Archive for the 'Keynes' Category

Jack Schwartz on the Weaknesses of the Mathematical Mind

I was recently rereading an essay by Karl Popper, “A Realistic View of Logic, Physics, and History” published in his collection of essays, Objective Knowledge: An Evolutionary Approach, because it discusses the role of reductivism in science and philosophy, a topic about which I’ve written a number of previous posts discussing the microfoundations of macroeconomics.

Here is an important passage from Popper’s essay:

What I should wish to assert is (1) that criticism is a most important methodological device: and (2) that if you answer criticism by saying, “I do not like your logic: your logic may be all right for you, but I prefer a different logic, and according to my logic this criticism is not valid”, then you may undermine the method of critical discussion.

Now I should distinguish between two main uses of logic, namely (1) its use in the demonstrative sciences – that is to say, the mathematical sciences – and (2) its use in the empirical sciences.

In the demonstrative sciences logic is used in the main for proofs – for the transmission of truth – while in the empirical sciences it is almost exclusively used critically – for the retransmission of falsity. Of course, applied mathematics comes in too, which implicitly makes use of the proofs of pure mathematics, but the role of mathematics in the empirical sciences is somewhat dubious in several respects. (There exists a wonderful article by Schwartz to this effect.)

The article to which Popper refers appears by Jack Schwartz in a volume edited by Ernst Nagel, Patrick Suppes, and Alfred Tarski, Logic, Methodology and Philosophy of Science. The title of the essay, “The Pernicious Influence of Mathematics on Science” caught my eye, so I tried to track it down. Unavailable on the internet except behind a paywall, I bought a used copy for $6 including postage. The essay was well worth the $6 I paid to read it.

Before quoting from the essay, I would just note that Jacob T. (Jack) Schwartz was far from being innocent of mathematical and scientific knowledge. Here’s a snippet from the Wikipedia entry on Schwartz.

His research interests included the theory of linear operatorsvon Neumann algebrasquantum field theorytime-sharingparallel computingprogramming language design and implementation, robotics, set-theoretic approaches in computational logicproof and program verification systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data.

He authored 18 books and more than 100 papers and technical reports.

He was also the inventor of the Artspeak programming language that historically ran on mainframes and produced graphical output using a single-color graphical plotter.[3]

He served as Chairman of the Computer Science Department (which he founded) at the Courant Institute of Mathematical SciencesNew York University, from 1969 to 1977. He also served as Chairman of the Computer Science Board of the National Research Council and was the former Chairman of the National Science Foundation Advisory Committee for Information, Robotics and Intelligent Systems. From 1986 to 1989, he was the Director of DARPA‘s Information Science and Technology Office (DARPA/ISTO) in Arlington, Virginia.

Here is a link to his obituary.

Though not trained as an economist, Schwartz, an autodidact, wrote two books on economic theory.

With that introduction, I quote from, and comment on, Schwartz’s essay.

Our announced subject today is the role of mathematics in the formulation of physical theories. I wish, however, to make use of the license permitted at philosophical congresses, in two regards: in the first place, to confine myself to the negative aspects of this role, leaving it to others to dwell on the amazing triumphs of the mathematical method; in the second place, to comment not only on physical science but also on social science, in which the characteristic inadequacies which I wish to discuss are more readily apparent.

Computer programmers often make a certain remark about computing machines, which may perhaps be taken as a complaint: that computing machines, with a perfect lack of discrimination, will do any foolish thing they are told to do. The reason for this lies of course in the narrow fixation of the computing machines “intelligence” upon the basely typographical details of its own perceptions – its inability to be guided by any large context. In a psychological description of the computer intelligence, three related adjectives push themselves forward: single-mindedness, literal-mindedness, simple-mindedness. Recognizing this, we should at the same time recognize that this single-mindedness, literal-mindedness, simple-mindedness also characterizes theoretical mathematics, though to a lesser extent.

It is a continual result of the fact that science tries to deal with reality that even the most precise sciences normally work with more or less ill-understood approximations toward which the scientist must maintain an appropriate skepticism. Thus, for instance, it may come as a shock to the mathematician to learn that the Schrodinger equation for the hydrogen atom, which he is able to solve only after a considerable effort of functional analysis and special function theory, is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole, and relativistic effects; that this corrected equation is itself only an ill-understood approximation to an infinite set of quantum field-theoretic equations; and finally that the quantum field theory, besides diverging, neglects a myriad of strange-particle interactions whose strength and form are largely unknown. The physicist looking at the original Schrodinger equation, learns to sense in it the presence of many invisible terms, integral, intergrodifferential, perhaps even more complicated types of operators, in addition to the differential terms visible, and this sense inspires an entirely appropriate disregard for the purely technical features of the equation which he sees. This very healthy self-skepticism is foreign to the mathematical approach. . . .

Schwartz, in other words, is noting that the mathematical equations that physicists use in many contexts cannot be relied upon without qualification as accurate or exact representations of reality. The understanding that the mathematics that physicists and other physical scientists use to express their theories is often inexact or approximate inasmuch as reality is more complicated than our theories can capture mathematically. Part of what goes into the making of a good scientist is a kind of artistic feeling for how to adjust or interpret a mathematical model to take into account what the bare mathematics cannot describe in a manageable way.

The literal-mindedness of mathematics . . . makes it essential, if mathematics is to be appropriately used in science, that the assumptions upon which mathematics is to elaborate be correctly chosen from a larger point of view, invisible to mathematics itself. The single-mindedness of mathematics reinforces this conclusion. Mathematics is able to deal successfully only with the simplest of situations, more precisely, with a complex situation only to the extent that rare good fortune makes this complex situation hinge upon a few dominant simple factors. Beyond the well-traversed path, mathematics loses its bearing in a jungle of unnamed special functions and impenetrable combinatorial particularities. Thus, mathematical technique can only reach far if it starts from a point close to the simple essentials of a problem which has simple essentials. That form of wisdom which is the opposite of single-mindedness, the ability to keep many threads in hand, to draw for an argument from many disparate sources, is quite foreign to mathematics. The inability accounts for much of the difficulty which mathematics experiences in attempting to penetrate the social sciences. We may perhaps attempt a mathematical economics – but how difficult would be a mathematical history! Mathematics adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased. Only with difficulty does it find its way to the scientist’s ready grasp of the relative importance of many factors. Quite typically, science leaps ahead and mathematics plods behind.

