way the auctioneer could clear the market would be by refusing to accept offers to buy unobtanium. But in a monetary exchange economy the market for unobtanium would be a market where unobtanium trades for money. There would be an excess demand for unobtanium, matched by an equal excess supply of money, in that particular market. No other market would be affected, if people knew they could not in fact buy any unobtanium for money, even if they want to.

Now this is a really embarrassing admission to make – and right after making another embarrassing admission in my previous post – I need to stop this – but I have no idea what Nick is saying here. There is no general-equilibrium system in which there is any notional trading taking place for a non-existent good, so I have no clue what this is all about. However, even though I can’t follow Nick’s reasoning, I totally agree with him that Walras’s Law is wrong. But the reason that it’s wrong is not that it implies that recessions could be caused by an excess demand for a non-existent good; the reason is that, in the only context in which a general-equilibrium model could be relevant for macroeconomics, i.e., an incomplete-markets model (aka the Radner model) in which individual agents are forming plans based on their expectations of future prices, prices that will only be observed in future periods, Walras’s Law cannot be true unless all agents have identical and correct expectations of all future prices.

Thus, the condition for macroeconomic coordination is that all agents have correct expectations of all currently unobservable future prices. When they have correct expectations, Walras’s Law is satisfied, and all is well with the world. When they don’t, Walras’s Law does not hold. When Walras’s Law doesn’t hold, things get messy; people default on their obligations, businesses go bankrupt, workers lose their jobs.

Nick thinks it’s all about money. Money is certainly one way in which things can get messed up. The government can cause inflation, and then stop it, as happened in 1920-21 and in 1981-82. People who expected inflation to continue, and made plans based on those expectations,were very likely unable to execute their plans when inflation stopped. But there are other reasons than incorrect inflation expectations that can cause people to have incorrect expectations of future prices.

Actually, Nick admits that coordination failures can be caused by factors other than an excess demand for money, but for some reason he seems to think that every coordination failure must be associated with an excess demand for money. But that is not so. I can envision a pure barter economy with incorrect price expectations in which individual plans are in a state of discoordination. Or consider a Fisherian debt-deflation economy in which debts are denominated in terms of gold and gold is appreciating. Debtors restrict consumption not because they are trying to accumulate more cash but because their debt burden is go great, any income they earn is being transferred to their creditors. In a monetary economy suffering from debt deflation, one would certainly want to use monetary policy to alleviate the debt burden, but using monetary policy to alleviate the debt burden is different from using monetary policy to eliminate an excess demand for money. Where is the excess demand for money?

Nick invokes Hayek’s paper (“The Use of Knowledge in Society“) to explain how markets work to coordinate the decentralized plans of individual agents. Nick assumes that Hayek failed to mention money in that paper because money is so pervasive a feature of a real-world economy, that Hayek simply took its existence for granted. That’s certainly an important paper, but the more important paper in this context is Hayek’s earlier paper (“Economics and Knowledge“) in which he explained the conditions for intertemporal equilibrium in which individual plans are coordinated, and why there is simply no market mechanism to ensure that intertemporal equilibrium is achieved. Money is not mentioned in that paper either.

Hey, Look at Me; I Turned Brad Delong into an Apologist for Milton Friedman

It’s always nice to be noticed, so I can hardly complain if Brad Delong wants to defend Milton Friedman on his blog against my criticism of his paper “Real and Pseudo Gold Standards.” I just find it a little bit rich to see Friedman being defended against my criticism by the arch-Keynesian Brad Delong.

But in the spirit of friendly disagreement in which Brad criticizes my criticism, I shall return the compliment and offer some criticisms of my own of Brad’s valiant effort to defend the indefensible.

So let me try to parse what Brad is saying and see if Brad can help me find sense where before I could find none.

