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Keynes on the Fisher Equation and Real Interest Rates

Published September 2, 2013 Fisher equation , Irving Fisher , Keynes , monetary policy , monetary theory , natural rate of interest , real interest rates , Uncategorized , zero lower bound 27 Comments
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Almost two months ago, I wrote a post (“Who Sets the Real Rate of Interest?”) about the Fisher equation, questioning the idea that the Fed can, at will, reduce the real rate of interest by printing money, an idea espoused by a lot of people who also deny that the Fed has the power to reduce the rate of unemployment by printing money. A few weeks later, I wrote another post (“On a Difficult Passage in the General Theory“) in which I pointed out the inconsistency between Keynes’s attack on the Fisher equation in chapter 11 of the General Theory and his analysis in chapter 17 of the liquidity premium and the conditions for asset-market equilibrium, an analysis that led Keynes to write down what is actually a generalized version of the Fisher equation. In both of those posts I promised a future post about how to understand the dynamic implications of the Fisher equation and the relationship between Fisher equation and the Keynesian analysis. This post is an attempt to make good on those promises.

As I observed in my earlier post, the Fisher equation is best understood as a property of equilibrium. If the Fisher equation does not hold, then it is reasonable to attribute the failure to some sort of disequilibrium. The most obvious, but not the only, source of disequilibrium is incorrectly expected inflation. Other sources of disequilibrium could be a general economic disorder, the entire economic system being (seriously) out of equilibrium, implying that the real rate of interest is somehow different from the “equilibrium” rate, or, as Milton Friedman might put it, that the real rate is different from the rate that would be ground out by the system of Walrasian (or Casselian or Paretian or Fisherian) equations.

Still a third possibility is that there is more than one equilibrium (i.e., more than one solution to whichever system of equations we are trying to solve). If so, as an economy moves from one equilibrium path to another through time, the nominal (and hence the real) rate of that economy could be changing independently of changes in expected inflation, thereby nullifying the empirical relationship implied (under the assumption of a unique equilibrium) by the Fisher equation.

Now in the canonical Fisherian theory of interest, there is, at any moment of time, a unique equilibrium rate of interest (actually a unique structure of equilibrium rates for all possible combinations of time periods), increasing thrift tending to reduce rates and increasing productivity of capital tending to raise them. While uniqueness of the interest rate cannot easily be derived outside a one-commodity model, the assumption did not seem all that implausible in the context of the canonical Fisherian model with a given technology and given endowments of present and future resources. In the real world, however, the future is unknown, so the future exists now only in our imagination, which means that, fundamentally, the determination of real interest rates cannot be independent of our expectations of the future. There is no unique set of expectations that is consistent with “fundamentals.” Fundamentals and expectations interact to create the future; expectations can be self-fulfilling. One of the reasons why expectations can be self-fulfilling is that often it is the case that individual expectations can only be realized if they are congruent with the expectations of others; expectations are subject to network effects. That was the valid insight in Keynes’s “beauty contest” theory of the stock market in chapter 12 of the GT.

There simply is no reason why there would be only one possible equilibrium time path. Actually, the idea that there is just one possible equilibrium time path seems incredible to me. It seems infinitely more likely that there are many potential equilibrium time paths, each path conditional on a corresponding set of individual expectations. To be sure, not all expectations can be realized. Expectations that can’t be realized produce bubbles. But just because expectations are not realized doesn’t mean that the observed price paths were bubbles; as long as it was possible, under conditions that could possibly have obtained, that the expectations could have been realized, the observed price paths were not bubbles.

Keynes was not the first economist to attribute economic fluctuations to shifts in expectations; J. S. Mill, Stanley Jevons, and A. C. Pigou, among others, emphasized recurrent waves of optimism and pessimism as the key source of cyclical fluctuations. The concept of the marginal efficiency of capital was used by Keynes to show the dependence of the desired capital stock, and hence the amount of investment, on the state of entrepreneurial expectations, but Keynes, just before criticizing the Fisher equation, explicitly identified the MEC with the Fisherian concept of “the rate of return over cost.” At a formal level, at any rate, Keynes was not attacking the Fisherian theory of interest.

So what I want to suggest is that, in attacking the Fisher equation, Keynes was really questioning the idea that a change in inflation expectations operates strictly on the nominal rate of interest without affecting the real rate. In a world in which there is a unique equilibrium real rate, and in which the world is moving along a time-path in the neighborhood of that equilibrium, a change in inflation expectations may operate strictly on the nominal rate and leave the real rate unchanged. In chapter 11, Keynes tried to argue the opposite: that the entire adjustment to a change in expected inflation is concentrated on real rate with the nominal rate unchanged. This idea seems completely unfounded. However, if the equilibrium real rate is not unique, why assume, as the standard renditions of the Fisher equation usually do, that a change in expected inflation affects only the nominal rate? Indeed, even if there is a unique real rate – remember that “unique real rate” in this context refers to a unique yield curve – the assumption that the real rate is invariant with respect to expected inflation may not be true in an appropriate comparative-statics exercise, such as the 1950s-1960s literature on inflation and growth, which recognized the possibility that inflation could induce a shift from holding cash to holding real assets, thereby increasing the rate of capital accumulation and growth, and, consequently, reducing the equilibrium real rate. That literature was flawed, or at least incomplete, in its analysis of inflation, but it was motivated by a valid insight.

In chapter 17, after deriving his generalized version of the Fisher equation, Keynes came back to this point when explaining why he had now abandoned the Wicksellian natural-rate analysis of the Treatise on Money. The natural-rate analysis, Keynes pointed out, presumes the existence of a unique natural rate of interest, but having come to believe that there could be an equilibrium associated with any level of employment, Keynes now concluded that there is actually a natural rate of interest corresponding to each level of employment. What Keynes failed to do in this discussion was to specify the relationship between natural rates of interest and levels of employment, leaving a major gap in his theoretical structure. Had he specified the relationship, we would have an explicit Keynesian IS curve, which might well differ from the downward-sloping Hicksian IS curve. As Earl Thompson, and perhaps others, pointed out about 40 years ago, the Hicksian IS curve is inconsistent with the standard neoclassical theory of production, which Keynes seems (provisionally at least) to have accepted when arguing that, with a given technology and capital stock, increased employment is possible only at a reduced real wage.

But if the Keynesian IS curve is upward-sloping, then Keynes’s criticism of the Fisher equation in chapter 11 is even harder to make sense of than it seems at first sight, because an increase in expected inflation would tend to raise, not (as Keynes implicitly assumed) reduce, the real rate of interest. In other words, for an economy operating at less than full employment, with all expectations except the rate of expected inflation held constant, an increase in the expected rate of inflation, by raising the marginal efficiency of capital, and thereby increasing the expected return on investment, ought to be associated with increased nominal and real rates of interest. If we further assume that entrepreneurial expectations are positively related to the state of the economy, then the positive correlation between inflation expectations and real interest rates would be enhanced. On this interpretation, Keynes’s criticism of the Fisher equation in chapter 11 seems indefensible.

That is one way of looking at the relationship between inflation expectations and the real rate of interest. But there is also another way.

The Fisher equation tells us that, in equilibrium, the nominal rate equals the sum of the prospective real rate and the expected rate of inflation. Usually that’s not a problem, because the prospective real rate tends to be positive, and inflation (at least since about 1938) is almost always positive. That’s the normal case. But there’s also an abnormal (even pathological) case, where the sum of expected inflation and the prospective real rate of interest is less than zero. We know right away that such a situation is abnormal, because it is incompatible with equilibrium. Who would lend money at a negative rate when it’s possible to hold the money and get a zero return? The nominal rate of interest can’t be negative. So if the sum of the prospective real rate (the expected yield on real capital) and the expected inflation rate (the negative of the expected yield on money with a zero nominal interest rate) is negative, then the return to holding money exceeds the yield on real capital, and the Fisher equation breaks down.

In other words, if r + dP/dt < 0, where r is the real rate of interest and dP/dt is the expected rate of inflation, then r < –dP/dt. But since i, the nominal rate of interest, cannot be less than zero, the Fisher equation does not hold, and must be replaced by the Fisher inequality

i > r + dP/dt.

If the Fisher equation can’t be satisfied, all hell breaks loose. Asset prices start crashing as asset owners try to unload their real assets for cash. (Note that I have not specified the time period over which the sum of expected inflation and the prospective yield on real capital are negative. Presumably the duration of that period is not indefinitely long. If it were, the system might implode.)

That’s what was happening in the autumn of 2008, when short-term inflation expectations turned negative in a contracting economy in which the short-term prospects for investment were really lousy and getting worse. The prices of real assets had to fall enough to raise the prospective yield on real assets above the expected yield from holding cash. However, falling asset prices don’t necessary restore equilibrium, because, once a panic starts it can become contagious, with falling asset prices reinforcing the expectation that asset prices will fall, depressing the prospective yield on real capital, so that, rather than bottoming out, the downward spiral feeds on itself.

Thus, for an economy at the zero lower bound, with the expected yield from holding money greater than the prospective yield on real capital, a crash in asset prices may not stabilize itself. If so, something else has to happen to stop the crash: the expected yield from holding money must be forced below the prospective yield on real capital. With the prospective yield on real capital already negative, forcing down the expected yield on money below the prospective yield on capital requires raising expected inflation above the absolute value of the prospective yield on real capital. Thus, if the prospective yield on real capital is -5%, then, to stop the crash, expected inflation would have to be raised to over 5%.