Schwartz having referenced mathematical economics, let me try to restate his point more concretely than he did by referring to the Walrasian theory of general equilibrium. “Mathematics,” Schwartz writes, “adjusts only with reluctance to the external, and vitally necessary, approximating of the scientists, and shudders each time a batch of small terms is cavalierly erased.” The Walrasian theory is at once too general and too special to be relied on as an applied theory. It is too general because the functional forms of most of its reliant equations can’t be specified or even meaningfully restricted on very special simplifying assumptions; it is too special, because the simplifying assumptions about the agents and the technologies and the constraints and the price-setting mechanism are at best only approximations and, at worst, are entirely divorced from reality.

Related to this deficiency of mathematics, and perhaps more productive of rueful consequence, is the simple-mindedness of mathematics – its willingness, like that of a computing machine, to elaborate upon any idea, however absurd; to dress scientific brilliancies and scientific absurdities alike in the impressive uniform of formulae and theorems. Unfortunately however, an absurdity in uniform is far more persuasive than an absurdity unclad. The very fact that a theory appears in mathematical form, that, for instance, a theory has provided the occasion for the application of a fixed-point theorem, or of a result about difference equations, somehow makes us more ready to take it seriously. And the mathematical-intellectual effort of applying the theorem fixes in us the particular point of view of the theory with which we deal, making us blind to whatever appears neither as a dependent nor as an independent parameter in its mathematical formulation. The result, perhaps most common in the social sciences, is bad theory with a mathematical passport. The present point is best established by reference to a few horrible examples. . . . I confine myself . . . to the citation of a delightful passage from Keynes’ General Theory, in which the issues before us are discussed with a characteristic wisdom and wit:

“It is the great fault of symbolic pseudomathematical methods of formalizing a system of economic analysis . . . that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep ‘at the back of our heads’ the necessary reserves and qualifications and adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials ‘at the back’ of several pages of algebra which assume they all vanish. Too large a proportion of recent ‘mathematical’ economics are mere concoctions, as imprecise as the initial assumptions they reset on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentions and unhelpful symbols.”

Although it would have been helpful if Keynes had specifically identified the pseudomathematical methods that he had in mind, I am inclined to think that he was expressing his impatience with the Walrasian general-equilibrium approach that was characteristic of the Marshallian tradition that he carried forward even as he struggled to transcend it. Walrasian general equilibrium analysis, he seems to be suggesting, is too far removed from reality to provide any reliable guide to macroeconomic policy-making, because the necessary qualifications required to make general-equilibrium analysis practically relevant are simply unmanageable within the framework of general-equilibrium analysis. A different kind of analysis is required. As a Marshallian he was less skeptical of partial-equilibrium analysis than of general-equilibrium analysis. But he also recognized that partial-equilibrium analysis could not be usefully applied in situations, e.g., analysis of an overall “market” for labor, where the usual ceteris paribus assumptions underlying the use of stable demand and supply curves as analytical tools cannot be maintained. But for some reason that didn’t stop Keynes from trying to explain the nominal rate of interest by positing a demand curve to hold money and a fixed stock of money supplied by a central bank. But we all have our blind spots and miss obvious implications of familiar ideas that we have already encountered and, at least partially, understand.

Schwartz concludes his essay with an arresting thought that should give us pause about how we often uncritically accept probabilistic and statistical propositions as if we actually knew how they matched up with the stochastic phenomena that we are seeking to analyze. But although there is a lot to unpack in his conclusion, I am afraid someone more capable than I will have to do the unpacking.

[M]athematics, concentrating our attention, makes us blind to its own omissions – what I have already called the single-mindedness of mathematics. Typically, mathematics, knows better what to do than why to do it. Probability theory is a famous example. . . . Here also, the mathematical formalism may be hiding as much as it reveals.

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What’s Wrong with DSGE Models Is Not Representative Agency

The basic DSGE macroeconomic model taught to students is based on a representative agent. Many critics of modern macroeconomics and DSGE models have therefore latched on to the representative agent as the key – and disqualifying — feature in DSGE models, and by extension, with modern macroeconomics. Criticism of representative-agent models is certainly appropriate, because, as Alan Kirman admirably explained some 25 years ago, the simplification inherent in a macoreconomic model based on a representative agent, renders the model entirely inappropriate and unsuitable for most of the problems that a macroeconomic model might be expected to address, like explaining why economies might suffer from aggregate fluctuations in output and employment and the price level.

While altogether fitting and proper, criticism of the representative agent model in macroeconomics had an unfortunate unintended consequence, which was to focus attention on representative agency rather than on the deeper problem with DSGE models, problems that cannot be solved by just throwing the Representative Agent under the bus.

Before explaining why representative agency is not the root problem with DSGE models, let’s take a moment or two to talk about where the idea of representative agency comes from. The idea can be traced back to F. Y. Edgeworth who, in his exposition of the ideas of W. S. Jevons – one of the three marginal revolutionaries of the 1870s – introduced two “representative particulars” to illustrate how trade could maximize the utility of each particular subject to the benchmark utility of the counterparty. That analysis of two different representative particulars, reflected in what is now called the Edgeworth Box, remains one of the outstanding achievements and pedagogical tools of economics. (See a superb account of the historical development of the Box and the many contributions to economic theory that it facilitated by Thomas Humphrey). But Edgeworth’s analysis and its derivatives always focused on the incentives of two representative agents rather than a single isolated representative agent.