I think that Friedman’s paper has somewhat more coherence than David does. From Milton Friedman’s standpoint (and from John Maynard Keynes’s) you need microeconomic [I think Brad meant to say macroeconomic] stability in order for private laissez-faire to be for the best in the best of possible worlds. Macroeconomic stability is:

  1. stable and predictable paths for total spending, the price level, and interest rates; hence
  2. a stable and predictable path for the velocity of money; hence
  3. (1) then achieved by a stable and predictable path for the money stock; and
  4. if (3) is secured by institutions, then expectations of (3) will generate the possibility of (1) and (2) so that if (3) is actually carried out then eppur si muove

I agree with Brad that macroeconomic stability can be described as a persistent circumstance in which the paths for total spending, the price level, and (perhaps) interest rates are stable and predictable. I also agree that a stable and predictable path for the velocity of money is conducive to macroeconomic stability. But note the difference between saying that the time paths for total spending, the price level and (perhaps) interest rates are stable and predictable and that the time path for the velocity of money is stable and predictable. It is, at least possibly the case, that it is within the power of an enlightened monetary authority to provide, or that it would be possible to construct a monetary regime that could provide, stable and predictable paths for total spending and the price level. Whether it is also possible for a monetary authority or a monetary regime to provide a stable and predictable path for interest rates would depend on the inherent variability in the real rate of interest. It may be that variations in the real rate are triggered by avoidable variations in nominal rates, so that if nominal rates are stabilized, real rates will be stabilized, too. But it may be that real rates are inherently variable and unpredictable. But it is at least plausible to argue that the appropriate monetary policy or monetary regime would result in a stable and predictable path of real and nominal interest rates. However, I find it highly implausible to think that it is within the power of any monetary authority or monetary regime to provide a stable and predictable path for the velocity of money. On the contrary, it seems much more likely that in order to provide stability and predictability in the paths for total spending, the price level, and interest rates, the monetary authority or the monetary regime would have to tolerate substantial variations in the velocity of money associated with changes in the public’s demand to hold money. So the notion that a stable and predictable path for the money stock is a characteristic of macroeconomic stability, much less a condition for monetary stability, strikes me as a complete misconception, a misconception propagated, more than anyone else, by Milton Friedman, himself.

Thus, contrary to Brad’s assertion, a stable and predictable path for the money stock is more likely than not to be a condition not for macroeconomic stability, but of macroeconomic instability. And to support my contention that a stable and predictable path for the money stock is macroeconomically destabilizing, let me quote none other than F. A. Hayek. I quote Hayek not because I think he is more authoritative than Friedman – Hayek having made more than his share of bad macroeconomic policy calls (e.g. his 1932 defense of the insane Bank of France) – but because in his own polite way he simply demolished the fallacy underlying Friedman’s fetish with a fixed rate of growth in the money stock (Full Empoyment at Any Price).

I wish I could share the confidence of my friend Milton Friedman who thinks that one could deprive the monetary authorities, in order to prevent the abuse of their powers for political purposes, of all discretionary powers by prescribing the amount of money they may and should add to circulation in any one year. It seems to me that he regards this as practicable because he has become used for statistical purposes to draw a sharp distinction between what is to be regarded as money and what is not. This distinction does not exist in the real world. I believe that, to ensure the convertibility of all kinds of near-money into real money, which is necessary if we are to avoid severe liquidity crises or panics, the monetary authorities must be given some discretion. But I agree with Friedman that we will have to try and get back to a more or less automatic system for regulating the quantity of money in ordinary times. The necessity of “suspending” Sir Robert Peel’s Bank Act of 1844 three times within 25 years after it was passed ought to have taught us this once and for all.

He was briefer and more pointed in a later comment (Denationalization of Money).

As regards Professor Friedman’s proposal of a legal limit on the rate at which a monopolistic issuer of money was to be allowed to increase the quantity in circulation, I can only say that I would not like to see what would happen if it ever became known that the amount of cash in circulation was approaching the upper limit and that therefore a need for increased liquidity could not be met.

And for good measure, Hayek added this footnote quoting Bagehot:

To such a situation the classic account of Walter Bagehot . . . would apply: “In a sensitive state of the English money market the near approach to the legal limit of reserve would be a sure incentive to panic; if one-third were fixed by law, the moment the banks were close to one-third, alarm would begin and would run like magic.

In other words if 3 is secured by institutions, all hell breaks loose.

But let us follow Brad a bit further in his quixotic quest to make Friedman seem sensible.

Now there are two different institutional setups that can produce (3):

  1. a monetarist central bank committed to targeting a k% growth rate of the money stock via open-market operations; or
  2. a gold standard in which a Humean price-specie flow mechanism leads inflating countries to lose and deflating countries to gain gold, tightly coupled to a banking system in which there is a reliable and stable money multiplier, and thus in which the money stock grows at the rate at which the world’s gold stock grows (plus the velocity trend).

