Posts Tagged 'Hayek'

Did David Hume Discover the Vertical Phillips Curve?

In my previous post about Nick Rowe and Milton Friedman, I pointed out to Nick Rowe that Friedman (and Phelps) did not discover the argument that the long-run Phillips Curve, defined so that every rate of inflation is correctly expected, is vertical. The argument I suggested can be traced back at least to Hume. My claim on Hume’s behalf was based on my vague recollection that Hume distinguished between the effect of a high price level and a rising price level, a high price level having no effect on output and employment, while a rising price level increases output and employment.

Scott Sumner offered the following comment, leaving it as an exercise for the reader to figure out what he meant by “didn’t quite get there.”:

As you know Friedman is one of the few areas where we disagree. Here I’ll just address one point, the expectations augmented Phillips Curve. Although I love Hume, he didn’t quite get there, although he did discuss the simple Phillips Curve.

I wrote the following response to Scott referring to the quote that I was thinking of without quoting it verbatim (because I couldn’t remember where to find it):

There is a wonderful quote by Hume about how low prices or high prices are irrelevant to total output, profits and employment, but that unexpected increases in prices are a stimulus to profits, output, and employment. I’ll look for it, and post it.

Nick Rowe then obligingly provided the quotation I was thinking of (but not all of it):

Here, to my mind, is the “money quote” (pun not originally intended) from David Hume’s “Of Money”:

“From the whole of this reasoning we may conclude, that it is of no manner of consequence, with regard to the domestic happiness of a state, whether money be in a greater or less quantity. The good policy of the magistrate consists only in keeping it, if possible, still encreasing; because, by that means, he keeps alive a spirit of industry in the nation, and encreases the stock of labour, in which consists all real power and riches.”

The first sentence is fine. But the second sentence is very clearly a problem.

Was it Friedman who said “we have only advanced one derivative since Hume”?

OK, so let’s see the whole relevant quotation from Hume’s essay “Of Money.”

Accordingly we find, that, in every kingdom, into which money begins to flow in greater abundance than formerly, everything takes a new face: labour and industry gain life; the merchant becomes more enterprising, the manufacturer more diligent and skilful, and even the farmer follows his plough with greater alacrity and attention. This is not easily to be accounted for, if we consider only the influence which a greater abundance of coin has in the kingdom itself, by heightening the price of Commodities, and obliging everyone to pay a greater number of these little yellow or white pieces for everything he purchases. And as to foreign trade, it appears, that great plenty of money is rather disadvantageous, by raising the price of every kind of labour.

To account, then, for this phenomenon, we must consider, that though the high price of commodities be a necessary consequence of the encrease of gold and silver, yet it follows not immediately upon that encrease; but some time is required before the money circulates through the whole state, and makes its effect be felt on all ranks of people. At first, no alteration is perceived; by degrees the price rises, first of one commodity, then of another; till the whole at last reaches a just proportion with the new quantity of specie which is in the kingdom. In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the encreasing quantity of gold and silver is favourable to industry. When any quantity of money is imported into a nation, it is not at first dispersed into many hands; but is confined to the coffers of a few persons, who immediately seek to employ it to advantage. Here are a set of manufacturers or merchants, we shall suppose, who have received returns of gold and silver for goods which they sent to CADIZ. They are thereby enabled to employ more workmen than formerly, who never dream of demanding higher wages, but are glad of employment from such good paymasters. If workmen become scarce, the manufacturer gives higher wages, but at first requires an encrease of labour; and this is willingly submitted to by the artisan, who can now eat and drink better, to compensate his additional toil and fatigue.

He carries his money to market, where he, finds everything at the same price as formerly, but returns with greater quantity and of better kinds, for the use of his family. The farmer and gardener, finding, that all their commodities are taken off, apply themselves with alacrity to the raising more; and at the same time can afford to take better and more cloths from their tradesmen, whose price is the same as formerly, and their industry only whetted by so much new gain. It is easy to trace the money in its progress through the whole commonwealth; where we shall find, that it must first quicken the diligence of every individual, before it encrease the price of labour. And that the specie may encrease to a considerable pitch, before it have this latter effect, appears, amongst other instances, from the frequent operations of the FRENCH king on the money; where it was always found, that the augmenting of the numerary value did not produce a proportional rise of the prices, at least for some time. In the last year of LOUIS XIV, money was raised three-sevenths, but prices augmented only one. Corn in FRANCE is now sold at the same price, or for the same number of livres, it was in 1683; though silver was then at 30 livres the mark, and is now at 50. Not to mention the great addition of gold and silver, which may have come into that kingdom since the former period.

