Posts Tagged 'Fisher'

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.

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.

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.

Does Macroeconomics Need Financial Foundations?

One of the little instances of collateral damage occasioned by the hue and cry following upon Stephen Williamson’s post arguing that quantitative easing has been deflationary was the dustup between Scott Sumner and financial journalist and blogger Izabella Kaminska. I am not going to comment on the specifics of their exchange except to say that the misunderstanding and hard feelings between them seem to have been resolved more or less amicably. However, in quickly skimming the exchange between them, I was rather struck by the condescending tone of Kaminska’s (perhaps understandable coming from the aggrieved party) comment about the lack of comprehension by Scott and Market Monetarists more generally of the basics of finance.

First I’d just like to say I feel much of the misunderstanding comes from the fact that market monetarists tend to ignore the influence of shadow banking and market plumbing in the monetary world. I also think (especially from my conversation with Lars Christensen) that they ignore technological disruption, and the influence this has on wealth distribution and purchasing decisions amongst the wealthy, banks and corporates. Also, as I outlined in the post, my view is slightly different to Williamson’s, it’s based mostly on the scarcity of safe assets and how this can magnify hoarding instincts and fragment store-of-value markets, in a Gresham’s law kind of way. Expectations obviously factor into it, and I think Williamson is absolutely right on that front. But personally I don’t think it’s anything to do with temporary or permanent money expansion expectations. IMO It’s much more about risk expectations, which can — if momentum builds — shift very very quickly, making something deflationary, inflationary very quickly. Though, that doesn’t mean I am worried about inflation (largely because I suspect we may have reached an important productivity inflection point).

This remark was followed up with several comments blasting Market Monetarists for their ignorance of the basics of finance and commending Kaminska for the depth of her understanding to which Kaminska warmly responded adding a few additional jibes at Sumner and Market Monetarists. Here is one.

Market monetarists are getting testy because now that everybody started scrutinizing QE they will be exposed as ignorant. The mechanisms they originally advocated QE would work through will be seen as hopelessly naive. For them the money is like glass beads squirting out of the Federal Reserve, you start talking about stuff like collateral, liquid assets, balance sheets and shadow banking and they are out of their depth.

For laughs: Sumner once tried to defend the childish textbook model of banks lending out reserves and it ended in a colossal embarrassment in the comments section http://www.themoneyillusion.com/?p=5893

For you to defend your credentials in front of such “experts” is absurd. There is a lot more depth to your understanding than to their sandbox vision of the monetary system. And yes, it *is* crazy that journalists and bloggers can talk about these things with more sense than academics. But this [is] the world we live in.

To which Kaminska graciously replied:

Thanks as well! And I tend to agree with your assessment of the market monetarist view of the world.

So what is the Market Monetarist view of the world of which Kaminska tends to have such a low opinion? Well, from reading Kaminska’s comments and those of her commenters, it seems to be that Market Monetarists have an insufficiently detailed and inaccurate view of financial intermediaries, especially of banks and shadow banks, and that Market Monetarists don’t properly understand the role of safe assets and collateral in the economy. But the question is why, and how, does any of this matter to a useful description of how the economy works?

Well, this whole episode started when Stephen Williamson had a blog post arguing that QE was deflationary, and the reason it’s deflationary is that creating more high powered money provides the economy with more safe assets and thereby reduces the liquidity premium associated with safe assets like short-term Treasuries and cash. By reducing the liquidity premium, QE causes the real interest rate to fall, which implies a lower rate of inflation.

Kaminska thinks that this argument, which Market Monetarists find hard to digest, makes sense, though she can’t quite bring herself to endorse it either. But she finds the emphasis on collateral and safety and market plumbing very much to her taste. In my previous post, I raised what I thought were some problems with Williamson’s argument.