Well, I have just – and not for the first time — disposed of 1, and in my previous post, I have disposed of 2. But having started to repeat myself, why not continue.

There are two points to make about the Humean price-specie-flow mechanism. First, it makes no sense, as Samuelson showed in his classic 1980 paper, inasmuch as it violates arbitrage conditions which do not allow the prices of tradable commodities to differ by more than the costs of transport. The Humean price-specie-flow mechanism presumes that the local domestic price levels are determined by local money supplies (either gold or convertible into gold), but that is simply not possible if arbitrage conditions obtain. There is no price-specie-flow mechanism under the gold standard, there is simply a movement of money sufficient to eliminate excess demands or supplies of money at the constant internationally determined price level. Domestic money supplies are endogenous and prices are (from the point of view of the monetary system) exogenously determined by the value of gold and the exchange rates of the local currencies in terms of gold. There is therefore no stable money multiplier at the level of a national currency (gold or convertible into gold). Friedman’s conception a pure [aka real] gold standard was predicated on a fallacy, namely the price-specie-flow mechanism. No gold standard in history ever operated as Friedman supposed that it operated. There were a few attempts to impose by statutory requirement a 100% (or sometime lower) marginal reserve requirement on banknotes, but that was statutory intervention, not a gold standard, which, at any operational level, is characterized by a fixed exchange rate between gold and the local currency with no restriction on the ability of economic agents to purchase gold at the going market price. the market price, under the gold standard, always equaling (or very closely approximating) the legal exchange rate between gold and the local currency.

Friedman calls (2) a “pure gold standard”. Anything else that claims to be a gold standard is and must be a “pseudo gold standard”. It might be a pseudo gold standard either because something disrupts the Humean price-specie flow mechanism–the “rules of the game” are not obeyed–so that deficit countries do not reliably lose and surplus countries do not reliably gain gold. It might be a pseudo gold standard because the money multiplier is not reliable and stable–because the banking system does not transparently and rapidly transmute a k% shift in the stock of gold into a k% shift in the money stock.

Friedman’s calling (2) “a pure [real] gold standard,” because it actualizes the Humean price-specie-flow-mechanism simply shows that Friedman understood neither the gold standard nor the price-specie-flow mechanism. The supposed rules of the game were designed to make the gold standard function in a particular way. In fact, the evidence shows that the classical gold standard in operation from roughly 1880 to 1914 operated with consistent departures from the “rules of the game.” What allows us to call the monetary regime in operation from 1880 to 1914 a gold standard is not that the rules of the game were observed but that the value of local currencies corresponded to the value of the gold with which they could be freely exchanged at the legal parities. No more and no less. And even Friedman was unwilling to call the gold standard in operation from 1880 to 1914 a pseudo gold standard, because if that was a pseudo-gold standard, there never was a real gold standard. So he was simply talking nonsense when he asserted that during the 1920s there a pseudo gold standard in operation even though gold was freely exchangeable for local currencies at the legal exchange rates.

Or, in short, to Friedman a gold standard is only a real gold standard if it produces a path for the money stock that is a k% rule. Anything else is a pseudo gold standard.

Yes! And that is what Friedman said, and it is absurd. And I am sure that Harry Johnson must have told him so.

The purpose of the paper, in short, is a Talmudic splitting-of-hairs. The point is to allow von Mises and Rueff and their not-so-deep-thinking latter-day followers (paging Paul Ryan! Paging Benn Steil! Paging Charles Koch! Paging Rand Paul!) to remain in their cloud-cuckoo-land of pledging allegiance to the gold standard as a golden calf while at the same time walling them off from and keeping them calm and supportive as the monetarist central bank does its job of keeping our fiat-money system stable by making Say’s Law true enough in practice.

As such, it succeeds admirably.

Or, at least, I think it does…

Have I just given an unconvincing Straussian reading of Friedman–that he knows what he is doing, and that what he is doing is leaving the theoretical husk to the fanatics von Mises and Rueff while keeping the rational kernel for himself, and making the point that a gold standard is a good monetary policy only if it turns out to mimic a good monetarist fiat-money standard policy? That his apparent confusion is simply a way of accomplishing those two tasks without splitting Mont Pelerin of the 1960s into yet more mutually-feuding camps?

I really sympathize with Brad’s effort to recruit Friedman into the worthy cause of combating nonsense. But you can’t combat nonsense with nonsense.