From the whole of this reasoning we may conclude, that it is of no manner of consequence, with regard to the domestic happiness of a state, whether money be in a greater or less quantity. The good policy of the magistrate consists only in keeping it, if possible, still encreasing; because, by that means, he keeps alive a spirit of industry in the nation, and encreases the stock of labour, in which consists all real power and riches. A nation, whose money decreases, is actually, at that time, weaker and more miserable than another nation, which possesses no more money, but is on the encreasing hand. This will be easily accounted for, if we consider, that the alterations in the quantity of money, either on one side or the other, are not immediately attended with proportionable alterations in the price of commodities. There is always an interval before matters be adjusted to their new situation; and this interval is as pernicious to industry, when gold and silver are diminishing, as it is advantageous when these metals are encreasing. The workman has not the same employment from the manufacturer and merchant; though he pays the same price for everything in the market. The farmer cannot dispose of his corn and cattle; though he must pay the same rent to his landlord. The poverty, and beggary, and sloth, which must ensue, are easily foreseen.

So Hume understands that once-and-for-all increases in the stock of money and in the price level are neutral, and also that in the transition from one price level to another, there will be a transitory effect on output and employment. However, when he says that the good policy of the magistrate consists only in keeping it, if possible, still increasing; because, by that means, he keeps alive a spirit of industry in the nation, he seems to be suggesting that the long-run Phillips Curve is actually positively sloped, thus confirming Milton Friedman (and Nick Rowe and Scott Sumner) in saying that Hume was off by one derivative.

While I think that is a fair reading of Hume, it is not the only one, because Hume really was thinking in terms of price levels, not rates of inflation. The idea that a good magistrate would keep the stock of money increasing could not have meant that the rate of inflation would indefinitely continue at a particular rate, only that the temporary increase in the price level would be extended a while longer. So I don’t think that Hume would ever have imagined that there could be a steady predicted rate of inflation lasting for an indefinite period of time. If he could have imagined a steady rate of inflation, I think he would have understood the simple argument that, once expected, the steady rate of inflation would not permanently increase output and employment.

At any rate, even if Hume did not explicitly anticipate Friedman’s argument for a vertical long-run Phillips Curve, certainly there many economists before Friedman who did. I will quote just one example from a source (Hayek’s Constitution of Liberty) that predates Friedman by about eight years. There is every reason to think that Friedman was familiar with the source, Hayek having been Friedman’s colleague at the University of Chicago between 1950 and 1962. The following excerpt is from p. 331 of the 1960 edition.

Inflation at first merely produces conditions in which more people make profits and in which profits are generally larger than usual. Almost everything succeeds, there are hardly any failures. The fact that profits again and again prove to be greater than had been expected and that an unusual number of ventures turn out to be successful produces a general atmosphere favorable to risk-taking. Even those who would have been driven out of business without the windfalls caused by the unexpected general rise in prices are able to hold on and to keep their employees in the expectation that they will soon share in the general prosperity. This situation will last, however, only until people begin to expect prices to continue to rise at the same rate. Once they begin to count on prices being so many per cent higher in so many months’ time, they will bid up the prices of the factors of production which determine the costs to a level corresponding to the future prices they expect. If prices then rise no more than had been expected, profits will return to normal, and the proportion of those making a profit also will fall; and since, during the period of exceptionally large profits, many have held on who would otherwise have been forced to change the direction of their efforts, a higher proportion than usual will suffer losses.

The stimulating effect of inflation will thus operate only so long as it has not been foreseen; as soon as it comes to be foreseen, only its continuation at an increased rate will maintain the same degree of prosperity. If in such a situation price rose less than expected, the effect would be the same as that of unforeseen deflation. Even if they rose only as much as was generally expected, this would no longer provide the expectational stimulus but would lay bare the whole backlog of adjustments that had been postponed while the temporary stimulus lasted. In order for inflation to retain its initial stimulating effect, it would have to continue at a rate always faster than expected.

This was certainly not the first time that Hayek made the same argument. See his Studies in Philosophy Politics and Economics, p. 295-96 for a 1958 version of the argument. Is there any part of Friedman’s argument in his 1968 essay (“The Role of Monetary Policy“) not contained in the quote from Hayek? Nor is there anything to indicate that Hayek thought he was making an argument that was not already familiar. The logic is so obvious that it is actually pointless to look for someone who “discovered” it. If Friedman somehow gets credit for making the discovery, it is simply because he was the one who made the argument at just the moment when the rest of the profession happened to be paying attention.