But there is a further practical problem. At the zero lower bound, not only is the prospective real rate not observable, it can’t even be inferred from the Fisher equation, the Fisher equation having become an inequality. All that can be said is that r < –dP/dt.

So, at the zero lower bound, achieving a recovery requires raising expected inflation. But how does raising expected inflation affect the nominal rate of interest? If r + dP/dt < 0, then increasing expected inflation will not increase the nominal rate of interest unless dP/dt increases enough to make r + dP/dt greater than zero. That’s what Keynes seemed to be saying in chapter 11, raising expected inflation won’t affect the nominal rate of interest, just the real rate. So Keynes’s criticism of the Fisher equation seems valid only in the pathological case when the Fisher equation is replaced by the Fisher inequality.

In my paper “The Fisher Effect Under Deflationary Expectations,” I found that a strongly positive correlation between inflation expectations (approximated by the breakeven TIPS spread on 10-year Treasuries) and asset prices (approximated by S&P 500) over the time period from spring 2008 through the end of 2010, while finding no such correlation over the period from 2003 to 2008. (Extending the data set through 2012 showed the relationship persisted through 2012 but may have broken down in 2013.) This empirical finding seems consistent with the notion that there has been something pathological about the period since 2008. Perhaps one way to think about the nature of the pathology is that the Fisher equation has been replaced by the Fisher inequality, a world in which changes in inflation expectations are reflected in changes in real interest rates instead of changes in nominal rates, the most peculiar kind of world described by Keynes in chapter 11 of the General Theory.

Friedman’s Dictum

Published August 16, 2013 Friedman , Great Depression , Keynes , monetary history , monetary theory , Scott Sumner , Uncategorized 15 Comments
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In his gallant, but in my opinion futile, attempts to defend Milton Friedman against the scandalous charge that Friedman was, gasp, a Keynesian, if not in his policy prescriptions, at least in his theoretical orientation, Scott Sumner has several times referred to the contrast between the implication of the IS-LM model that expansionary monetary policy implies a reduced interest rate, and Friedman’s oft-repeated dictum that high interest rates are a sign of easy money, and low interest rates a sign of tight money. This was a very clever strategic and rhetorical move by Scott, because it did highlight a key difference between Keynesian and Monetarist ideas while distracting attention from the overlap between Friedman and Keynesians on the basic analytics of nominal-income determination.

Alghough I agree with Scott that Friedman’s dictum that high interest rates distinguishes him from Keynes and Keynesian economists, I think that Scott leaves out an important detail: Friedman’s dictum also distinguishes him from just about all pre-Keynesian monetary economists. Keynes did not invent the terms “dear money” and “cheap money.” Those terms were around for over a century before Keynes came on the scene, so Keynes and the Keynesians were merely reflecting the common understanding of all (or nearly all) economists that high interest rates were a sign of “dear” or “tight” money, and low interest rates a sign of “cheap” or “easy” money. For example, in his magisterial A Century of Bank Rate, Hawtrey actually provided numerical bounds on what constituted cheap or dear money in the period he examined, from 1844 to 1938. Cheap money corresponded to a bank rate less than 3.5% and dear money to a bank rate over 4.5%, 3.5 to 4.5% being the intermediate range.

Take the period just leading up to the Great Depression, when Britain returned to the gold standard in 1925. The Bank of England kept its bank rate over 5% almost continuously until well into 1930. Meanwhile the discount rate of the Federal Reserve System from 1925 to late 1928 was between 3.5 and 5%, the increase in the discount rate in 1928 to 5% representing a decisive shift toward tight money that helped drive the world economy into the Great Depression. We all know – and certainly no one better than Scott – that, in the late 1920s, the bank rate was an absolutely reliable indicator of the stance of monetary policy. So what are we to make of Friedman’s dictum?

I think that the key point is that traditional notions of central banking – the idea of “cheap” or “dear” money – were arrived at during the nineteenth century when almost all central banks were operating either in terms of a convertible (gold or silver or bimetallic) standard or with reference to such a standard, so that the effect of monetary policy on prices could be monitored by observing the discount of the currency relative to gold or silver. In other words, there was an international price level in terms of gold (or silver), and the price level of every country could be observed by looking at the relationship of its currency to gold (or silver). As long as convertibility was maintained between a currency and gold (or silver), the price level in terms of that currency was fixed.

If a central bank changed its bank rate, as long as convertibility was maintained (and obviously most changes in bank rate occurred with no change in convertibility), the effect of the change in bank rate was not reflected in the country’s price level (which was determined by convertibility). So what was the point of a change in bank rate under those circumstances? Simply for the central bank to increase or decrease its holding of reserves (usually gold or silver). By increasing bank rate, the central bank would accumulate additional reserves, and, by decreasing bank rate, it would reduce its reserves. A “dear money” policy was the means by which a central bank could add to its reserve and an “easy money” policy was the means by which it could disgorge reserves.

So the idea that a central bank operating under a convertible standard could control its price level was based on a misapprehension — a widely held misapprehension to be sure — but still a mistaken application of the naive quantity theory of money to a convertible monetary standard. Nevertheless, although the irrelevance of bank rate to the domestic price level was not always properly understood in the nineteenth century – economists associated with the Currency School were especially confused on this point — the practical association between interest rates and the stance of monetary policy was well understood, which is why all monetary theorists in the nineteenth and early twentieth centuries agreed that high interest rates were a sign of dear money and low interest rates a sign of cheap money. Keynes and the Keynesians were simply reflecting the conventional wisdom.

Now after World War II, when convertibility was no longer a real constraint on the price level (despite the sham convertibility of the Bretton Woods system), it was a true innovation of Friedman to point out that the old association between dear (cheap) money and high (low) interest rates was no longer a reliable indicator of the stance of monetary policy. However, as a knee-jerk follower of the Currency School – the 3% rule being Friedman’s attempt to adapt the Bank Charter Act of 1844 to a fiat currency, and with equally (and predictably) lousy results – Friedman never understood that under the gold standard, it is the price level which is fixed and the money supply that is endogenously determined, which is why much of the Monetary History, especially the part about the Great Depression (not, as Friedman called it, “Contraction,” erroneously implying that the change in the quantity of money was the cause, rather than the effect, of the deflation that characterized the Great Depression) is fundamentally misguided owing to its comprehensive misunderstanding of the monetary adjustment mechanism under a convertible standard.

PS This is written in haste, so there may be some errors insofar as I relying on my memory without checking my sources. I am sure that readers will correct my lapses of memory

PPS I also apologize for not responding to recent comments, I will try to rectify that transgression over the next few days.

Leijonhufvud on Friedman

Published August 13, 2013 Axel Leijonfuvud , Keynes , Milton Friedman 13 Comments
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Before it was hijacked by Paul Krugman, Scott Sumner and I were having a friendly little argument about whether Milton Friedman repackaged the Keynesian theory of the demand for money as the quantity theory of money transmitted to him via a fictitious Chicago oral tradition, as I, relying on Don Patinkin and Harry Johnson, claim, or whether Friedman was a resolute anti-Keynesian, as Scott claims. We have been trading extended quotations from the literature to try to support our positions.

I now offer some additional quotations, all but one from Axel Leijonhufvud’s wonderful essay “The Wicksell Connection: Variations on a Theme,” published in Leijonfuvud’s volume Information and Coordination (Oxford University Press, 1981). By some coincidence, the quotations tend to support my position, but, more importantly, they shed important light on problems of interpreting what Keynes was really talking about, and suggest a way of thinking about Keynes that takes us beyond the sterile ideological debates into which we tend lapse at the mere mention of the name John Maynard Keynes, or for that matter, Milton Friedman. Of course, the main lesson that readers should take away is: read the whole essay.

Herewith are a few extracts in which Leijonhufvud comments on Friedman and his doctrinal relationship with Keynes.

Milton Friedman has emphatically denied that the elasticity of LM is at issue [in the Monetarist v. Keynesian controversies]. At the same time his use of what is basically an IS-LM structure in presenting his own theory, and his oft-repeated insistence that no theoretical issues but only questions of empirical magnitudes within this shared theoretical frame separate him from his opponents, have apparently fortified others in their belief that (whatever he says) this elasticity must be crucial. Furthermore, Friedman has himself played around with elasticities, for example in advancing the notion of a horizontal IS curve. (p. 144, fn. 22)

The troubles with keeping track of the Wicksellian theme in its Keynesian guises and disguises go far back in time. The original “Savings-equals-Investment” debate did not reach a clear-cut collective verdict. As Lipsey [“The Foundations of the Theory of National Income: An Analysis of Some Fundamental Errors”] has recently shown, confusion persists to the present day. The IS-LM framework did not lend itself too well to a sharp characterization of the question whether the excess demand for bonds or the excess demand for money governs the interest rate. It was concluded that the distinction between the Loanable Funds and Liquidity Preference hypotheses was probably either pointless or misleading and that, in either case, the issue could safely be left unresolved. Correspondingly, Hansen found, Keynes’ insistence that saving and investment determine income while money stock and liquidity preference determine the rate of interest (rather than the other way around) makes no sense once you realize that, in IS-LM, everything simultaneously determines everything.

In Hansen’s reading Keynes’ interest theory was “indeterminate” – money supply and demand could not determine the interest rate, as Keynes would have it, but only give you the LM curve, etc. This way of looking at it missed the issue of which excess demand governs the interest rate.