Sterilizing Gold Inflows: The Anatomy of a Misconception

In my previous post about Milton Friedman’s problematic distinction between real and pseudo-gold standards, I mentioned that one of the signs that Friedman pointed to in asserting that the Federal Reserve Board in the 1920s was managing a pseudo gold standard was the “sterilization” of gold inflows to the Fed. What Friedman meant by sterilization is that the incremental gold reserves flowing into the Fed did not lead to a commensurate increase in the stock of money held by the public, the failure of the stock of money to increase commensurately with an inflow of gold being the standard understanding of sterilization in the context of the gold standard.

Of course “commensurateness” is in the eye of the beholder. Because Friedman felt that, given the size of the gold inflow, the US money stock did not increase “enough,” he argued that the gold standard in the 1920s did not function as a “real” gold standard would have functioned. Now Friedman’s denial that a gold standard in which gold inflows are sterilized is a “real” gold standard may have been uniquely his own, but his understanding of sterilization was hardly unique; it was widely shared. In fact it was so widely shared that I myself have had to engage in a bit of an intellectual struggle to free myself from its implicit reversal of the causation between money creation and the holding of reserves. For direct evidence of my struggles, see some of my earlier posts on currency manipulation (here, here and here), in which I began by using the concept of sterilization as if it actually made sense in the context of international adjustment, and did not fully grasp that the concept leads only to confusion. In an earlier post about Hayek’s 1932 defense of the insane Bank of France, I did not explicitly refer to sterilization, and got the essential analysis right. Of course Hayek, in his 1932 defense of the Bank of France, was using — whether implicitly or explicitly I don’t recall — the idea of sterilization to defend the Bank of France against critics by showing that the Bank of France was not guilty of sterilization, but Hayek’s criterion for what qualifies as sterilization was stricter than Friedman’s. In any event, it would be fair to say that Friedman’s conception of how the gold standard works was broadly consistent with the general understanding at the time of how the gold standard operates, though, even under the orthodox understanding, he had no basis for asserting that the 1920s gold standard was fraudulent and bogus.

To sort out the multiple layers of confusion operating here, it helps to go back to the classic discussion of international monetary adjustment under a pure gold currency, which was the basis for later discussions of international monetary adjustment under a gold standard (i.e, a paper currency convertible into gold at a fixed exchange rate). I refer to David Hume’s essay “Of the Balance of Trade” in which he argued that there is an equilibrium distribution of gold across different countries, working through a famous thought experiment in which four-fifths of the gold held in Great Britain was annihilated to show that an automatic adjustment process would redistribute the international stock of gold to restore Britain’s equilibrium share of the total world stock of gold.

The adjustment process, which came to be known as the price-specie flow mechanism (PSFM), is widely considered one of Hume’s greatest contributions to economics and to monetary theory. Applying the simple quantity theory of money, Hume argued that the loss of 80% of Britain’s gold stock would mean that prices and wages in Britain would fall by 80%. But with British prices 80% lower than prices elsewhere, Britain would stop importing goods that could now be obtained more cheaply at home than they could be obtained abroad, while foreigners would begin exporting all they could from Britain to take advantage of low British prices. British exports would rise and imports fall, causing an inflow of gold into Britain. But, as gold flowed into Britain, British prices would rise, thereby reducing the British competitive advantage, causing imports to increase and exports to decrease, and consequently reducing the inflow of gold. The adjustment process would continue until British prices and wages had risen to a level equal to that in other countries, thus eliminating the British balance-of-trade surplus and terminating the inflow of gold.

This was a very nice argument, and Hume, a consummate literary stylist, expressed it beautifully. There is only one problem: Hume ignored that the prices of tradable goods (those that can be imported or exported or those that compete with imports and exports) are determined not in isolated domestic markets, but in international markets, so the premise that all British prices, like the British stock of gold, would fall by 80% was clearly wrong. Nevertheless, the disconnect between the simple quantity theory and the idea that the prices of tradable goods are determined in international markets was widely ignored by subsequent writers. Although Adam Smith, David Ricardo, and J. S. Mill avoided the fallacy, but without explicit criticism of Hume, while Henry Thornton, in his great work The Paper Credit of Great Britain, alternately embraced it and rejected it, the Humean analysis, by the end of the nineteenth century, if not earlier, had become the established orthodoxy.