What Is Free Banking All About?

I notice that there has been a bit of a dustup lately about free banking, triggered by two posts by Izabella Kaminska, first on FTAlphaville followed by another on her own blog. I don’t want to get too deeply into the specifics of Kaminska’s posts, save to correct a couple of factual misstatements and conceptual misunderstandings (see below). At any rate, George Selgin has a detailed reply to Kaminska’s errors with which I mostly agree, and Scott Sumner has scolded her for not distinguishing between sensible free bankers, e.g., Larry White, George Selgin, Kevin Dowd, and Bill Woolsey, and the anti-Fed, gold-bug nutcases who, following in the footsteps of Ron Paul, have adopted free banking as a slogan with which to pursue their anti-Fed crusade.

Now it just so happens that, as some readers may know, I wrote a book about free banking, which I began writing almost 30 years ago. The point of the book was not to call for a revolutionary change in our monetary system, but to show that financial innovations and market forces were causing our modern monetary system to evolve into something like the theoretical model of a free banking system that had been worked out in a general sort of way by some classical monetary theorists, starting with Adam Smith, who believed that a system of private banks operating under a gold standard would supply as much money as, but no more money than, the public wanted to hold. In other words, the quantity of money produced by a system of competing banks, operating under convertibility, could be left to take care of itself, with no centralized quantitative control over either the quantity of bank liabilities or the amount of reserves held by the banking system.

So I especially liked the following comment by J. V. Dubois to Scott’s post

[M]y thing against free banking is that we actually already have it. We already have private banks issuing their own monies directly used for transactions – they are called bank accounts and debit/credit cards. There are countries like Sweden where there are now shops that do not accept physical cash (only bank monies) – a policy actively promoted government, if you can believe it.

There are now even financial products like Xapo Debit Card that automatically converts all payments received on your account into non-monetary assets (with Xapo it is bitcoins) and back into monies when you use the card for payment. There is a very healthy international bank money market so no matter what money you personally use, you can travel all around the world and pay comfortably without ever seeing or touching official local government currency.

In opposition to the Smithian school of thought, there was the view of Smith’s close friend David Hume, who famously articulated what became known as the Price-Specie-Flow Mechanism, a mechanism that Smith wisely omitted from his discussion of international monetary adjustment in the Wealth of Nations, despite having relied on PSFM with due acknowledgment of Hume, in his Lectures on Jurisprudence. In contrast to Smith’s belief that there is a market mechanism limiting the competitive issue of convertible bank liabilities (notes and deposits) to the amount demanded by the public, Hume argued that banks were inherently predisposed to overissue their liabilities, the liabilities being issuable at almost no cost, so that private banks, seeking to profit from the divergence between the face value of their liabilities and the cost of issuing them, were veritable engines of inflation.

These two opposing views of banks later morphed into what became known almost 70 years later as the Banking and Currency Schools. Taking the Humean position, the Currency School argued that without quantitative control over the quantity of banknotes issued, the banking system would inevitably issue an excess of banknotes, causing overtrading, speculation, inflation, a drain on the gold reserves of the banking system, culminating in financial crises. To prevent recurring financial crises, the Currency School proposed a legal limit on the total quantity of banknotes beyond which limit, additional banknotes could be only be issued (by the Bank of England) in exchange for an equivalent amount of gold at the legal gold parity. Taking the Smithian position, the Banking School argued that there were market mechanisms by which any excess liabilities created by the banking system would automatically be returned to the banking system — the law of reflux. Thus, as long as convertibility obtained (i.e., the bank notes were exchangeable for gold at the legal gold parity), any overissue would be self-correcting, so that a legal limit on the quantity of banknotes was, at best, superfluous, and, at worst, would itself trigger a financial crisis.

As it turned out, the legal limit on the quantity of banknotes proposed by the Currency School was enacted in the Bank Charter Act of 1844, and, just as the Banking School predicted, led to a financial crisis in 1847, when, as soon as the total quantity of banknotes approached the legal limit, a sudden precautionary demand for banknotes led to a financial panic that was subdued only after the government announced that the Bank of England would incur no legal liability for issuing banknotes beyond the legal limit. Similar financial panics ensued in 1857 and 1866, and they were also subdued by suspending the relevant statutory limits on the quantity of banknotes. There were no further financial crises in Great Britain in the nineteenth century (except possibly for a minicrisis in 1890), because bank deposits increasingly displaced banknotes as the preferred medium of exchange, the quantity of bank deposits being subject to no statutory limit, and because the market anticipated that, in a crisis, the statutory limit on the quantity of banknotes would be suspended, so that a sudden precautionary demand for banknotes never materialized in the first place.