One is reminded of Hansen’s indeterminacy charge by Friedman’s more recent argument that Keynes’ theory suffered from a “missing equation” – and should be completed by adding an exogenously determined price level. Keynes’ theory . . . was of the dynamic-historical variety. In describing the state of the system at some point in the sequential process, such theories make use of information about the system’s initial (historical) state. Static models do not use historical information, of course, but have to have equations for all endogenous variables. Reading a dynamic-historical theory on the presumption that it is static, therefore, is apt to lead to the mistaken impression that it lacks equations and is indeterminate. (pp. 180-81 and fn. 84)

Friedman, like so many others, filters Keynes and Keynesian theory through the IS-LM model and, consequently, ends up where everyone else ends up: bogged down in the Neoclassical Synthesis, which is to say, with the conclusion that exogenous fixity of money wages was Keynes’ explanation of unemployment. His discussion is notable for a sophisticated treatment of Keynes’ demand for money function and for its sweeping endorsement of the Pigou-effect. . . . (p. 189)

I break off from the final quotation, which is just a small part of an extended discussion of Friedman, because the argument is too dense to summarize adequately, and the entire lengthy passage (pp. 187-94) has to be read to grasp its full import. But I close with one final quotation from Leijonhufvud’s essay “Schools, ‘Revolutions,’ and Research Programmes in Economic Theory,” also contained in Information and Coordination (pp. 291-345).

The most widely known “monetarist,” Professor Milton Friedman, has for a long time consistently voiced the position that “monetarists” and “(neo)-Keynesians” share essentially the same theory and that their differences all derive from contrasting hypotheses concerning certain crucial empirical magnitudes. (He has also, however, persistently denied that the issues can be defined as a “simple” matter of the magnitude of the interest-elasticity of the excess demand for money – an otherwise oft-repeated contention in the debate.) In his recent attempts to provide an explicit representation for his theory, accordingly, Friedman chose ot use the “Keynesian” so-called “IS-LM” framework as his language of formal discourse.

In my opinion, there are “hard core” differences between the two theories and ones, moreover, that the “IS-LM” framework will not help us define. Not only are these differences at the “cosmological” level not accurately represented by the models used, but they will also lead to divergent interpretations of empirical results. (pp. 298-99, fn. 10)

The last paragraph, I suspect, probably sums up not just the inconclusiveness of the debate between Monetarists and Keynesians, but also the inconclusiveness of the debate about whether Friedman was or wasn’t a Keynesian. So be it.

Sumner Sticks with Friedman

Published August 11, 2013 demand for money , Don Patinkin , J. R. Hicks , Keynes , Mark Blaug , Milton Friedman , Scott Sumner 8 Comments

Scott Sumner won’t let go. Scott had another post today trying to show that the Cambridge Theory of the demand for money was already in place before Keynes arrived on the scene. He quotes from Hicks’s classic article “Mr. Keynes and the Classics” to dispute the quotation from another classic article by Hicks, “A Suggestions for Simplifying the Theory of Money,” which I presented in a post last week, demonstrating that Hicks credited Keynes with an important contribution to the demand for money that went beyond what Pigou, and even Lavington, had provided in their discussions of the demand for money.

In this battle of dueling quotations, I will now call upon Mark Blaug, perhaps the greatest historian of economics since Schumpeter, who in his book Economic Theory in Retrospect devotes an entire chapter (15) to the neoclassical theory of money, interest and prices. I quote from pp. 636-37 (4th edition).

Marshall and his followers went some way to move the theory of the demand for money in the direction of ordinary demand analysis, first, by relating money to net output or national income rather than the broader category of total transactions, and, second, by shifting from money’s rate of turnover to the proportion of annual income that the public wishes to hold in the form of money. In purely formal terms, there I nothing to choose between the Fisherian transaction approach and the Cambridge cash-balance approach, but the Cambridge formulation held out the potential of a genuine portfolio theory of the demand for money, which potential, however, was never fully exploited. . . .

The Cambridge formulation implies a demand for money equation, D_m = kPY, which contains no variable to represent the opportunity costs of holding cash, namely the rate of interest or the yield of alternative non-money assets, analogous to the relative price arguments of ordinary demand functions.
Yet a straight-forward application of utility-maximizing principles would have suggested that a rise in interest rates is likely to induce a fall in k as people strive to substitute interest-earning assets for passive money balances in their asset portfolios. Similarly, a fall in interest rates, by lowering the opportunity cost of holding money, is likely to cause a rise in k. Strangely enough, however, the Cambridge monetary theory never explicitly recognized the functional dependence of k on either the rate of interest or the rate on all non-monetary assets. After constructing a framework highly suggestive of a study of all the factors influencing cash-holding decisions, the Cambridge writers tended to lapse back to a list of the determinants of k that differed in no important respects from the list of institutional factors that Fisher had cited in his discussion of V. One can find references in Marshall, Pigou and particularly Lavington to a representative individual striking a balance between the costs of cash holdings in terms of interest foregone (minus the brokerage costs that would have been incurred by the movement into stocks and bonds) and their returns in terms of convenience and security against default but such passages were never systematically integrated with the cash-balance equation. As late as 1923, we find the young Keynes in A Tract on Monetary Reform interpreting k as a stable constant, representing an invariant link in the transmission mechanism connecting money to prices. If only Keynes at that date had read Wicksell instead of Marshall, he might have arrived at a money demand function that incorporates variations in the interest rate years before The General Theory (1936).

Moving to pp. 645-46, we find the following under the heading “The Demand for Money after Keynes.”

In giving explicit consideration to the yields on assets that compete with money, Keynes became one of the founders of the portfolio balance approach to monetary analysis. However, it is Hicks rather than Keynes who ought to be regarded as the founder of the view that the demand for money is simply an aspect of the problem of choosing an optimum portfolio of assets. In a remarkable paper published a year before the appearance of the General Theory, modestly entitled “A Suggestion for Simplifying the Theory of Money,” Hicks argued that money held at least partly as a store of value must be considered a type of capital asset. Hence the demand for money equation must include total wealth and expected rates of return on non-monetary assets as explanatory variables. Because individuals can choose to hold their entire wealth portfolios in the form of cash, the wealth variable represents the budget constraint on money holdings. The yield variables, on the other hand, represent both the opportunity costs of holding money and the substitutions effects of changes in relative rates of return. Individuals optimize their portfolio balances by comparing these yields with the imputed yield in terms of convenience and security of holding money. By these means, Hicks in effect treated the demand for money as a problem of balance sheet equilibrium analyzed along the same lines as those employed in ordinary demand theory.

It was Milton Friedman who carried this Hicksian analysis of money as a capital asset to its logical conclusion. In a 1956 essay, he set out a precise and complete specification of the relevant constraints and opportunity cost variable entering a household’s money demand function. His independent variable included wealth or permanent income – the present value of expected future receipts from all sources, whether personal earning or the income from real property and financial assets – the ratio of human to non-human wealth, expected rates of return on stocks, bonds and real assets, the nominal interest rate, the actual price level, and, finally, the expected percentage change in the price level. Like Hicks, Friedman specified wealth as the appropriate budget constraint but his concept of wealth was much broader than that adopted by Hicks. Whereas Keynes had viewed bonds as the only asset competing with cash, Friedman regarded all types of wealth as potential substitutes for cash holdings in an individual’s balance sheet; thus, instead of a single interest variable in the Keynesian liquidity preference equation, we get a whole list of relative yield variables in Friedman. An additional novel feature, entirely original with Friedman, is the inclusion of the expected rate of change in P as a measure of the anticipated rate of depreciation in the purchasing power of cash balances.

This formulation of the money demand function was offered in a paper entitled “The Quantity Theory of Money: A Restatement.” Friedman claimed not only that the quantity theory of money had always been a theory about the demand for money but also that his reformulation corresponded closely to what some of the great Chicago monetary economists, such as H.C. Simons and L. W. Mints, had always meant by the quantity theory. It is clear, however, from our earlier discussion that the quantity theory of money, while embodying an implicit conception of the demand for money, had always stood first and foremost for a theory of the determination of prices and nominal income; it contained much more than a particular theory of the demand for money.

Finally, Blaug remarks in his “notes for further reading” at the end of chapter 15,

In an influential essay, “The Quantity Theory of Money – A Restatement,” . . . M. Friedman claimed that his restatement was nothing more than the University of Chicago “oral” tradition. That claim was effectively destroyed by D. Patinkin, “The Chicago Tradition, the Quantity Theory, and Friedman, JMCB, 1969 .

Well, just a couple of quick comments on Blaug. I don’t entirely agree with everything he says about Cambridge monetary theory, and about the relative importance of Hicks and Keynes in advancing the theory of the demand for money. Cambridge economists may have been a bit more aware that the demand for money was a function of the rate of interest than he admits, and I think Keynes in chapter 17, definitely formulated a theory of the demand for money in a portfolio balance context, so I think that Friedman was indebted to both Hicks and Keynes for his theory of the demand for money.

As for Scott Sumner’s quotation from Hicks’s Mr. Keynes and the Classics, I think the point of that paper was not so much the theory of the demand for money, which had already been addressed in the 1935 paper from which I quoted, as to sketch out a way of generalizing the argument of the General Theory to encompass both the liquidity trap and the non-liquidity trap cases within a single graph. From the standpoint of the IS-LM diagram, the distinctive Keynesian contribution was the case of absolute liquidity preference, that doesn’t mean that Hicks meant that nothing had been added to the theory of the demand for money since Lavington. If that were the case, Hicks would have been denying that his 1935 paper had made any contribution. I don’t think that’s what he meant to suggest.