First, what is the actual evidence that there is a substantial liquidity premium on short-term Treasuries? If I compare the rates on short-term Treasuries with the rates on commercial paper issued by non-Financial institutions, I don’t find much difference. If there is a substantial unmet demand for good collateral, and there is only a small difference in yield between commercial paper and short-term Treasuries, one would think that non-financial firms could make a killing by issuing a lot more commercial paper. When I wrote the post, I was wondering whether I, a financial novice, might be misreading the data or mismeasuring the liquidity premium on short-term Treasuries. So far, no one has said anything about that, but If I am wrong, I am happy to be enlightened.

Here’s something else I don’t get. What’s so special about so-called safe assets? Suppose, as Williamson claims, that there’s a shortage of safe assets. Why does that imply a liquidity premium? One could still compensate for the lack of safety by over-collateralizing the loan using an inferior asset. If that is a possibility, why is the size of the liquidity premium not constrained?

I also pointed out in my previous post that a declining liquidity premium would be associated with a shift out of money and into real assets, which would cause an increase in asset prices. An increase in asset prices would tend to be associated with an increase in the value of the underlying service flows embodied in the assets, in other words in an increase in current prices, so that, if Williamson is right, QE should have caused measured inflation to rise even as it caused inflation expectations to fall. Of course Williamson believes that the decrease in liquidity premium is associated with a decline in real interest rates, but it is not clear that a decline in real interest rates has any implications for the current price level. So Williamson’s claim that his model explains the decline in observed inflation since QE was instituted does not seem all that compelling.

Now, as one who has written a bit about banking and shadow banking, and as one who shares the low opinion of the above-mentioned commenter on Kaminska’s blog about the textbook model (which Sumner does not defend, by the way) of the money supply via a “money multiplier,” I am in favor of changing how the money supply is incorporated into macromodels. Nevertheless, it is far from clear that changing the way that the money supply is modeled would significantly change any important policy implications of Market Monetarism. Perhaps it would, but if so, that is a proposition to be proved (or at least argued), not a self-evident truth to be asserted.

I don’t say that finance and banking are not important. Current spreads between borrowing and lending rates, may not provide a sufficient margin for banks to provide the intermediation services that they once provided to a wide range of customers. Businesses have a wider range of options in obtaining financing than they used to, so instead of holding bank accounts with banks and foregoing interest on deposits to be able to have a credit line with their banker, they park their money with a money market fund and obtain financing by issuing commercial paper. This works well for firms large enough to have direct access to lenders, but smaller businesses can’t borrow directly from the market and can only borrow from banks at much higher rates or by absorbing higher costs on their bank accounts than they would bear on a money market fund.

At any rate, when market interest rates are low, and when perceived credit risks are high, there is very little margin for banks to earn a profit from intermediation. If so, the money multiplier — a crude measure of how much intermediation banks are engaging in goes down — it is up to the monetary authority to provide the public with the liquidity they demand by increasing the amount of bank reserves available to the banking system. Otherwise, total spending would contract sharply as the public tried to build up their cash balances by reducing their own spending – not a pretty picture.

So finance is certainly important, and I really ought to know more about market plumbing and counterparty risk  and all that than I do, but the most important thing to know about finance is that the financial system tends to break down when the jointly held expectations of borrowers and lenders that the loans that they agreed to would be repaid on schedule by the borrowers are disappointed. There are all kinds of reasons why, in a given case, those jointly held expectations might be disappointed. But financial crises are associated with a very large cluster of disappointed expectations, and try as they might, the finance guys have not provided a better explanation for that clustering of disappointed expectations than a sharp decline in aggregate demand. That’s what happened in the Great Depression, as Ralph Hawtrey and Gustav Cassel and Irving Fisher and Maynard Keynes understood, and that’s what happened in the Little Depression, as Market Monetarists, especially Scott Sumner, understand. Everything else is just commentary.

That Oh So Elusive Natural Rate of Interest

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

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

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

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

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


About Me

David Glasner
Washington, DC

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

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