Towards the middle of the nineteenth century, there was a famous series of controversies over the Bank Charter Act of 1844, in which two groups of economists the Currency School in support and the Banking School in opposition argued about the key provisions of the Act: to centralize the issue of Banknotes in Great Britain within the Bank of England and to prohibit the Bank of England from issuing additional banknotes, beyond the fixed quantity of “unbacked” notes (i.e. without gold cover) already in circulation, unless the additional banknotes were issued in exchange for a corresponding amount of gold coin or bullion. In other words, the Bank Charter Act imposed a 100% marginal reserve requirement on the issue of additional banknotes by the Bank of England, thereby codifying what was then known as the Currency Principle, the idea being that the fluctuation in the total quantity of Banknotes ought to track exactly the Humean mechanism in which the quantity of money in circulation changes pound for pound with the import or export of gold.

The doctrinal history of the controversies about the Bank Charter Act are very confused, and I have written about them at length in several papers (this, this, and this) and in my book on free banking, so I don’t want to go over that ground again here. But until the advent of the monetary approach to the balance of payments in the late 1960s and early 1970s, the thinking of the economics profession about monetary adjustment under the gold standard was largely in a state of confusion, the underlying fallacy of PSFM having remained largely unrecognized. One of the few who avoided the confusion was R. G. Hawtrey, who had anticipated all the important elements of the monetary approach to the balance of payments, but whose work had been largely forgotten in the wake of the General Theory.

Two important papers changed the landscape. The first was a 1976 paper by Donald McCloskey and Richard Zecher “How the Gold Standard Really Worked” which explained that a whole slew of supposed anomalies in the empirical literature on the gold standard were easily explained if the Humean PSFM was disregarded. The second was Paul Samuelson’s 1980 paper “A Corrected Version of Hume’s Equilibrating Mechanisms for International Trade,” showing that the change in relative price levels — the mechanism whereby international monetary equilibrium is supposedly restored according to PSFM — is irrelevant to the adjustment process when arbitrage constraints on tradable goods are effective. The burden of the adjustment is carried by changes in spending patterns that restore desired asset holdings to their equilibrium levels, independently of relative-price-level effects. Samuelson further showed that even when, owing to the existence of non-tradable goods, there are relative-price-level effects, those effects are irrelevant to the adjustment process that restores equilibrium.

What was missing from Hume’s analysis was the concept of a demand to hold money (or gold). The difference between desired and actual holdings of cash imply corresponding changes in expenditure, and those changes in expenditure restore equilibrium in money (gold) holdings independent of any price effects. Lacking any theory of the demand to hold money (or gold), Hume had to rely on a price-level adjustment to explain how equilibrium is restored after a change in the quantity of gold in one country. Hume’s misstep set monetary economics off on a two-century detour, avoided by only a relative handful of economists, in explaining the process of international adjustment.

So historically there have been two paradigms of international adjustment under the gold standard: 1) the better-known, but incorrect, Humean PSFM based on relative-price-level differences which induce self-correcting gold flows that, in turn, are supposed to eliminate the price-level differences, and 2) the not-so-well-known, but correct, arbitrage-monetary-adjustment theory. Under the PSFM, the adjustment can occur only if gold flows give rise to relative-price-level adjustments. But, under PSFM, for those relative-price-level adjustments to occur, gold flows have to change the domestic money stock, because it is the quantity of domestic money that governs the domestic price level.

That is why if you believe, as Milton Friedman did, in PSFM, sterilization is such a big deal. Relative domestic price levels are correlated with relative domestic money stocks, so if a gold inflow into a country does not change its domestic money stock, the necessary increase in the relative price level of the country receiving the gold inflow cannot occur. The “automatic” adjustment mechanism under the gold standard has been blocked, implying that if there is sterilization, the gold standard is rendered fraudulent.

But we now know that that is not how the gold standard works. The point of gold flows was not to change relative price levels. International adjustment required changes in domestic money supplies to be sure, but, under the gold standard, changes in domestic money supplies are essentially unavoidable. Thus, in his 1932 defense of the insane Bank of France, Hayek pointed out that the domestic quantity of money had in fact increased in France along with French gold holdings. To Hayek, this meant that the Bank of France was not sterilizing the gold inflow. Friedman would have said that, given the gold inflow, the French money stock ought to have increased by a far larger amount than it actually did.