To sum up: 1) there was no Chicago oral tradition of the demand for money; 2) Friedman’s restatement of the quantity theory owed more to Keynes (and Hicks) than he admitted; 3) Friedman adapted the Cambridge/Keynes/Hicks theory of the demand for money in novel ways that allowed him to develop an analysis of price level changes that was more straightforward than was possible in the IS-LM model, thereby de-emphasizing the link between money and interest rates, which had been a such a prominent feature of the Keynesian models. That of course is a point that Scott Sumner likes to stress. In an upcoming post, I will comment on the fact that it was not just Keynesian models which stressed the link between money and interest rates. Pre-Keynesian monetary models also stressed the connection between easy money and low interest rates and dear money and high interest rates. Friedman’s argument was thus an innovation not only relative to Keynesian models but to orthodox monetary models. What accounts for this innovation?

Hicks on Keynes and the Theory of the Demand for Money

Published August 6, 2013 Friedman , J. R. Hicks , Keynes 17 Comments
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One of my favorite papers is one published by J. R. Hicks in 1935 “A Suggestion for Simplifying the Demand for Theory of Money.” The aim of that paper was to explain how to reconcile the concept of a demand for money into the theory of rational choice. Although Marshall had attempted to do so in his writings, his formulations of the idea were not fully satisfactory, and other Cambridge economists, notably Pigou, Lavington, Robertson, and Keynes, struggled to express the idea in a more satisfactory way than Marshall had done.

In Hicks’s introductory essay to volume II of his Collected Essays on Economic Theory in which his 1935 essay appears, Hicks recounts that Keynes told him after reading his essay that the essay was similar to the theory of liquidity preference, on which Keynes was then working.

To anyone who comes over from the theory of value to the theory of money, there are a number of things which are rather startling. Chief of these is the preoccupation of monetary theorists with a certain equation, which states that the price of goods multiplied by the quantity of goods equals the amount of money which is spent on them. The equation crops up again and again, and it has all sorts of ingenious little arithmetical tricks performed on it. Sometimes it comes out as MV = PT . . .

Now we, of the theory of value, are not unfamiliar with this equation, and there was a time when we used to attach as much importance to it as monetary theorists seem to do still. This was in the middle of the last century, when we used to talk about value being “a ratio between demand and supply.” Even now, we accept the equation, and work it, more or less implicitly, into our systems. But we are rather inclined to take it for granted, since it is rather tautologous, and since we have found that another equation, not alternative to the quantity equation, but complementary with it, is much more significant. This is the equation which states that the relative value of two commodities depends upon their relative marginal utility.

Now to an ingénue, who comes over to monetary theory, it is extremely trying to be deprived of this sheet-anchor. It was marginal utility that really made sense of the theory of value; and to come to a branch of economics which does without marginal utility altogether! No wonder there are such difficulties and such differences! What is wanted is a “marginal revolution!”

That is my suggestion. But I know that it will meet with apparently crushing objections. I shall be told that the suggestion has been tried out before. It was tried by Wicksell, and though it led to interesting results, it did not lead to a marginal utility theory of money. It was tried by Mises, and led to the conclusion that money is a ghost of gold – because, so it appeared, money as such has no marginal utility. The suggestion has a history, and its history is not encouraging.

This would be enough to frighten one off, were it not for two things. Both in the theory of value and in the theory of money there have been developments in the twenty of thirty years since Wicksell and Mises wrote. And these developments have considerably reduced the barriers that blocked their way.

In the theory of value, the work of Pareto, Wicksteed, and their successors, has broadened and deepened our whole conception of marginal utility. We now realize that the marginal utility analysis is nothing else than a general theory of choice, which is applicable whenever the choice is between alternatives that are capable of quantitative expression. Now money is obviously capable of quantitative expression, and therefore the objection that money has no marginal utility must be wrong. People do choose to have money rather than other things, and therefore, in the relevant sense, money must have a marginal utility.

But merely to call their marginal utility X, and then proceed to draw curves, would not be very helpful. Fortunately the developments in monetary theory to which I alluded come to our rescue.

Mr. Keynes’s Treatise, so far as I have been able to discover, contains at least three theories of money. One of them is the Savings and Investment theory, which . . . seems to me only a quantity theory much glorified. One of them is a Wicksellian natural rate theory. But the third is altogether more interesting. It emerges when Mr. Keynes begins to talk about the price-level of investment goods; when he shows that this price-level depends upon the relative preference of the investor – to hold bank-deposits or to hold securities. Here at last we have something which to a value theorist looks sensible and interesting! Here at last we have a choice at the margin! And Mr. Keynes goes on to put substance into our X, by his doctrine that the relative preference depends upon the “bearishness” or “bullishness” of the public, upon their relative desire for liquidity or profit.

My suggestion may, therefore, be reformulated. It seems to me that this third theory of Mr. Keynes really contains the most important of his theoretical contribution; that here, at last, we have something which, on the analogy (the approximate analogy) of value theory, does begin to offer a chance of making the whole thing easily intelligible; that it si form this point, not from velocity of circulation, or Saving and Investment, that we ought to start in constructing the theory of money. But in saying this I am being more Keynesian than Keynes [note to Blue Aurora this was written in 1934 and published in 1935].

The point of this extended quotation, in case it is not obvious to the reader, is that Hicks is here crediting Keynes in his Treatise on Money with a crucial conceptual advance in formulating a theory of the demand for money consistent with the marginalist theory of value. Hicks himself recognized that Keynes in the General Theory worked out a more comprehensive version of the theory than that which he presented in his essay, even though they were not entirely the same. So there was no excuse for Friedman to present a theory of the demand for money which he described “as part of capital or wealth theory, concerned with the composition of the balance sheet or portfolio of assets,” without crediting Keynes for that theory, just because he rejected the idea of absolute liquidity preference.

Here is how Hicks summed up the relationship in his introductory essay referred to above.

Keynes’s Liquidity theory was so near to mine, and was put over in so much more effective a way than I could hope to achieve, that it seemed pointless, at first, to emphasize differences. Sometimes, indeed, he put his in such a way that there was hardly any difference. But, as time went on, what came to be regarded in many quarters, as Keynesian theory was something much more mechanical than he had probably intended. It was certainly more mechanical than I had intended. So in the end I had ot go back to “Simplifying,” and to insist that its message was a Declaration of Independence, not only from the “free market” school from which I was expressly liberating myself, but also from what came to pass as Keynesian economics.

Second Thoughts on Friedman

Published August 5, 2013 Friedman , Great Depression , Harry Johnson , Keynes , Monetarism 82 Comments
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After blowing off some steam about Milton Friedman in my previous post, thereby antagonizing a sizable segment of my readership, and after realizing that I had been guilty of a couple of memory lapses in citing sources that I was relying on, I thought that I should go back and consult some of the relevant primary sources. So I looked up Friedman’s 1966 article “Interest Rates and the Demand for Money” published in the Journal of Law and Economics in which he denied that he had ever asserted that the demand for money did not depend on the rate of interest and that the empirical magnitude of the elasticity of money demand with respect to the interest rate was not important unless it approached the very high elasticity associated with the Keynesian liquidity trap. I also took a look at Friedman’s reply to Don Patinkin essay “Friedman on the Quantity Theory and Keynesian Economics” in Milton Friedman’s Monetary Framework: A Debate with his Critics.

Perhaps on another occasion, I will offer some comments on Friedman and the interest elasticity of the demand for money, but, for now, I will focus on Friedman’s reply to Patinkin, which is most relevant to my previous post. Patinkin’s essay, entitled, “Friedman on the Quantity Theory and Keynesian Economics,” charged that Friedman had repackaged the Keynesian theory as a quantity theory and tried to sell it with a Chicago oral tradition label stuck on the package. That’s an overstatement of a far more sophisticated argument than my one sentence summary can do justice to, but it captures the polemical gist of Patinkin’s argument, an argument that he had made previously in a paper, “The Chicago Tradition, the Quantity Theory, and Friedman” published in the Journal of Money, Credit and Banking which Harry Johnson relied on in his 1970 Richard T. Ely lecture, “The Keynesian Revolution and the Monetarist Counterrevolution.” Friedman took personal offense at what he regarded as attacks on his scholarly integrity in those papers, and his irritation (to put it mildly) with Patinkin is plainly in evidence in his reply to Patinkin. Much, but not all, of my criticism of Friedman stems from my memory of the two papers by Patinkin and Johnson.

Now to give Friedman his due – and to reiterate what I have already said a number of times, Friedman was a great economist and you can learn a lot by reading his arguments carefully because he was a very skillful applied theorist — he makes a number of effective responses to Patinkin’s accusation that he was merely peddling a disguised version of Keynesianism under the banners of the quantity theory and the Chicago oral tradition. These are basically the same arguments that Scott Sumner used in the post that he wrote defending Friedman against my recycling of the Patinkin/Johnson criticism.

First, like earlier quantity theorists, and unlike Keynes in the General Theory, Friedman assumed that the price level is determined (not, as in the GT, somehow fixed exogenously) by the demand for money and the supply (effectively under the complete discretionary control of the monetary authority) of money.