Let me pause here to comment on the factual and conceptual misunderstandings in Kaminska’s first post. Discussing the role of the Bank of England in the British monetary system in the first half of the nineteenth century, she writes:

But with great money-issuance power comes great responsibility, and more specifically the great temptation to abuse that power via the means of imprudent money-printing. This fate befell the BoE — as it does most banks — not helped by the fact that the BoE still had to compete with a whole bunch of private banks who were just as keen as it to issue money to an equally imprudent degree.

And so it was that by the 1840s — and a number of Napoleonic Wars later — a terrible inflation had begun to grip the land.

So Kaminska seems to have fallen for the Humean notion that banks are inherently predisposed to overissue and, without some quantitative restraint on their issue of liabilities, are engines of inflation. But, as the law of reflux teaches us, this is not true, especially when banks, as they inevitably must, make their liabilities convertible on demand into some outside asset whose supply is not under their control. After 1821, the gold standard having been officially restored in England, the outside asset was gold. So what was happening to the British price level after 1821 was determined not by the actions of the banking system (at least to a first approximation), but by the value of gold which was determined internationally. That’s the conceptual misunderstanding that I want to correct.

Now for the factual misunderstanding. The chart below shows the British Retail Price Index between 1825 and 1850. The British price level was clearly falling for most of the period. After falling steadily from 1825 to about 1835, the price level rebounded till 1839, but it prices again started to fall reaching a low point in 1844, before starting another brief rebound and rising sharply in 1847 until the panic when prices again started falling rapidly.

uk_rpi_1825-50

From a historical perspective, the outcome of the implicit Smith-Hume disagreement, which developed into the explicit dispute over the Bank Charter Act of 1844 between the Banking and Currency Schools, was highly unsatisfactory. Not only was the dysfunctional Bank Charter Act enacted, but the orthodox view of how the gold standard operates was defined by the Humean price-specie-flow mechanism and the Humean fallacy that banks are engines of inflation, which made it appear that, for the gold standard to function, the quantity of money had to be tied rigidly to the gold reserve, thereby placing the burden of adjustment primarily on countries losing gold, so that inflationary excesses would be avoided. (Fortunately, for the world economy, gold supplies increased fairly rapidly during the nineteenth century, the spread of the gold standard meant that the monetary demand for gold was increasing faster than the supply of gold, causing gold to appreciate for most of the nineteenth century.)

When I set out to write my book on free banking, my intention was to clear up the historical misunderstandings, largely attributable to David Hume, surrounding the operation of the gold standard and the behavior of competitive banks. In contrast to the Humean view that banks are inherently inflationary — a view endorsed by quantity theorists of all stripes and enshrined in the money-multiplier analysis found in every economics textbook — that the price level would go to infinity if banks were not constrained by a legal reserve requirement on their creation of liabilities, there was an alternative view that the creation of liabilities by the banking system is characterized by the same sort of revenue and cost considerations governing other profit-making enterprises, and that the equilibrium of a private banking system is not that value of money is driven down to zero, as Milton Friedman, for example, claimed in his Program for Monetary Stability.

The modern discovery (or rediscovery) that banks are not inherently disposed to debase their liabilities was made by James Tobin in his classic paper “Commercial Banks and Creators of Money.” Tobin’s analysis was extended by others (notably Ben Klein, Earl Thompson, and Fischer Black) to show that the standard arguments for imposing quantitative limits on the creation of bank liabilities were unfounded, because, even with no legal constraints, there are economic forces limiting their creation of liabilities. A few years after these contributions, F. A. Hayek also figured out that there are competitive forces constraining the creation of liabilities by the banking system. He further developed the idea in a short book Denationalization of Money which did much to raise the profile of the idea of free banking, at least in some circles.