Only a few years later, Alfred Marshall in his Principles of Economics, offered an analysis of how the equilibrium price for the product of a competitive industry is determined by the demand for (derived from the marginal utility accruing to consumers from increments of the product) and the supply of that product (derived from the cost of production). The concepts of the marginal cost of an individual firm as a function of quantity produced and the supply of an individual firm as a function of price not yet having been formulated, Marshall, in a kind of hand-waving exercise, introduced a hypothetical representative firm as a stand-in for the entire industry.

The completely ad hoc and artificial concept of a representative firm was not well-received by Marshall’s contemporaries, and the young Lionel Robbins, starting his long career at the London School of Economics, subjected the idea to withering criticism in a 1928 article. Even without Robbins’s criticism, the development of the basic theory of a profit-maximizing firm quickly led to the disappearance of Marshall’s concept from subsequent economics textbooks. James Hartley wrote about the short and unhappy life of Marshall’s Representative Firm in the Journal of Economic Perspectives.

One might have thought that the inauspicious career of Marshall’s Representative Firm would have discouraged modern macroeconomists from resurrecting the Representative Firm in the barely disguised form of a Representative Agent in their DSGE models, but the convenience and relative simplicity of solving a DSGE model for a single agent was too enticing to be resisted.

Therein lies the difference between the theory of the firm and a macroeconomic theory. The gain in convenience from adopting the Representative Firm was radically reduced by Marshall’s Cambridge students and successors who, without the representative firm, provided a more rigorous, more satisfying and more flexible exposition of the industry supply curve and the corresponding partial-equilibrium analysis than Marshall had with it. Providing no advantages of realism, logical coherence, analytical versatility or heuristic intuition, the Representative Firm was unceremoniously expelled from the polite company of economists.

However, as a heuristic device for portraying certain properties of an equilibrium state — whose existence is assumed not derived — even a single representative individual or agent proved to be a serviceable device with which to display the defining first-order conditions, the simultaneous equality of marginal rates of substitution in consumption and production with the marginal rate of substitution at market prices. Unlike the Edgeworth Box populated by two representative agents whose different endowments or preference maps result in mutually beneficial trade, the representative agent, even if afforded the opportunity to trade, can find no gain from engaging in it.

An excellent example of this heuristic was provided by Jack Hirshleifer in his 1970 textbook Investment, Interest, and Capital, wherein he adapted the basic Fisherian model of intertemporal consumption, production and exchange opportunities, representing the canonical Fisherian exposition in a single basic diagram. But the representative agent necessarily represents a state of no trade, because, for a single isolated agent, production and consumption must coincide, and the equilibrium price vector must have the property that the representative agent chooses not to trade at that price vector. I reproduce Hirshleifer’s diagram (Figure 4-6) in the attached chart.

Here is how Hirshleifer explained what was going on.

Figure 4-6 illustrates a technique that will be used often from now on: the representative-individual device. If one makes the assumption that all individuals have identical tastes and are identically situated with respect to endowments and productive opportunities, it follows that the individual optimum must be a microcosm of the social equilibrium. In this model the productive and consumptive solutions coincide, as in the Robinson Crusoe case. Nevertheless, market opportunities exist, as indicated by the market line M’M’ through the tangency point P* = C*. But the price reflected in the slope of M’M’ is a sustaining price, such that each individual prefers to hold the combination attained by productive transformations rather than engage in market transactions. The representative-individual device is helpful in suggesting how the equilibrium will respond to changes in exogenous data—the proviso being that such changes od not modify the distribution of wealth among individuals.

While not spelling out the limitations of the representative-individual device, Hirshleifer makes it clear that the representative-agent device is being used as an expository technique to describe, not as an analytical tool to determine, intertemporal equilibrium. The existence of intertemporal equilibrium does not depend on the assumptions necessary to allow a representative individual to serve as a stand-in for all other agents. The representative-individual is portrayed only to provide the student with a special case serving as a visual aid with which to gain an intuitive grasp of the necessary conditions characterizing an intertemporal equilibrium in production and consumption.

But the role of the representative agent in the DSGE model is very different from the representative individual in Hirshleifer’s exposition of the canonical Fisherian theory. In Hirshleifer’s exposition, the representative individual is just a special case and a visual aid with no independent analytical importance. In contrast to Hirshleifer’s deployment of the representative-individual, representative-agent in the DSGE model is used as an assumption whereby an analytical solution to the DSGE model can be derived, allowing the modeler to generate quantitative results to be compared with existing time-series data, to generate forecasts of future economic conditions, and to evaluate the effects of alternative policy rules.

The prominent and dubious role of the representative agent in DSGE models provided a convenient target for critics of DSGE models to direct their criticisms. In Congressional testimony, Robert Solow famously attacked DSGE models and used their reliance on the representative-agents to make them seem, well, simply ridiculous.

Most economists are willing to believe that most individual “agents” – consumers investors, borrowers, lenders, workers, employers – make their decisions so as to do the best that they can for themselves, given their possibilities and their information. Clearly they do not always behave in this rational way, and systematic deviations are well worth studying. But this is not a bad first approximation in many cases. The DSGE school populates its simplified economy – remember that all economics is about simplified economies just as biology is about simplified cells – with exactly one single combination worker-owner-consumer-everything-else who plans ahead carefully and lives forever. One important consequence of this “representative agent” assumption is that there are no conflicts of interest, no incompatible expectations, no deceptions.

This all-purpose decision-maker essentially runs the economy according to its own preferences. Not directly, of course: the economy has to operate through generally well-behaved markets and prices. Under pressure from skeptics and from the need to deal with actual data, DSGE modellers have worked hard to allow for various market frictions and imperfections like rigid prices and wages, asymmetries of information, time lags, and so on. This is all to the good. But the basic story always treats the whole economy as if it were like a person, trying consciously and rationally to do the best it can on behalf of the representative agent, given its circumstances. This cannot be an adequate description of a national economy, which is pretty conspicuously not pursuing a consistent goal. A thoughtful person, faced with the thought that economic policy was being pursued on this basis, might reasonably wonder what planet he or she is on.