Second, because differences between the demand for money and the supply of money (in nominal terms) are equilibrated primarily by changes in the price level (not, as in the GT, by changes in the rate of interest), the link between monetary policy and the economy that Friedman focused on was the price level not the rate of interest.

Third, Friedman did not deny that the demand for money was affected by the rate of interest, but he maintained that monetary policy would become ineffective only under conditions of a liquidity trap, which was therefore, in Friedman’s view, the chief theoretical innovation of the General Theory, but one which, on empirical grounds, Friedman flatly rejected.

So if I were to restate Patinkin’s objection in somewhat different terms, I would say that Friedman, in 1956 and in later expositions, described the quantity theory as a theory of the demand for money, which as a historical matter is a travesty, because the quantity theory was around for centuries before the concept of a demand for money was even articulated, but the theory of the demand for money that Friedman described was, in fact, very much influenced by the Keynesian theory of liquidity preference, an influence not mentioned by Friedman in 1956 but acknowledged in later expositions. Friedman explained away this failure by saying that Keynes was merely adding to a theory of the demand for money that had been evolving at Cambridge since Marshall’s day, and that the novel element in the General Theory, absolute liquidity preference, was empirically unsupported. That characterization of Keynes’s theory of liquidity preference strikes me as being ungenerous, but both Friedman and Patinkin neglected to point out that Keynes erroneously thought that his theory of liquidity preference was actually a complete theory of the rate of interest that displaced the real theory of interest.

So, my take on the dispute between Friedman and Patinkin is that Patinkin was right that Friedman did not sufficiently acknowledge the extent to which he was indebted to Keynes for the theory of the demand for money that he erroneously identified with the quantity theory of money. On the other hand, because Friedman explicitly allowed for the price level to be determined within his model, he avoided the Keynesian liquidity-preference relationship between the quantity of money and the rate of interest, allowing the real rate of interest to be determined by real factors not liquidity preference. In some sense, Friedman may have exaggerated the conceptual differences between himself and the Keynesians, but, by making a strategic assumption that the price level responds to changes in the quantity of money, Friedman minimized the effect of changes in the quantity of money on interest rates, except via changes in price level expectations.

But, having granted Friedman partial exoneration of the charge that he was a crypto-Keynesian, I want to explore a bit more carefully Friedman’s remarkable defense against the accusation by Patinkin and Johnson that he invented a non-existent Chicago oral tradition under whose name he could present his quasi-Keynesian theory of the demand for money. Friedman began his response to Patinkin with the following expression of outrage.

Patinkin . . . and Johnson criticize me for linking my work to a “Chicago tradition” rather than recognizing that, as they see it, my work is Keynesian. In the course of their criticism, they give a highly misleading impression of the Chicago tradition. . . .

Whether I conveyed the flavor of that tradition or not, there was such a tradition; it was significantly different from the quantity theory tradition that prevailed at other institutions of learning, notably the London School of Economics; that Chicago tradition had a great deal to do with the differential impact of Keynes’s General Theory on economists at Chicago and elsewhere; and it was responsible for the maintenance of interest in the quantity theory at Chicago. (Friedman’s Monetary Framework p. 158 )

Note the reference to the London School of Economics, as if LSE in the 1930s was in any way notable for its quantity theory tradition. There were to be sure monetary theorists of some distinction working at the LSE in the 1930s, but their relationship to the quantity theory was, at best, remote.

Friedman elaborates on this tidbit a few pages later, recalling that in the late 1940s or early 1950s he once debated Abba Lerner at a seminar at the University of Chicago. Despite agreeing with each other about many issues, Friedman recalled that they were in sharp disagreement about the Keynesian Revolution, Lerner being an avid Keynesian, and Friedman being opposed. The reason for their very different reaction to the Keynesian Revolution, Friedman conjectured, was that Lerner had been trained at the London School of Economics “where the dominant view was that the depression was an inevitable result of the prior boom, that it was deepened by the attempts ot prevent prices and wages from falling and firms from going bankrupt, that the monetary authorities had brought on the depression by inflationary policies before the crash and had prolonged it by ‘easy money’ policies thereafter; that the only sound policy was to let the depression run its course, bring down money costs, and eliminate the weak and unsound firms.” For someone trained in such a view, Friedman suggested, the Keynesian program would seem very attractive. Friedman continued:

It was the London School (really Austrian) view that I referred to in my “Restatement” when I spoke of “the atrophied and rigid caricature [of the quantity theory] that is so frequently described by the proponents of the new income-expenditure approach – and with some justice, to judge by much of the literature on policy that was spawned by the quantity theorists.”

The intellectual climate at Chicago had been wholly different. My teachers regarded the depression as largely the product of misguided government policy – or at least greatly intensified by such policies. They blamed the monetary and fiscal authorities for permitting banks to fail and the quantity of deposits to decline. Far from preaching the need to let deflation and bankruptcy run their course, they issued repeated pronouncements calling for governmental action to stem the deflation. . . .

It was this view the the quantity theory that I referred to in my “Restatement” as “a more subtle and relevant version, one in which the quantity theory was connected and integrated with general price theory and became a flexible and sensitive tool for interpreting movements in aggregate economic activity and for developing relevant policy prescriptions.” (pp. 162-63)

After quoting at length from a talk Jacob Viner gave in 1933 calling for monetary expansion, Friedman winds up with this gem.

What, in the field of interpretation and policy, did Keynes have to offer those of us who learned their economics at a Chicago filled with these views? Can anyone who knows my work read Viner’s comments and not see the direct links between them and Anna Schwartz’s and my Monetary History or between them and the empirical Studies in the Quantity Theory of Money? Indeed, as I have read Viner’s talk for purposes of this paper, I have myself been amazed to discover how precisely it foreshadows the main thesis of our Monetary History for the depression period, and have been embarrassed that we made no reference to it in our account. Can you find any similar link between [Lionel] Robbins’s [of LSE] comments [in his book The Great Depression] and our work? (p. 167)

So what is the evidence that Friedman provides to counter the scandalous accusation by Patinkin and Johnson that Friedman invented a Chicago oral tradition of the quantity theory? (And don’t forget: the quantity theory is a theory of the demand for money) Well, it’s that, at the London School of Economics, there were a bunch of guys who had crazy views about just allowing the Great Depression to run its course, and those guys were quantity theorists, which is why Keynes had to start a revolution to get rid of them all, but at Chicago, they didn’t allow any of those guys to spout their crazy ideas in the first place, so we didn’t need any damn Keynesian revolution.

Good grief! Is there a single word that makes sense? To begin with those detestable guys at LSE were Austrians, as Friedman acknowledges. What he didn’t say, or didn’t know, is that Austrians, either by self-description or by any reasonable definition of the term, are not quantity theorists. So the idea that there was anything special about the Chicago quantity theory as opposed to any other species of the quantity theory is total humbug.

But hold on, it only gets worse. Friedman holds up Jacob Viner as an exemplar of the Chicago quantity theory oral tradition. Jacob Viner was a superb economist, a magnificent scholar, and a legendary teacher for whom I have the utmost admiration, and I am sure that Friedman learned a lot from him at Chicago, But isn’t it strange that Friedman writes: “as I have read Viner’s talk for purposes of this paper, I have myself been amazed to discover how precisely it foreshadows the main thesis of our Monetary History for the depression period, and have been embarrassed that we made no reference to it in our account.” OMG! This is the oral tradition that exerted such a powerful influence on Friedman and his fellow students? Viner explains how to get out of the depression in 1933, and in 1971 Friedman is “amazed to discover” how precisely Viner’s talk foreshadowed the main thesis of his explanation of the Great Depression? That sounds more like a subliminal tradition than an oral tradition.

Responding to Patinkin’s charge that his theory of the demand for money – remember the quantity theory, according to Friedman is a theory of the demand for money — is largely derived from Keynes, Friedman plays a word game.

Is everything in the General Theory Keynesian? Obviously yes, in the trivial sense that the words were set down on paper by John Maynard Keynes. Obviously no, in the more important sense that the term Keynesian has come to refer to a theory of short-term economic change – or a way of analyzing such change – presented in the General Theory and distinctively different from the theory that preceded it. To take a noncontroversial example: in his chapter 20 on “The Employment Function” and elsewhere, Keynes uses the law of diminishing returns to conclude that an increase of employment requires a decline in real-wage rates. Clearly that does not make the “law of diminishing returns” Keynesian or justify describing the “analytical framework” of someone who embodies the law of diminishing returns in his theoretical structure as Keynesian.

In just the same sense, I maintain that Keynes’s discussion of the demand curve for money in the General Theory is for the most part a continuation of earlier quantity theory approaches, improved and refined but not basically modified. As evidence, I shall cite Keynes’s own writings in the Tract on Monetary Reform – long before he became a Keynesian in the present sense. (p. 168)

There are two problems with this line of defense. First, the analogy to the law of diminishing returns would have been appropriate only if Keynes had played a major role in the discovery of the law of diminishing returns just as, on Friedman’s own admission, he played a major role in discovering the theory of liquidity preference. Second, it is, to say the least, debatable to what extent “Keynes’s discussion of the demand curve for money was merely a continuation of earlier quantity theory approaches, improved and refined but not basically modified.” But there is no basis at all for the suggestion that a Chicago oral tradition was the least bit implicated in those earlier quantity theory approaches. So Friedman’s invocation of a Chicago oral tradition was completely fanciful.