If there is an economic constraint on the creation of bank liabilities, and if, accordingly, the creation of bank liabilities was responsive to the demands of individuals to hold those liabilities, the Friedman/Monetarist idea that the goal of monetary policy should be to manage the total quantity of bank liabilities so that it would grow continuously at a fixed rate was really dumb. It was tried unsuccessfully by Paul Volcker in the early 1980s, in his struggle to bring inflation under control. It failed for precisely the reason that the Bank Charter Act had to be suspended periodically in the nineteenth century: the quantitative limit on the growth of the money supply itself triggered a precautionary demand to hold money that led to a financial crisis. In order to avoid a financial crisis, the Volcker Fed constantly allowed the monetary aggregates to exceed their growth targets, but until Volcker announced in the summer of 1982 that the Fed would stop paying attention to the aggregates, the economy was teetering on the verge of a financial crisis, undergoing the deepest recession since the Great Depression. After the threat of a Friedman/Monetarist financial crisis was lifted, the US economy almost immediately began one of the fastest expansions of the post-war period.

Nevertheless, for years afterwards, Friedman and his fellow Monetarists kept warning that rapid growth of the monetary aggregates meant that the double-digit inflation of the late 1970s and early 1980s would soon return. So one of my aims in my book was to use free-banking theory – the idea that there are economic forces constraining the issue of bank liabilities and that banks are not inherently engines of inflation – to refute the Monetarist notion that the key to economic stability is to make the money stock grow at a constant 3% annual rate of growth.

Another goal was to explain that competitive banks necessarily have to select some outside asset into which to make their liabilities convertible. Otherwise those liabilities would have no value, or at least so I argued, and still believe. The existence of what we now call network effects forces banks to converge on whatever assets are already serving as money in whatever geographic location they are trying to draw customers from. Thus, free banking is entirely consistent with an already existing fiat currency, so that there is no necessary link between free banking and a gold (or other commodity) standard. Moreover, if free banking were adopted without abolishing existing fiat currencies and legal tender laws, there is almost no chance that, as Hayek argued, new privately established monetary units would arise to displace the existing fiat currencies.

My final goal was to suggest a new way of conducting monetary policy that would enhance the stability of a free banking system, proposing a monetary regime that would ensure the optimum behavior of prices over time. When I wrote the book, I had been convinced by Earl Thompson that the optimum behavior of the price level over time would be achieved if an index of nominal wages was stabilized. He proposed accomplishing this objective by way of indirect convertibility of the dollar into an index of nominal wages by way of a modified form of Irving Fisher’s compensated dollar plan. I won’t discuss how or why that goal could be achieved, but I am no longer convinced of the optimality of stabilizing an index of nominal wages. So I am now more inclined toward nominal GDP level targeting as a monetary policy regime than the system I proposed in my book.

But let me come back to the point that I think J. V. Dubois was getting at in his comment. Historically, idea of free banking meant that private banks should be allowed to issue bank notes of their own (with the issuing bank clearly identified) without unreasonable regulations, restrictions or burdens not generally applied to other institutions. During the period when private banknotes were widely circulating, banknotes were a more prevalent form of money than bank deposits. So in the 21st century, the right of banks to issue hand to hand circulating banknotes is hardly a crucial issue for monetary policy. What really matters is the overall legal and regulatory framework under which banks operate.

The term “free banking” does very little to shed light on most of these issues. For example, what kind of functions should banks perform? Should commercial banks also engage in investment banking? Should commercial bank liabilities be ensured by the government, and if so under what terms, and up to what limits? There are just a couple of issues; there are many others. And they aren’t necessarily easily resolved by invoking the free-banking slogan. When I was writing, I meant by “free banking” a system in which the market determined the total quantity of bank liabilities. I am still willing to use “free banking” in that sense, but there are all kinds of issues concerning the asset side of bank balance sheets that also need to be addressed, and I don’t find it helpful to use the term free banking to address those issues.

John Cochrane Explains Neo-Fisherism

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

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

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

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

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

cochrane1

Again, we don’t have to be that pure.

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

cochrane2

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

cochrane3

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

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

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

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

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

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

Nick Rowe Teaches Us a Lot about Apples and Bananas

Last week I wrote a post responding to a post by Nick Rowe about money and coordination failures. Over the weekend, Nick posted a response to my post (and to one by Brad Delong). Nick’s latest post was all about apples and bananas. It was an interesting post, though for some reason – no doubt unrelated to its form or substance – I found the post difficult to read and think about. But having now read, and I think, understood (more or less), what Nick wrote, I confess to being somewhat underwhelmed. Let me try to explain why I don’t think that Nick has adequately addressed the point that I was raising.

That point being that while coordination failures can indeed be, and frequently are, the result of a monetary disturbance, one that creates an excess demand for money, thereby leading to a contraction of spending, and thus to a reduction of output and employment, it is also possible that a coordination failure can occur independently of a monetary disturbance, at least a disturbance that could be characterized as an excess demand for money that triggers a reduction in spending, income, output, and employment.