An obvious example is that the DSGE story has no real room for unemployment of the kind we see most of the time, and especially now: unemployment that is pure waste. There are competent workers, willing to work at the prevailing wage or even a bit less, but the potential job is stymied by a market failure. The economy is unable to organize a win-win situation that is apparently there for the taking. This sort of outcome is incompatible with the notion that the economy is in rational pursuit of an intelligible goal. The only way that DSGE and related models can cope with unemployment is to make it somehow voluntary, a choice of current leisure or a desire to retain some kind of flexibility for the future or something like that. But this is exactly the sort of explanation that does not pass the smell test.

While Solow’s criticism of the representative agent was correct, he left himself open to an effective rejoinder by defenders of DSGE models who could point out that the representative agent was adopted by DSGE modelers not because it was an essential feature of the DSGE model but because it enabled DSGE modelers to simplify the task of analytically solving for an equilibrium solution. With enough time and computing power, however, DSGE modelers were able to write down models with a few heterogeneous agents (themselves representative of particular kinds of agents in the model) and then crank out an equilibrium solution for those models.

Unfortunately for Solow, V. V. Chari also testified at the same hearing, and he responded directly to Solow, denying that DSGE models necessarily entail the assumption of a representative agent and identifying numerous examples even in 2010 of DSGE models with heterogeneous agents.

What progress have we made in modern macro? State of the art models in, say, 1982, had a representative agent, no role for unemployment, no role for Financial factors, no sticky prices or sticky wages, no role for crises and no role for government. What do modern macroeconomic models look like? The models have all kinds of heterogeneity in behavior and decisions. This heterogeneity arises because people’s objectives dier, they differ by age, by information, by the history of their past experiences. Please look at the seminal work by Rao Aiyagari, Per Krusell and Tony Smith, Tim Kehoe and David Levine, Victor Rios Rull, Nobu Kiyotaki and John Moore. All of them . . . prominent macroeconomists at leading departments . . . much of their work is explicitly about models without representative agents. Any claim that modern macro is dominated by representative-agent models is wrong.

So on the narrow question of whether DSGE models are necessarily members of the representative-agent family, Solow was debunked by Chari. But debunking the claim that DSGE models must be representative-agent models doesn’t mean that DSGE models have the basic property that some of us at least seek in a macro-model: the capacity to explain how and why an economy may deviate from a potential full-employment time path.

Chari actually addressed the charge that DSGE models cannot explain lapses from full employment (to use Pigou’s rather anodyne terminology for depressions). Here is Chari’s response:

In terms of unemployment, the baseline model used in the analysis of labor markets in modern macroeconomics is the Mortensen-Pissarides model. The main point of this model is to focus on the dynamics of unemployment. It is specifically a model in which labor markets are beset with frictions.

Chari’s response was thus to treat lapses from full employment as “frictions.” To treat unemployment as the result of one or more frictions is to take a very narrow view of the potential causes of unemployment. The argument that Keynes made in the General Theory was that unemployment is a systemic failure of a market economy, which lacks an error-correction mechanism that is capable of returning the economy to a full-employment state, at least not within a reasonable period of time.

The basic approach of DSGE is to treat the solution of the model as an optimal solution of a problem. In the representative-agent version of a DSGE model, the optimal solution is optimal solution for a single agent, so optimality is already baked into the model. With heterogeneous agents, the solution of the model is a set of mutually consistent optimal plans, and optimality is baked into that heterogenous-agent DSGE model as well. Sophisticated heterogeneous-agent models can incorporate various frictions and constraints that cause the solution to deviate from a hypothetical frictionless, unconstrained first-best optimum.

The policy message emerging from this modeling approach is that unemployment is attributable to frictions and other distortions that don’t permit a first-best optimum that would be achieved automatically in their absence from being reached. The possibility that the optimal plans of individuals might be incompatible resulting in a systemic breakdown — that there could be a failure to coordinate — does not even come up for discussion.

One needn’t accept Keynes’s own theoretical explanation of unemployment to find the attribution of cyclical unemployment to frictions deeply problematic. But, as I have asserted in many previous posts (e.g., here and here) a modeling approach that excludes a priori any systemic explanation of cyclical unemployment, attributing instead all cyclical unemployment to frictions or inefficient constraints on market pricing, cannot be regarded as anything but an exercise in question begging.

 

My Paper “Hawtrey and Keynes” Is Now Available on SSRN

About five or six years ago, I was invited by Robert Dimand and Harald Hagemann to contribute an article on Hawtrey for The Elgar Companion to John Maynard Keynes, which they edited. I have now posted an early (2014) version of my article on SSRN.

Here is the abstract of my article on Hawtrey and Keynes

R. G. Hawtrey, like his younger contemporary J. M. Keynes, was a Cambridge graduate in mathematics, an Apostle, deeply influenced by the Cambridge philosopher G. E. Moore, attached, if only peripherally, to the Bloomsbury group, and largely an autodidact in economics. Both entered the British Civil Service shortly after graduation, publishing their first books on economics in 1913. Though eventually overshadowed by Keynes, Hawtrey, after publishing Currency and Credit in 1919, was in the front rank of monetary economists in the world and a major figure at the 1922 Genoa International Monetary Conference planning for a restoration of the international gold standard. This essay explores their relationship during the 1920s and 1930s, focusing on their interactions concerning the plans for restoring an international gold standard immediately after World War I, the 1925 decision to restore the convertibility of sterling at the prewar dollar parity, Hawtrey’s articulation of what became known as the Treasury view, Hawtrey’s commentary on Keynes’s Treatise on Money, including his exposition of the multiplier, Keynes’s questioning of Hawtrey after his testimony before the Macmillan Committee, their differences over the relative importance of the short-term and long-term rates of interest as instruments of monetary policy, Hawtrey’s disagreement with Keynes about the causes of the Great Depression, and finally the correspondence between Keynes and Hawtrey while Keynes was writing the General Theory, a correspondence that failed to resolve theoretical differences culminating in Hawtrey’s critical review of the General Theory and their 1937 exchange in the Economic Journal.