Neither Hayek nor Friedman understood what was happening. The French public wanted to increase their holdings of money. Because the French government imposed high gold reserve requirements (but less than 100%) on the creation of French banknotes and deposits, increasing holdings of money required the French to restrict their spending sufficiently to create a balance-of-trade surplus large enough to induce the inflow of gold needed to satisfy the reserve requirements on the desired increase in cash holdings. The direction of causation was exactly the opposite of what Friedman thought. It was the desired increase in the amount of francs that the French wanted to hold that (given the level of gold reserve requirements) induced the increase in French gold holdings.

But this doesn’t mean, as Hayek argued, that the insane Bank of France was not wreaking havoc on the international monetary system. By advocating a banking law that imposed very high gold reserve requirements and by insisting on redeeming almost all of its non-gold foreign exchange reserves into gold bullion, the insane Bank of France, along with the clueless Federal Reserve, generated a huge increase in the international monetary demand for gold, which was the proximate cause of the worldwide deflation that began in 1929 and continued till 1933. The problem was not a misalignment between relative price levels, which is sterilization supposedly causes; the problem was a worldwide deflation that afflicted all countries on the gold standard, and was avoidable only by escaping from the gold standard.

At any rate, the concept of sterilization does nothing to enhance our understanding of that deflationary process. And whatever defects there were in the way that central banks were operating under the gold standard in the 1920s, the concept of sterilization averts attention from the critical problem which was the increasing demand of the world’s central banks, especially the Bank of France and the Federal Reserve, for gold reserves.

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.

How to Think about Own Rates of Interest

Phil Pilkington has responded to my post about the latest version of my paper (co-authored by Paul Zimmerman) on the Sraffa-Hayek debate about the natural rate of interest. For those of you who haven’t been following my posts on the subject, here’s a quick review. Almost three years ago I wrote a post refuting Sraffa’s argument that Hayek’s concept of the natural rate of interest is incoherent, there being a multiplicity of own rates of interest in a barter economy (Hayek’s benchmark for the rate of interest undisturbed by monetary influences), which makes it impossible to identify any particular own rate as the natural rate of interest.

Sraffa maintained that if there are many own rates of interest in a barter economy, none of them having a claim to priority over the others, then Hayek had no basis for singling out any particular one of them as the natural rate and holding it up as the benchmark rate to guide monetary policy. I pointed out that Ludwig Lachmann had answered Sraffa’s attack (about 20 years too late) by explaining that even though there could be many own rates for individual commodities, all own rates are related by the condition that the cost of borrowing in terms of all commodities would be equalized, differences in own rates reflecting merely differences in expected appreciation or depreciation of the different commodities. Different own rates are simply different nominal rates; there is a unique real own rate, a point demonstrated by Irving Fisher in 1896 in Appreciation and Interest.

Let me pause here for a moment to explain what is meant by an own rate of interest. It is simply the name for the rate of interest corresponding to a loan contracted in terms of a particular commodity, the borrower receiving the commodity now and repaying the lender with the same commodity when the term of the loan expires. Sraffa correctly noted that in equilibrium 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.

Now what is tricky about Sraffa’s argument against Hayek is that he actually acknowledges at the beginning of his argument that in a stationary equilibrium, presumably meaning that prices remain at their current equilibrium levels over time, all own rates would be equal. In fact if prices remain (and are expected to remain) constant period after period, the ratio of forward to spot prices would equal unity for all commodities implying that the natural rate of interest would be zero. Sraffa did not make that point explicitly, but it seems to be a necessary implication of his analysis. (This implication seems to bear on an old controversy in the theory of capital and interest, which is whether the rate of interest would be positive in a stationary equilibrium with constant real income). Schumpeter argued that the equilibrium rate of interest would be zero, and von Mises argued that it would be positive, because time preference implying that the rate of interest is necessarily always positive is a kind of a priori praxeological law of nature, the sort of apodictic gibberish to which von Mises was regrettably predisposed. The own-rate analysis supports Schumpeter against Mises.