Without evaluating his reasoning, I will just restate key elements of Nick’s model – actually two parallel models. There are apple trees and banana trees, and people like to consume both apples and bananas. Some people own apple trees, and some people own banana trees. Owners of apple trees and owners of banana trees trade apples for bananas, so that they can consume a well-balanced diet of both apples and bananas. Oh, and there’s also some gold around. People like gold, but it’s not clear why. In one version of the model, people use it as a medium of exchange, selling bananas for gold and using gold to buy apples or selling apples for gold and using gold to buy bananas. In the other version of the model, people just barter apples for bananas. Nick then proceeds to show that if trade is conducted by barter, an increase in the demand for gold, does not affect the allocation of resources, because agents continue to trade apples for bananas to achieve the desired allocation, even if the value of gold is held fixed. However, if trade is mediated by gold, the increased demand for gold, with prices held fixed, implies corresponding excess supplies of both apples and bananas, preventing the optimal reallocation of apples and bananas through trade, which Nick characterizes as a recession. However, if there is a shift in demand from bananas to apples or vice versa, with prices fixed in either model, there will be an excess demand for bananas and an excess supply of apples (or vice versa). The outcome is suboptimal because Pareto-improving trade is prevented, but there is no recession in Nick’s view because the excess supply of one real good is exactly offset by an excess demand for the other real good. Finally, Nick considers a case in which there is trade in apple trees and banana trees. An increase in the demand for fruit trees, owing to a reduced rate of time preference, causes no problems in the barter model, because there is no impediment to trading apples for bananas. However, in the money model, the reduced rate of time preference causes an increase in the amount of gold people want to hold, the foregone interest from holding more having been reduced, which prevents optimal trade with prices held fixed.

Here are the conclusions that Nick draws from his two models.

Bottom line. My conclusions.

For the second shock (a change in preferences away from apples towards bananas), we get the same reduction in the volume of trade whether we are in a barter or a monetary economy. Monetary coordination failures play no role in this sort of “recession”. But would we call that a “recession”? Well, it doesn’t look like a normal recession, because there is an excess demand for bananas.

For both the first and third shocks, we get a reduction in the volume of trade in a monetary economy, and none in the barter economy. Monetary coordination failures play a decisive role in these sorts of recessions, even though the third shock that caused the recession was not a monetary shock. It was simply an increased demand for fruit trees, because agents became more patient. And these sorts of recessions do look like recessions, because there is an excess supply of both apples and bananas.

Or, to say the same thing another way: if we want to understand a decrease in output and employment caused by structural unemployment, monetary coordination failures don’t matter, and we can ignore money. Everything else is a monetary coordination failure. Even if the original shock was not a monetary shock, that non-monetary shock can cause a recession because it causes a monetary coordination failure.

Why am I underwhelmed by Nick’s conclusions? Well, it just seems that, WADR, he is making a really trivial point. I mean in a two-good world with essentially two representative agents, there is not really that much that can go wrong. To put this model through its limited endowment of possible disturbances, and to show that only an excess demand for money implies a “recession,” doesn’t seem to me to prove a great deal. And I was tempted to say that the main thing that it proves is how minimal is the contribution to macroeconomic understanding that can be derived from a two-good, two-agent model.

But, in fact, even within a two-good, two-agent model, it turns out there is room for a coordination problem, not considered by Nick, to occur. In his very astute comment on Nick’s post, Kevin Donoghue correctly pointed out that even trade between an apple grower and a banana grower depends on the expectations of each that the other will actually have what to sell in the next period. How much each one plants depends on his expectations of how much the other will plant. If neither expects the other to plant, the output of both will fall.

Commenting on an excellent paper by Backhouse and Laidler about the promising developments in macroeconomics that were cut short because of the IS-LM revolution, I made reference to a passage quoted by Backhouse and Laidler from Bjorn Hansson about the Stockholm School. It was the Stockholm School along with Hayek who really began to think deeply about the relationship between expectations and coordination failures. Keynes also thought about that, but didn’t grasp the point as deeply as did the Swedes and the Austrians. Sorry to quote myself, but it’s already late and I’m getting tired. I think the quote explains what I think is so lacking in a lot of modern macroeconomics, and, I am sorry to say, in Nick’s discussion of apples and bananas.

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%).

own_rates_in_terms_of_tomatoes_cucumbers_onions

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.

own_rates_in_terms_of_tomatoes_cucumbers_onions_2

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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