Irving Fisher Demolishes the Loanable-Funds Theory of Interest

In some recent posts (here, here and here) I have discussed the inappropriate application of partial-equilibrium analysis (aka supply-demand analysis) when the conditions under which the ceteris paribus assumption underlying partial-equilibrium analysis are not satisfied. The two examples of inappropriate application of partial equilibrium analysis I have mentioned were: 1) drawing a supply curve of labor and demand curve for labor to explain aggregate unemployment in the economy, and 2) drawing a supply curve of loanable funds and a demand curve for loanable funds to explain the rate of interest. In neither case can one assume that a change in the wage of labor or in the rate of interest can occur without at the same time causing the demand curve and the supply curve to shift from their original position to a new one. Because of the feedback effects from a change in the wage or a change in the rate of interest inevitably cause the demand and supply curves to shift, the standard supply-and-demand analysis breaks down in the face of such feedback effects.

I pointed out that while Keynes correctly observed that demand-and-supply analysis of the labor market was inappropriate, it is puzzling that it did not occur to him that demand-and-supply analysis could not be used to explain the rate of interest.

Keynes explained the rate of interest as a measure of the liquidity premium commanded by holders of money for parting with liquidity when lending money to a borrower. That view is sometimes contrasted with Fisher’s explanation of the rate interest as a measure of the productivity of capital in shifting output from the present to the future and the time preference of individuals for consuming in the present rather waiting to consume in the future. Sometimes the Fisherian theory of the rate of interest is juxtaposed with the Keynesian theory by contrasting the liquidity preference theory with a loanable-funds theory. But that contrast between liquidity preference and loanable funds misrepresents Fisher’s view, because a loanable funds theory is also an inappropriate misapplication of partial-equilibrium analysis when general-equilibrium anlaysis is required.

I recently came upon a passage from Fisher’s classic 1907 treatise, The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena, which explicitly rejects supply-demand analysis of the market for loanable funds as a useful way of explaining the rate of interest. Here is how Fisher made that fundamental point.

If a modern business man is asked what determines the rate of interest, he may usually be expected to answer, “the supply and demand of loanable money.” But “supply and demand” is a phrase which has been too often into service to cover up difficult problems. Even economists have been prone to employ it to describe economic causation which they could not unravel. It was once wittily remarked of the early writers on economic problems, “Catch a parrot and teach him to say ‘supply and demand,’ and you have an excellent economist.” Prices, wages, rent, interest, and profits were thought to be fully “explained” by this glib phrase. It is true that every ratio of exchange is due to the resultant of causes operating on the buyer and seller, and we may classify these as “demand” and supply.” But this fact does not relieve us of the necessity of examining specifically the two sets of causes, including utility in its effect on demand, and cost in its effect on supply. Consequently, when we say that the rate of interest is due to the supply and demand of “capital” or of “money” or of “loans,” we are very far from having an adequate explanation. It is true that when merchants seek to discount bills at a bank in large numbers and for large amounts, the rate of interest will tend to be low. But we must inquire for what purposes and from what causes merchants thus apply to a bank for the discount of loans and others supply the bank with the funds to be loaned. The real problem is: What causes make the demand for loans and what causes make the supply? This question is not answered by the summary “supply and demand” theory. The explanation is not simply that those who have little capital demand them. In fact, the contrary is often the case. The depositors in savings banks are the lenders, and they are usually poor, whereas those to whom the savings bank in turn lends the funds are relatively rich. (pp. 6-7)

Phillips Curve Musings: Second Addendum on Keynes and the Rate of Interest

In my two previous posts (here and here), I have argued that the partial-equilibrium analysis of a single market, like the labor market, is inappropriate and not particularly relevant, in situations in which the market under analysis is large relative to other markets, and likely to have repercussions on those markets, which, in turn, will have further repercussions on the market under analysis, violating the standard ceteris paribus condition applicable to partial-equilibrium analysis. When the standard ceteris paribus condition of partial equilibrium is violated, as it surely is in analyzing the overall labor market, the analysis is, at least, suspect, or, more likely, useless and misleading.

I suggested that Keynes in chapter 19 of the General Theory was aiming at something like this sort of argument, and I think he was largely right in his argument. But, in all modesty, I think that Keynes would have done better to have couched his argument in terms of the distinction between partial-equilibrium and general-equilibrium analysis. But his Marshallian training, which he simultaneously embraced and rejected, may have made it difficult for him to adopt the Walrasian general-equilibrium approach that Marshall and the Marshallians regarded as overly abstract and unrealistic.

In my next post, I suggested that the standard argument about the tendency of public-sector budget deficits to raise interest rates by competing with private-sector borrowers for loanable funds is fundamentally misguided, because it, too, inappropriately applies the partial-equilibrium analysis of a narrow market for government securities, or even a more broadly defined market for loanable funds in general.

That is a gross mistake, because the rate of interest is determined in a general-equilibrium system along with markets for all long-lived assets, embodying expected flows of income that must be discounted to the present to determine an estimated present value. Some assets are riskier than others and that risk is reflected in those valuations. But the rate of interest is distilled from the combination of all of those valuations, not prior to, or apart from, those valuations. Interest rates of different duration and different risk are embeded in the entire structure of current and expected prices for all long-lived assets. To focus solely on a very narrow subset of markets for newly issued securities, whose combined value is only a small fraction of the total value of all existing long-lived assets, is to miss the forest for the trees.

What I want to point out in this post is that Keynes, whom I credit for having recognized that partial-equilibrium analysis is inappropriate and misleading when applied to an overall market for labor, committed exactly the same mistake that he condemned in the context of the labor market, by asserting that the rate of interest is determined in a single market: the market for money. According to Keynes, the market rate of interest is that rate which equates the stock of money in existence with the amount of money demanded by the public. The higher the rate of interest, Keynes argued, the less money the public wants to hold.

Keynes, applying the analysis of Marshall and his other Cambridge predecessors, provided a wonderful analysis of the factors influencing the amount of money that people want to hold (usually expressed in terms of a fraction of their income). However, as superb as his analysis of the demand for money was, it was a partial-equilibrium analysis, and there was no recognition on his part that other markets in the economy are influenced by, and exert influence upon, the rate of interest.