So to make the case against Hayek, Sraffa had to posit a change, a shift in demand from one product to another, that disrupts the pre-existing equilibrium. Here is the key passage from Sraffa:

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. (p. 50)

This is a difficult passage, and in previous posts, and in my paper with Zimmerman, I did not try to parse this passage. But I am going to parse it now. Assume that demand shifts from tomatoes to cucumbers. In the original equilibrium, let the prices of both be $1 a pound. With a zero own rate of interest in terms of both tomatoes and cucumbers, you could borrow a pound of tomatoes today and discharge your debt by repaying the lender a pound of tomatoes at the expiration of the loan. However, after the demand shift, the price of tomatoes falls to, say, $0.90 a pound, and the price of cucumbers rises to, say, $1.10 a pound. Sraffa posits that the price changes are temporary, not because the demand shift is temporary, but because the supply curves of tomatoes and cucumbers are perfectly elastic at $1 a pound. However, supply does not adjust immediately, so Sraffa believes that there can be a temporary deviation from the long-run equilibrium prices of tomatoes and cucumbers.

The ratio of the forward prices to the spot prices tells you what the own rates are for tomatoes and cucumbers. For tomatoes, the ratio is 1/.9, implying an own rate of 11.1%. For cucumbers the ratio is 1/1.1, implying an own rate of -9.1%. Other prices have not changed, so all other own rates remain at 0. Having shown that own rates can diverge, Sraffa thinks that he has proven Hayek’s concept of a natural rate of interest to be a nonsense notion. He was mistaken.

There are at least two mistakes. First, the negative own rate on cucumbers simply means that no one will lend in terms of cucumbers for negative interest when other commodities allow lending at zero interest. It also means that no one will hold cucumbers in this period to sell at a lower price in the next period than the cucumbers would fetch in the current period. Cucumbers are a bad investment, promising a negative return; any lending and investing will be conducted in terms of some other commodity. The negative own rate on cucumbers signifies a kind of corner solution, reflecting the impossibility of transporting next period’s cucumbers into the present. If that were possible cucumber prices would be equal in the present and the future, and the cucumber own rate would be equal to all other own rates at zero. But the point is that if any lending takes place, it will be at a zero own rate.

Second, the positive own rate on tomatoes means that there is an incentive to lend in terms of tomatoes rather than lend in terms of other commodities. But as long as it is possible to borrow in terms of other commodities at a zero own rate, no one borrows in terms of tomatoes. Thus, if anyone wanted to lend in terms of tomatoes, he would have to reduce the rate on tomatoes to make borrowers indifferent between borrowing in terms of tomatoes and borrowing in terms of some other commodity. However, if tomatoes today can be held at zero cost to be sold at the higher price prevailing next period, currently produced tomatoes would be sold in the next period rather than sold today. So if there were no costs of holding tomatoes until the next period, the price of tomatoes in the next period would be no higher than the price in the current period. In other words, the forward price of tomatoes cannot exceed the current spot price by more than the cost of holding tomatoes until the next period. If the difference between the spot and the forward price reflects no more than the cost of holding tomatoes till the next period, then, as Keynes showed in chapter 17 of the General Theory, the own rates are indeed effectively equalized after appropriate adjustment for storage costs and expected appreciation.

Thus, it was Keynes, who having selected Sraffa to review Hayek’s Prices and Production in the Economic Journal, of which Keynes was then the editor, adapted Sraffa’s own rate analysis in the General Theory, but did so in a fashion that, at least partially, rehabilitated the very natural-rate analysis that had been the object of Sraffa’s scorn in his review of Prices and Production. Keynes also rejected the natural-rate analysis, but he did so not because it is nonsensical, but because the natural rate is not independent of the level of employment. Keynes’s argument that the natural rate depends on the level of employment seems to me to be inconsistent with the idea that the IS curve is downward sloping. But I will have to think about that a bit and reread the relevant passage in the General Theory and perhaps revisit the point in a future post.

 UPDATE (07/28/14 13:02 EDT): Thanks to my commenters for pointing out that my own thinking about the own rate of interest was not quite right. I should have defined the own rate in terms of a real numeraire instead of $, which was a bit of awkwardness that I should have fixed before posting. I will try to publish a corrected version of this post later today or tomorrow. Sorry for posting without sufficient review and revision.

UPDATE (08/04/14 11:38 EDT): I hope to post the long-delayed sequel to this post later today. A number of personal issues took precedence over posting, but I also found it difficult to get clear on several minor points, which I hope that I have now resolved adequately, for example I found that defining the own rate in terms of a real numeraire was not really the source of my problem with this post, though it was a useful exercise to work through. Anyway, stay tuned.

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

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.

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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