This post has gone on too long already. I have more to say about Friedman’s discussion of the relationship between money, price levels, and interest rates. But that will have to wait till next time.

My Milton Friedman Problem

Published August 1, 2013 Cassel , Earl Thompson , Friedman , Great Depression , Hawtrey , Keynes , macroeconomics , Paul Krugman , Scott Sumner , Uncategorized 32 Comments
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In my previous post , I discussed Keynes’s perplexing and problematic criticism of the Fisher equation in chapter 11 of the General Theory, perplexing because it is difficult to understand what Keynes is trying to say in the passage, and problematic because it is not only inconsistent with Keynes’s reasoning in earlier writings in which he essentially reproduced Fisher’s argument, it is also inconsistent with Keynes’s reasoning in chapter 17 of the General Theory in his exposition of own rates of interest and their equilibrium relationship. Scott Sumner honored me with a whole post on his blog which he entitled “Glasner on Keynes and the Fisher Effect,” quite a nice little ego boost.

After paraphrasing some of what I had written in his own terminology, Scott quoted me in responding to a dismissive comment that Krugman recently made about Milton Friedman, of whom Scott tends to be highly protective. Here’s the passage I am referring to.

PPS.  Paul Krugman recently wrote the following:

Just stabilize the money supply, declared Milton Friedman, and we don’t need any of this Keynesian stuff (even though Friedman, when pressured into providing an underlying framework, basically acknowledged that he believed in IS-LM).

Actually Friedman hated IS-LM.  I don’t doubt that one could write down a set of equilibria in the money market and goods market, as a function of interest rates and real output, for almost any model.  But does this sound like a guy who “believed in” the IS-LM model as a useful way of thinking about macro policy?

Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy.

It turns out that IS-LM curves will look very different if one moves away from the interest rate transmission mechanism of the Keynesians.  Again, here’s David:

Before closing, I will just make two side comments. First, my interpretation of Keynes’s take on the Fisher equation is similar to that of Allin Cottrell in his 1994 paper “Keynes and the Keynesians on the Fisher Effect.” Second, I would point out that the Keynesian analysis violates the standard neoclassical assumption that, in a two-factor production function, the factors are complementary, which implies that an increase in employment raises the MEC schedule. The IS curve is not downward-sloping, but upward sloping. This is point, as I have explained previously (here and here), was made a long time ago by Earl Thompson, and it has been made recently by Nick Rowe and Miles Kimball.I hope in a future post to work out in more detail the relationship between the Keynesian and the Fisherian analyses of real and nominal interest rates.

Please do.  Krugman reads Glasner’s blog, and if David keeps posting on this stuff then Krugman will eventually realize that hearing a few wisecracks from older Keynesians about various non-Keynesian traditions doesn’t make one an expert on the history of monetary thought.

I wrote a comment on Scott’s blog responding to this post in which, after thanking him for mentioning me in the same breath as Keynes and Fisher, I observed that I didn’t find Krugman’s characterization of Friedman as someone who basically believed in IS-LM as being in any way implausible.

Then, about Friedman, I don’t think he believed in IS-LM, but it’s not as if he had an alternative macromodel. He didn’t have a macromodel, so he was stuck with something like an IS-LM model by default, as was made painfully clear by his attempt to spell out his framework for monetary analysis in the early 1970s. Basically he just tinkered with the IS-LM to allow the price level to be determined, rather than leaving it undetermined as in the original Hicksian formulation. Of course in his policy analysis and historical work he was not constained by any formal macromodel, so he followed his instincts which were often reliable, but sometimes not so.

So I am afraid that my take may on Friedman may be a little closer to Krugman’s than to yours. But the real point is that IS-LM is just a framework that can be adjusted to suit the purposes of the modeler. For Friedman the important thing was to deny that that there is a liquidity trap, and introduce an explicit money-supply-money-demand relation to determine the absolute price level. It’s not just Krugman who says that, it’s also Don Patinkin and Harry Johnson. Whether Krugman knows the history of thought, I don’t know, but surely Patinkin and Johnson did.

Scott responded:

I’m afraid I strongly disagree regarding Friedman. The IS-LM “model” is much more than just the IS-LM graph, or even an assumption about the interest elasticity of money demand. For instance, suppose a shift in LM also causes IS to shift. Is that still the IS-LM model? If so, then I’d say it should be called the “IS-LM tautology” as literally anything would be possible.

When I read Friedman’s work it comes across as a sort of sustained assault on IS-LM type thinking.

To which I replied:

I think that if you look at Friedman’s responses to his critics the volume Milton Friedman’s Monetary Framework: A Debate with his Critics, he said explicitly that he didn’t think that the main differences among Keynesians and Monetarists were about theory, but about empirical estimates of the relevant elasticities. So I think that in this argument Friedman’s on my side.

And finally Scott:

This would probably be easier if you provided some examples of monetary ideas that are in conflict with IS-LM. Or indeed any ideas that are in conflict with IS-LM. I worry that people are interpreting IS-LM too broadly.

For instance, do Keynesians “believe” in MV=PY? Obviously yes. Do they think it’s useful? No.

Everyone agrees there are a set of points where the money market is in equilibrium. People don’t agree on whether easy money raises interest rates or lowers interest rates. In my view the term “believing in IS-LM” implies a belief that easy money lowers rates, which boosts investment, which boosts RGDP. (At least when not at the zero bound.) Friedman may agree that easy money boosts RGDP, but may not agree on the transmission mechanism.

People used IS-LM to argue against the Friedman and Schwartz view that tight money caused the Depression. They’d say; “How could tight money have caused the Depression? Interest rates fell sharply in 1930?”

I think that Friedman meant that economists agreed on some of the theoretical building blocks of IS-LM, but not on how the entire picture fit together.

Oddly, your critique of Keynes reminds me a lot of Friedman’s critiques of Keynes.

Actually, this was not the first time that I provoked a negative response by writing critically about Friedman. Almost a year and a half ago, I wrote a post (“Was Milton Friedman a Closet Keynesian?”) which drew some critical comments from such reliably supportive commenters as Marcus Nunes, W. Peden, and Luis Arroyo. I guess Scott must have been otherwise occupied, because I didn’t hear a word from him. Here’s what I said:

Commenting on a supremely silly and embarrassingly uninformed (no, Ms. Shlaes, A Monetary History of the United States was not Friedman’s first great work, Essays in Positive Economics, Studies in the Quantity Theory of Money, A Theory of the Consumption Function, A Program for Monetary Stability, and Capitalism and Freedom were all published before A Monetary History of the US was published) column by Amity Shlaes, accusing Ben Bernanke of betraying the teachings of Milton Friedman, teachings that Bernanke had once promised would guide the Fed for ever more, Paul Krugman turned the tables and accused Friedman of having been a crypto-Keynesian.

The truth, although nobody on the right will ever admit it, is that Friedman was basically a Keynesian — or, if you like, a Hicksian. His framework was just IS-LM coupled with an assertion that the LM curve was close enough to vertical — and money demand sufficiently stable — that steady growth in the money supply would do the job of economic stabilization. These were empirical propositions, not basic differences in analysis; and if they turn out to be wrong (as they have), monetarism dissolves back into Keynesianism.

Krugman is being unkind, but he is at least partly right.  In his famous introduction to Studies in the Quantity Theory of Money, which he called “The Quantity Theory of Money:  A Restatement,” Friedman gave the game away when he called the quantity theory of money a theory of the demand for money, an almost shockingly absurd characterization of what anyone had ever thought the quantity theory of money was.  At best one might have said that the quantity theory of money was a non-theory of the demand for money, but Friedman somehow got it into his head that he could get away with repackaging the Cambridge theory of the demand for money — the basis on which Keynes built his theory of liquidity preference — and calling that theory the quantity theory of money, while ascribing it not to Cambridge, but to a largely imaginary oral tradition at the University of Chicago.  Friedman was eventually called on this bit of scholarly legerdemain by his old friend from graduate school at Chicago Don Patinkin, and, subsequently, in an increasingly vitriolic series of essays and lectures by his then Chicago colleague Harry Johnson.  Friedman never repeated his references to the Chicago oral tradition in his later writings about the quantity theory. . . . But the simple fact is that Friedman was never able to set down a monetary or a macroeconomic model that wasn’t grounded in the conventional macroeconomics of his time.

As further evidence of Friedman’s very conventional theoretical conception of monetary theory, I could also cite Friedman’s famous (or, if you prefer, infamous) comment (often mistakenly attributed to Richard Nixon) “we are all Keynesians now” and the not so famous second half of the comment “and none of us are Keynesians anymore.” That was simply Friedman’s way of signaling his basic assent to the neoclassical synthesis which was built on the foundation of Hicksian IS-LM model augmented with a real balance effect and the assumption that prices and wages are sticky in the short run and flexible in the long run. So Friedman meant that we are all Keynesians now in the sense that the IS-LM model derived by Hicks from the General Theory was more or less universally accepted, but that none of us are Keynesians anymore in the sense that this framework was reconciled with the supposed neoclassical principle of the monetary neutrality of a unique full-employment equilibrium that can, in principle, be achieved by market forces, a principle that Keynes claimed to have disproved.