What makes Keynes’s partial-equilibrium analysis of the interest rate so difficult to understand is that in chapter 17 of the General Theory, a magnificent tour de force of verbal general-equilibrium theorizing, explained the relationships that must exist between the expected returns for alternative long-lived assets that are held in equilibrium. Yet, disregarding his own analysis of the equilibrium relationship between returns on alternative assets, Keynes insisted on explaining the rate of interest in a one-period model (a model roughly corresponding to IS-LM) with only two alternative assets: money and bonds, but no real capital asset.

A general-equilibrium analysis of the rate of interest ought to have at least two periods, and it ought to have a real capital good that may be held in the present for use or consumption in the future, a possibility entirely missing from the Keynesian model. I have discussed this major gap in the Keynesian model in a series of posts (here, here, here, here, and here) about Earl Thompson’s 1976 paper “A Reformulation of Macroeconomic Theory.”

Although Thompson’s model seems to me too simple to account for many macroeconomic phenomena, it would have been a far better starting point for the development of macroeconomics than any of the models from which modern macroeconomic theory has evolved.

Phillips Curve Musings

There’s a lot of talk about the Phillips Curve these days; people wonder why, with the unemployment rate reaching historically low levels, nominal and real wages have increased minimally with inflation remaining securely between 1.5 and 2%. The Phillips Curve, for those untutored in basic macroeconomics, depicts a relationship between inflation and unemployment. The original empirical Philips Curve relationship showed that high rates of unemployment were associated with low or negative rates of wage inflation while low rates of unemployment were associated with high rates of wage inflation. This empirical relationship suggested a causal theory that the rate of wage increase tends to rise when unemployment is low and tends to fall when unemployment is high, a causal theory that seems to follow from a simple supply-demand model in which wages rise when there is an excess demand for labor (unemployment is low) and wages fall when there is an excess supply of labor (unemployment is high).

Viewed in this light, low unemployment, signifying a tight labor market, signals that inflation is likely to rise, providing a rationale for monetary policy to be tightened to prevent inflation from rising at it normally does when unemployment is low. Seeming to accept that rationale, the Fed has gradually raised interest rates for the past two years or so. But the increase in interest rates has now slowed the expansion of employment and decline in unemployment to historic lows. Nor has the improving employment situation resulted in any increase in price inflation and at most a minimal increase in the rate of increase in wages.

In a couple of previous posts about sticky wages (here and here), I’ve questioned whether the simple supply-demand model of the labor market motivating the standard interpretation of the Phillips Curve is a useful way to think about wage adjustment and inflation-employment dynamics. I’ve offered a few reasons why the supply-demand model, though applicable in some situations, is not useful for understanding how wages adjust.

The particular reason that I want to focus on here is Keynes’s argument in chapter 19 of the General Theory (though I express it in terms different from his) that supply-demand analysis can’t explain how wages and employment are determined. The upshot of his argument I believe is that supply demand-analysis only works in a partial-equilibrium setting in which feedback effects from the price changes in the market under consideration don’t affect equilibrium prices in other markets, so that the position of the supply and demand curves in the market of interest can be assumed stable even as price and quantity in that market adjust from one equilibrium to another (the comparative-statics method).

Because the labor market, affecting almost every other market, is not a small part of the economy, partial-equilibrium analysis is unsuitable for understanding that market, the normal stability assumption being untenable if we attempt to trace the adjustment from one labor-market equilibrium to another after an exogenous disturbance. In the supply-demand paradigm, unemployment is a measure of the disequilibrium in the labor market, a disequilibrium that could – at least in principle — be eliminated by a wage reduction sufficient to equate the quantity of labor services supplied with the amount demanded. Viewed from this supply-demand perspective, the failure of the wage to fall to a supposed equilibrium level is attributable to some sort of endogenous stickiness or some external impediment (minimum wage legislation or union intransigence) in wage adjustment that prevents the normal equilibrating free-market adjustment mechanism. But the habitual resort to supply-demand analysis by economists, reinforced and rewarded by years of training and professionalization, is actually misleading when applied in an inappropriate context.

So Keynes was right to challenge this view of a potentially equilibrating market mechanism that is somehow stymied from behaving in the manner described in the textbook version of supply-demand analysis. Instead, Keynes argued that the level of employment is determined by the level of spending and income at an exogenously given wage level, an approach that seems to be deeply at odds with idea that price adjustments are an essential part of the process whereby a complex economic system arrives at, or at least tends to move toward, an equilibrium.

One of the main motivations for a search for microfoundations in the decades after the General Theory was published was to be able to articulate a convincing microeconomic rationale for persistent unemployment that was not eliminated by the usual tendency of market prices to adjust to eliminate excess supplies of any commodity or service. But Keynes was right to question whether there is any automatic market mechanism that adjusts nominal or real wages in a manner even remotely analogous to the adjustment of prices in organized commodity or stock exchanges – the sort of markets that serve as exemplars of automatic price adjustments in response to excess demands or supplies.

Keynes was also correct to argue that, even if there was a mechanism causing automatic wage adjustments in response to unemployment, the labor market, accounting for roughly 60 percent of total income, is so large that any change in wages necessarily affects all other markets, causing system-wide repercussions that might well offset any employment-increasing tendency of the prior wage adjustment.

But what I want to suggest in this post is that Keynes’s criticism of the supply-demand paradigm is relevant to any general-equilibrium system in the following sense: if a general-equilibrium system is considered from an initial non-equilibrium position, does the system have any tendency to move toward equilibrium? And to make the analysis relatively tractable, assume that the system is such that a unique equilibrium exists. Before proceeding, I also want to note that I am not arguing that traditional supply-demand analysis is necessarily flawed; I am just emphasizing that traditional supply-demand analysis is predicated on a macroeconomic foundation: that all markets but the one under consideration are in, or are in the neighborhood of, equilibrium. It is only because the system as a whole is in the neighborhood of equilibrium, that the microeconomic forces on which traditional supply-demand analysis relies appear to be so powerful and so stabilizing.