But to be fair, I should also observe that missing from Krugman’s take down of Friedman was any mention that in the original HIcksian IS-LM model, the price level was left undetermined, so that as late as 1970, most Keynesians were still in denial that inflation was a monetary phenomenon, arguing instead that inflation was essentially a cost-push phenomenon determined by the rate of increase in wages. Control of inflation was thus not primarily under the control of the central bank, but required some sort of “incomes policy” (wage-price guidelines, guideposts, controls or what have you) which opened the door for Nixon to cynically outflank his Democratic (Keynesian) opponents by coopting their proposals for price controls when he imposed a wage-price freeze (almost 42 years ago on August 15, 1971) to his everlasting shame and discredit.

Scott asked me to list some monetary ideas that I believe are in conflict with IS-LM. I have done so in my earlier posts (here, here, here and here) on Earl Thompson’s paper “A Reformulation of Macroeconomic Theory” (not that I am totally satisfied with Thompson’s model either, but that’s a topic for another post). Three of the main messages from Thompson’s work are that IS-LM mischaracterizes the monetary sector, because in a modern monetary economy the money supply is endogenous, not exogenous as Keynes and Friedman assumed. Second, the IS curve (or something corresponding to it) is not negatively sloped as Keynesians generally assume, but upward-sloping. I don’t think Friedman ever said a word about an upward-sloping IS curve. Third, the IS-LM model is essentially a one-period model which makes it difficult to carry out a dynamic analysis that incorporates expectations into that framework. Analysis of inflation, expectations, and the distinction between nominal and real interest rates requires a richer model than the HIcksian IS-LM apparatus. But Friedman didn’t scrap IS-LM, he expanded it to accommodate expectations, inflation, and the distinction between real and nominal interest rates.

Scott’s complaint about IS-LM seems to be that it implies that easy money reduces interest rates and that tight money raises rates, but, in reality, it’s the opposite. But I don’t think that you need a macro-model to understand that low inflation implies low interest rates and that high inflation implies high interest rates. There is nothing in IS-LM that contradicts that insight; it just requires augmenting the model with a term for expectations. But there’s nothing in the model that prevents you from seeing the distinction between real and nominal interest rates. Similarly, there is nothing in MV = PY that prevented Friedman from seeing that increasing the quantity of money by 3% a year was not likely to stabilize the economy. If you are committed to a particular result, you can always torture a model in such a way that the desired result can be deduced from it. Friedman did it to MV = PY to get his 3% rule; Keynesians (or some of them) did it to IS-LM to argue that low interest rates always indicate easy money (and it’s not only Keynesians who do that, as Scott knows only too well). So what? Those are examples of the universal tendency to forget that there is an identification problem. I blame the modeler, not the model.

OK, so why am I not a fan of Friedman’s? Here are some reasons. But before I list them, I will state for the record that he was a great economist, and deserved the professional accolades that he received in his long and amazingly productive career. I just don’t think that he was that great a monetary theorist, but his accomplishments far exceeded his contributions to monetary theory. The accomplishments mainly stemmed from his great understanding of price theory, and his skill in applying it to economic problems, and his great skill as a mathematical statistician.

1 His knowledge of the history of monetary theory was very inadequate. He had an inordinately high opinion of Lloyd Mints’s History of Banking Theory which was obsessed with proving that the real bills doctrine was a fallacy, uncritically adopting its pro-currency-school and anti-banking-school bias.

2 He covered up his lack of knowledge of the history of monetary theory by inventing a non-existent Chicago oral tradition and using it as a disguise for his repackaging the Cambridge theory of the demand for money and aspects of the Keynesian theory of liquidity preference as the quantity theory of money, while deliberately obfuscating the role of the interest rate as the opportunity cost of holding money.

3 His theory of international monetary adjustment was a naïve version of the Humean Price-Specie-Flow mechanism, ignoring the tendency of commodity arbitrage to equalize price levels under the gold standard even without gold shipments, thereby misinterpreting the significance of gold shipments under the gold standard.

4 In trying to find a respectable alternative to Keynesian theory, he completely ignored all pre-Keynesian monetary theories other than what he regarded as the discredited Austrian theory, overlooking or suppressing the fact that Hawtrey and Cassel had 40 years before he published the Monetary History of the United States provided (before the fact) a monetary explanation for the Great Depression, which he claimed to have discovered. And in every important respect, Friedman’s explanation was inferior to and retrogression from Hawtrey and Cassel explanation.

5 For example, his theory provided no explanation for the beginning of the downturn in 1929, treating it as if it were simply routine business-cycle downturn, while ignoring the international dimensions, and especially the critical role played by the insane Bank of France.

6 His 3% rule was predicated on the implicit assumption that the demand for money (or velocity of circulation) is highly stable, a proposition for which there was, at best, weak empirical support. Moreover, it was completely at variance with experience during the nineteenth century when the model for his 3% rule — Peel’s Bank Charter Act of 1844 — had to be suspended three times in the next 22 years as a result of financial crises largely induced, as Walter Bagehot explained, by the restriction on creation of banknotes imposed by the Bank Charter Act. However, despite its obvious shortcomings, the 3% rule did serve as an ideological shield with which Friedman could defend his libertarian credentials against criticism for his opposition to the gold standard (so beloved of libertarians) and to free banking (the theory of which Friedman did not comprehend until late in his career).

7 Despite his professed libertarianism, he was an intellectual bully who abused underlings (students and junior professors) who dared to disagree with him, as documented in Perry Mehrling’s biography of Fischer Black, and confirmed to me by others who attended his lectures. Black was made so uncomfortable by Friedman that Black fled Chicago to seek refuge among the Keynesians at MIT.

On a Difficult Passage in the General Theory

Published July 25, 2013 Earl Thompson , expectations , Fisher equation , inflation , Irving Fisher , Keynes , natural rate of interest 32 Comments
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Keynes’s General Theory is not, in my estimation, an easy read. The terminology is often unfamiliar, and, so even after learning one of his definitions, I have trouble remembering what the term means the next time it’s used.. And his prose style, though powerful and very impressive, is not always clear, so you can spend a long time reading and rereading a sentence or a paragraph before you can figure out exactly what he is trying to say. I am not trying to be critical, just to point out that the General Theory is a very challenging book to read, which is one, but not the only, reason why it is subject to a lot of conflicting interpretations. And, as Harry Johnson once pointed out, there is an optimum level of difficulty for a book with revolutionary aspirations. If it’s too simple, it won’t be taken seriously. And if it’s too hard, no one will understand it. Optimally, a revolutionary book should be hard enough so that younger readers will be able to figure it out, and too difficult for the older guys to understand or to make the investment in effort to understand.

In this post, which is, in a certain sense, a follow-up to an earlier post about what, or who, determines the real rate of interest, I want to consider an especially perplexing passage in the General Theory about the Fisher equation. It is perplexing taken in isolation, and it is even more perplexing when compared to other passages in both the General Theory itself and in Keynes’s other writings. Here’s the passage that I am interested in.

The expectation of a fall in the value of money stimulates investment, and hence employment generally, because it raises the schedule of the marginal efficiency of capital, i.e., the investment demand-schedule; and the expectation of a rise in the value of money is depressing, because it lowers the schedule of the marginal efficiency of capital. This is the truth which lies behind Professor Irving Fisher’s theory of what he originally called “Appreciation and Interest” – the distinction between the money rate of interest and the real rate of interest where the latter is equal to the former after correction for changes in the value of money. It is difficult to make sense of this theory as stated, because it is not clear whether the change in the value of money is or is not assumed to be foreseen. There is no escape from the dilemma that, if it is not foreseen, there will be no effect on current affairs; whilst, if it is foreseen, the prices of exiting goods will be forthwith so adjusted that the advantages of holding money and of holding goods are again equalized, and it will be too late for holders of money to gain or to suffer a change in the rate of interest which will offset the prospective change during the period of the loan in the value of the money lent. For the dilemma is not successfully escaped by Professor Pigou’s expedient of supposing that the prospective change in the value of money is foreseen by one set of people but not foreseen by another. (p. 142)

The statement is problematic on just about every level, and one hardly knows where to begin in discussing it. But just for starters, it is amazing that Keynes seems (or, for rhetorical purposes, pretends) to be in doubt whether Fisher is talking about anticipated or unanticipated inflation, because Fisher himself explicitly distinguished between anticipated and unanticipated inflation, and Keynes could hardly have been unaware that Fisher was explicitly speaking about anticipated inflation. So the implication that the Fisher equation involves some confusion on Fisher’s part between anticipated and unanticipated inflation was both unwarranted and unseemly.

What’s even more puzzling is that in his Tract on Monetary Reform, Keynes expounded the covered interest arbitrage principle that the nominal-interest-rate-differential between two currencies corresponds to the difference between the spot and forward rates, which is simply an extension of Fisher’s uncovered interest arbitrage condition (alluded to by Keynes in referring to “Appreciation and Interest”). So when Keynes found Fisher’s distinction between the nominal and real rates of interest to be incoherent, did he really mean to exempt his own covered interest arbitrage condition from the charge?

But it gets worse, because if we flip some pages from chapter 11, where the above quotation is found, to chapter 17, we see on page 224, the following passage in which Keynes extends the idea of a commodity or “own rate of interest” to different currencies.

It may be added that, just as there are differing commodity-rates of interest at any time, so also exchange dealers are familiar with the fact that the rate of interest is not even the same in terms of two different moneys, e.g. sterling and dollars. For here also the difference between the “spot” and “future” contracts for a foreign money in terms of sterling are not, as a rule, the same for different foreign moneys. . . .