However, if our focus is a general-equilibrium system, microeconomic supply-demand analysis of a single market in isolation provides no basis on which to argue that the system as a whole has a self-correcting tendency toward equilibrium. To make such an argument is to commit a fallacy of composition. The tendency of any single market toward equilibrium is premised on an assumption that all markets but the one under analysis are already at, or in the neighborhood of, equilibrium. But when the system as a whole is in a disequilibrium state, the method of partial equilibrium analysis is misplaced; partial-equilibrium analysis provides no ground – no micro-foundation — for an argument that the adjustment of market prices in response to excess demands and excess supplies will ever – much less rapidly — guide the entire system back to an equilibrium state.

The lack of automatic market forces that return a system not in the neighborhood — for purposes of this discussion “neighborhood” is left undefined – of equilibrium back to equilibrium is implied by the Sonnenschein-Mantel-Debreu Theorem, which shows that, even if a unique general equilibrium exists, there may be no rule or algorithm for increasing (decreasing) prices in markets with excess demands (supplies) by which the general-equilibrium price vector would be discovered in a finite number of steps.

The theorem holds even under a Walrasian tatonnement mechanism in which no trading at disequilibrium prices is allowed. The reason is that the interactions between individual markets may be so complicated that a price-adjustment rule will not eliminate all excess demands, because even if a price adjustment reduces excess demand in one market, that price adjustment may cause offsetting disturbances in one or more other markets. So, unless the equilibrium price vector is somehow hit upon by accident, no rule or algorithm for price adjustment based on the excess demand in each market will necessarily lead to discovery of the equilibrium price vector.

The Sonnenschein Mantel Debreu Theorem reinforces the insight of Kenneth Arrow in an important 1959 paper “Toward a Theory of Price Adjustment,” which posed the question: how does the theory of perfect competition account for the determination of the equilibrium price at which all agents can buy or sell as much as they want to at the equilibrium (“market-clearing”) price? As Arrow observed, “there exists a logical gap in the usual formulations of the theory of perfectly competitive economy, namely, that there is no place for a rational decision with respect to prices as there is with respect to quantities.”

Prices in perfect competition are taken as parameters by all agents in the model, and optimization by agents consists in choosing optimal quantities. The equilibrium solution allows the mutually consistent optimization by all agents at the equilibrium price vector. This is true for the general-equilibrium system as a whole, and for partial equilibrium in every market. Not only is there no positive theory of price adjustment within the competitive general-equilibrium model, as pointed out by Arrow, but the Sonnenschein-Mantel-Debreu Theorem shows that there’s no guarantee that even the notional tatonnement method of price adjustment can ensure that a unique equilibrium price vector will be discovered.

While acknowledging his inability to fill the gap, Arrow suggested that, because perfect competition and price taking are properties of general equilibrium, there are inevitably pockets of market power, in non-equilibrium states, so that some transactors in non-equilibrium states, are price searchers rather than price takers who therefore choose both an optimal quantity and an optimal price. I have no problem with Arrow’s insight as far as it goes, but it still doesn’t really solve his problem, because he couldn’t explain, even intuitively, how a disequilibrium system with some agents possessing market power (either as sellers or buyers) transitions into an equilibrium system in which all agents are price-takers who can execute their planned optimal purchases and sales at the parametric prices.

One of the few helpful, but, as far as I can tell, totally overlooked, contributions of the rational-expectations revolution was to solve (in a very narrow sense) the problem that Arrow identified and puzzled over, although Hayek, Lindahl and Myrdal, in their original independent formulations of the concept of intertemporal equilibrium, had already provided the key to the solution. Hayek, Lindahl, and Myrdal showed that an intertemporal equilibrium is possible only insofar as agents form expectations of future prices that are so similar to each other that, if future prices turn out as expected, the agents would be able to execute their planned sales and purchases as expected.

But if agents have different expectations about the future price(s) of some commodity(ies), and if their plans for future purchases and sales are conditioned on those expectations, then when the expectations of at least some agents are inevitably disappointed, those agents will necessarily have to abandon (or revise) the plans that their previously formulated plans.

What led to Arrow’s confusion about how equilibrium prices are arrived at was the habit of thinking that market prices are determined by way of a Walrasian tatonnement process (supposedly mimicking the haggling over price by traders). So the notion that a mythical market auctioneer, who first calls out prices at random (prix cries au hasard), and then, based on the tallied market excess demands and supplies, adjusts those prices until all markets “clear,” is untenable, because continual trading at disequilibrium prices keeps changing the solution of the general-equilibrium system. An actual system with trading at non-equilibrium prices may therefore be moving away from, rather converging on, an equilibrium state.

Here is where the rational-expectations hypothesis comes in. The rational-expectations assumption posits that revisions of previously formulated plans are never necessary, because all agents actually do correctly anticipate the equilibrium price vector in advance. That is indeed a remarkable assumption to make; it is an assumption that all agents in the model have the capacity to anticipate, insofar as their future plans to buy and sell require them to anticipate, the equilibrium prices that will prevail for the products and services that they plan to purchase or sell. Of course, in a general-equilibrium system, all prices being determined simultaneously, the equilibrium prices for some future prices cannot generally be forecast in isolation from the equilibrium prices for all other products. So, in effect, the rational-expectations hypothesis supposes that each agent in the model is an omniscient central planner able to solve an entire general-equilibrium system for all future prices!

But let us not be overly nitpicky about details. So forget about false trading, and forget about the Sonnenschein-Mantel-Debreu theorem. Instead, just assume that, at time t, agents form rational expectations of the future equilibrium price vector in period (t+1). If agents at time t form rational expectations of the equilibrium price vector in period (t+1), then they may well assume that the equilibrium price vector in period t is equal to the expected price vector in period (t+1).

Now, the expected price vector in period (t+1) may or may not be an equilibrium price vector in period t. If it is an equilibrium price vector in period t as well as in period (t+1), then all is right with the world, and everyone will succeed in buying and selling as much of each commodity as he or she desires. If not, prices may or may not adjust in response to that disequilibrium, and expectations may or may not change accordingly.