If no change is expected in the relative value of two alternative standards, then the marginal efficiency of a capital-asset will be the same in whichever of the two standards it is measured, since the numerator and denominator of the fraction which leads up to the marginal efficiency will be changed in the same proportion. If, however, one of the alternative standards is expected to change in value in terms of the other, the marginal efficiencies of capital-assets will be changed by the same percentage, according to which standard they are measured in. To illustrate this let us take the simplest case where wheat, one of the alternative standards, is expected to appreciate at a steady rate of a percent per annum in terms of money; the marginal efficiency of an asset, which is x percent in terms of money, will then be x – a percent in terms of wheat. Since the marginal efficiencies of all capital assets will be altered by the same amount, it follows that their order of magnitude will be the same irrespective of the standard which is selected.

So Keynes in chapter 17 explicitly allows for the nominal rate of interest to be adjusted to reflect changes in the expected value of the asset (whether a money or a commodity) in terms of which the interest rate is being calculated. Mr. Keynes, please meet Mr. Keynes.

I think that one source of Keynes’s confusion in attacking the Fisher equation was his attempt to force the analysis of a change in inflation expectations, clearly a disequilibrium, into an equilibrium framework. In other words, Keynes is trying to analyze what happens when there has been a change in inflation expectations as if the change had been foreseen. But any change in inflation expectations, by definition, cannot have been foreseen, because to say that an expectation has changed means that the expectation is different from what it was before. Perhaps that is why Keynes tied himself into knots trying to figure out whether Fisher was talking about a change in the value of money that was foreseen or not foreseen. In any equilibrium, the change in the value of money is foreseen, but in the transition from one equilibrium to another, the change is not foreseen. When an unforeseen change occurs in expected inflation, leading to a once-and-for-all change in the value of money relative to other assets, the new equilibrium will be reestablished given the new value of money relative to other assets.

But I think that something else is also going on here, which is that Keynes was implicitly assuming that a change in inflation expectations would alter the real rate of interest. This is a point that Keynes makes in the paragraph following the one I quoted above.

The mistake lies in supposing that it is the rate of interest on which prospective changes in the value of money will directly react, instead of the marginal efficiency of a given stock of capital. The prices of existing assets will always adjust themselves to changes in expectation concerning the prospective value of money. The significance of such changes in expectation lies in their effect on the readiness to produce new assets through their reaction on the marginal efficiency of capital. The stimulating effect of the expectation of higher prices is due, not to its raising the rate of interest (that would be a paradoxical way of stimulating output – insofar as the rate of interest rises, the stimulating effect is to that extent offset) but to its raising the marginal efficiency of a given stock of capital. If the rate of interest were to rise pari passu with the marginal efficiency of capital, there would be no stimulating effect from the expectation of rising prices. For the stimulating effect depends on the marginal efficiency of capital rising relativevly to the rate of interest. Indeed Professor Fisher’s theory could best be rewritten in terms of a “real rate of interest” defined as being the rate of interest which would have to rule, consequently on change in the state of expectation as to the future value of money, in order that this change should have no effect on current output. (pp. 142-43)

Keynes’s mistake lies in supposing that an increase in inflation expectations could not have a stimulating effect except as it raises the marginal efficiency of capital relative to the rate of interest. However, the increase in the value of real assets relative to money will increase the incentive to produce new assets. It is the rise in the value of existing assets relative to money that raises the marginal efficiency of those assets, creating an incentive to produce new assets even if the nominal interest rate were to rise by as much as the rise in expected inflation.

Keynes comes back to this point at the end of chapter 17, making it more forcefully than he did the first time.

In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest – namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of of Wicksell’s “natural rate of interest,” which was, according to him, the rate which would preserve the stability of some, not quite clearly specified, price-level.

I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus, it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. . . .

If there is any such rate of interest, which is unique and significant, it must be the rate which we might term the neutral rate of interest, namely, the natural rate in the above sense which is consistent with full employment, given the other parameters of the system; though this rate might be better described, perhaps, as the optimum rate. (pp. 242-43)

So what Keynes is saying, I think, is this. Consider an economy with a given fixed marginal efficiency of capital (MEC) schedule. There is some interest rate that will induce sufficient investment expenditure to generate enough spending to generate full employment. That interest rate Keynes calls the “neutral” rate of interest. If the nominal rate of interest is more than the neutral rate, the amount of investment will be less than the amount necessary to generate full employment. In such a situation an expectation that the price level will rise will shift up the MEC schedule by the amount of the expected increase in inflation, thereby generating additional investment spending. However, because the MEC schedule is downward-sloping, the upward shift in the MEC schedule that induces increased investment spending will correspond to an increase in the rate of interest that is less than the increase in expected inflation, the upward shift in the MEC schedule being partially offset by the downward movement along the MEC schedule. In other words, the increase in expected inflation raises the nominal rate of interest by less than increase in expected inflation by inducing additional investment that is undertaken only because the real rate of interest has fallen.

However, for an economy already operating at full employment, an increase in expected inflation would not increase employment, so whether there was any effect on the real rate of interest would depend on the extent to which there was a shift from holding money to holding real capital assets in order to avoid the inflation tax.

Before closing, I will just make two side comments. First, my interpretation of Keynes’s take on the Fisher equation is similar to that of Allin Cottrell in his 1994 paper “Keynes and the Keynesians on the Fisher Effect.” Second, I would point out that the Keynesian analysis violates the standard neoclassical assumption that, in a two-factor production function, the factors are complementary, which implies that an increase in employment raises the MEC schedule. The IS curve is not downward-sloping, but upward sloping. This is point, as I have explained previously (here and here), was made a long time ago by Earl Thompson, and it has been made recently by Nick Rowe and Miles Kimball.

I hope in a future post to work out in more detail the relationship between the Keynesian and the Fisherian analyses of real and nominal interest rates.

Hawtrey on the Keynesian Explanation of Unemployment

Published July 11, 2013 Hawtrey , Keynes , Say's Law , W. H. Hutt 14 Comments
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Here is a tidbit I just found the end of R. G. Hawtrey’s long chapter on the General Theory in his volume Capital and Employment, (second edition, 1952) pp. 218-19.

Unemployment in Great Britain seemed at the time [1935 when Keynes finished writing the General Theory] to be chronic: the number of unemployed had never fallen below a million since 1921. Keynes was looking for an explanation of chronic unemployment, but it was hardly plausible to attribute it to the low long-term rate of interest [i.e., to a liquidity trap]. The yield of Government securities had been exceptionally high till the Conversion of 1932.

And in reality there is no school of thought for which the explanation of unemployment presents any difficulty. If wages are too high for full employment, and resist reduction, unemployment is bound to result. Adam Smith held that for a growing population a corresponding growth of capital was essential to maintain wages at or above subsistence level; the penalty for the failure of capital to grow was unemployment as well as starvation. For his successors it was self-evident that the employment afforded by the “wage fund” was inversely proportional to the rate of wages, and, when the theory of the wage fund was superseded by that of the marginal yield of labour, it was no less self-evident that a wage-level held above marginal yield would prevent full employment. Say’s loi des debouches declared that production generated its own demand; but if for any reason production was below capacity and there was unemployment, the demand generated would be no more than sufficient to absorb output at that level.

What I find especially interesting in the passage is Hawtrey’s correct understanding of Say’s Law, so that it constitutes not, as Keynes supposed, an assertion that unemployment is impossible, but an explanation of how aggregate demand is itself just the flip side of aggregate supply. Contractions of supply can be cumulative. It’s not just Keynesians who forget this essential point. RBC theorists and others who model the business cycle as a general-equilibrium phenomenon miss an essential feature of what constitutes the business cycle.

A Newly Revised Version of My Paper (with Ron Batchelder) on Hawtrey and Cassel Is Now Available on SSRN

Published May 7, 2013 Cassel , Friedman , Great Depression , Hawtrey , Hayek , Keynes 6 Comments
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This may not be the most important news of the day, but for those wishing to immerse themselves in the economics of Hawtrey and Cassel, a newly revised version of my paper with Ron Batchelder “Pre-Keynesian Monetary Explanations of the Great Depression: Whatever Happened to Hawtrey and Cassel?” is now available on SSRN.

The paper has also recently been submitted to a journal for review, so we are hoping that it will finally be published before too long. Wish us luck. Here’s the slightly revised abstract.

A strictly monetary theory of the Great Depression is generally thought to have originated with Milton Friedman. Designed to counter the Keynesian notion that the Depression resulted from instabilities inherent in modern capitalist economies, Friedman’s explanation identified the culprit as an ill-conceived monetary policy pursued by an inept Federal Reserve Board. More recent work on the Depression suggests that the causes of the Depression, rooted in the attempt to restore an international gold standard that had been suspended after World War I started, were more international in scope than Friedman believed. We document that current views about the causes of the Depression were anticipated in the 1920s by Ralph Hawtrey and Gustav Cassel who independently warned that restoring the gold standard risked causing a disastrous deflation unless the resulting increase in the international monetary demand for gold could be limited. Although their early warnings of potential disaster were validated, and their policy advice after the Depression started was consistently correct, their contributions were later ignored or forgotten. This paper explores the possible reasons for the remarkable disregard by later economists of the Hawtrey-Cassel monetary explanation of the Great Depression.

About Me

David Glasner
Washington, DC

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

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

Follow me on Twitter @david_glasner

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