Thus, instead of positing a mythical auctioneer in a contrived tatonnement process as the mechanism whereby prices are determined for currently executed transactions, the rational-expectations hypothesis posits expected future prices as the basis for the prices at which current transactions are executed, providing a straightforward solution to Arrow’s problem. The prices at which agents are willing to purchase or sell correspond to their expectations of prices in the future. If they find trading partners with similar expectations of future prices, they will reach agreement and execute transactions at those prices. If they don’t find traders with similar expectations, they will either be unable to transact, or will revise their price expectations, or they will assume that current market conditions are abnormal and then decide whether to transact at prices different from those they had expected.

When current prices are more favorable than expected, agents will want to buy or sell more than they would have if current prices were equal to their expectations for the future. If current prices are less favorable than they expect future prices to be, they will not transact at all or will seek to buy or sell less than they would have bought or sold if current prices had equaled expected future prices. The dichotomy between observed current prices, dictated by current demands and supplies, and expected future prices is unrealistic; all current transactions are made with an eye to expected future prices and to their opportunities to postpone current transactions until the future, or to advance future transactions into the present.

If current prices for similar commodities are not uniform in all current transactions, a circumstance that Arrow attributes to the existence of varying degrees of market power across imperfectly competitive suppliers, price dispersion may actually be caused, not by market power, but by dispersion in the expectations of future prices held by agents. Sellers expecting future prices to rise will be less willing to sell at relatively low prices now than are suppliers with pessimistic expectations about future prices. Equilibrium occurs when all transactors share the same expectations of future prices and expected future prices correspond to equilibrium prices in the current period.

Of course, that isn’t the only possible equilibrium situation. There may be situations in which a future event that will change a subset of prices can be anticipated. If the anticipation of the future event affects not only expected future prices, it must also and necessarily affect current prices insofar as current supplies can be carried into the future from the present or current purchases can be postponed until the future or future consumption shifted into the present.

The practical upshot of these somewhat disjointed reflections is, I think,primarily to reinforce skepticism that the traditional Phillips Curve supposition that low and falling unemployment necessarily presages an increase in inflation. Wages are not primarily governed by the current state of the labor market, whatever the labor market might even mean in macroeconomic context.

Expectations rule! And the rational-expectations revolution to the contrary notwithstanding, we have no good theory of how expectations are actually formed and there is certainly no reason to assume that, as a general matter, all agents share the same set of expectations.

The current fairly benign state of the economy reflects the absence of any serious disappointment of price expectations. If an economy is operating not very far from an equilibrium, although expectations are not the same, they likely are not very different. They will only be very different after the unexpected strikes. When that happens, borrowers and traders who had taken positions based on overly optimistic expectations find themselves unable to meet their obligations. It is only then that we will see whether the economy is really as strong and resilient as it now seems.

Expecting the unexpected is hard to do, but you can be sure that, sooner or later, the unexpected is going to happen.

More on Sticky Wages

It’s been over four and a half years since I wrote my second most popular post on this blog (“Why are Wages Sticky?”). Although the post was linked to and discussed by Paul Krugman (which is almost always a guarantee of getting a lot of traffic) and by other econoblogosphere standbys like Mark Thoma and Barry Ritholz, unlike most of my other popular posts, it has continued ever since to attract a steady stream of readers. It’s the posts that keep attracting readers long after their original expiration date that I am generally most proud of.

I made a few preliminary points about wage stickiness before getting to my point. First, although Keynes is often supposed to have used sticky wages as the basis for his claim that market forces, unaided by stimulus to aggregate demand, cannot automatically eliminate cyclical unemployment within the short or even medium term, he actually devoted a lot of effort and space in the General Theory to arguing that nominal wage reductions would not increase employment, and to criticizing economists who blamed unemployment on nominal wages fixed by collective bargaining at levels too high to allow all workers to be employed. So, the idea that wage stickiness is a Keynesian explanation for unemployment doesn’t seem to me to be historically accurate.

I also discussed the search theories of unemployment that in some ways have improved our understanding of why some level of unemployment is a normal phenomenon even when people are able to find jobs fairly easily and why search and unemployment can actually be productive, enabling workers and employers to improve the matches between the skills and aptitudes that workers have and the skills and aptitudes that employers are looking for. But search theories also have trouble accounting for some basic facts about unemployment.

First, a lot of job search takes place when workers have jobs while search theories assume that workers can’t or don’t search while they are employed. Second, when unemployment rises in recessions, it’s not because workers mistakenly expect more favorable wage offers than employers are offering and mistakenly turn down job offers that they later regret not having accepted, which is a very skewed way of interpreting what happens in recessions; it’s because workers are laid off by employers who are cutting back output and idling production lines.

I then suggested the following alternative explanation for wage stickiness:

Consider the incentive to cut price of a firm that can’t sell as much as it wants [to sell] at the current price. The firm is off its supply curve. The firm is a price taker in the sense that, if it charges a higher price than its competitors, it won’t sell anything, losing all its sales to competitors. Would the firm have any incentive to cut its price? Presumably, yes. But let’s think about that incentive. Suppose the firm has a maximum output capacity of one unit, and can produce either zero or one units in any time period. Suppose that demand has gone down, so that the firm is not sure if it will be able to sell the unit of output that it produces (assume also that the firm only produces if it has an order in hand). Would such a firm have an incentive to cut price? Only if it felt that, by doing so, it would increase the probability of getting an order sufficiently to compensate for the reduced profit margin at the lower price. Of course, the firm does not want to set a price higher than its competitors, so it will set a price no higher than the price that it expects its competitors to set.

Now consider a different sort of firm, a firm that can easily expand its output. Faced with the prospect of losing its current sales, this type of firm, unlike the first type, could offer to sell an increased amount at a reduced price. How could it sell an increased amount when demand is falling? By undercutting its competitors. A firm willing to cut its price could, by taking share away from its competitors, actually expand its output despite overall falling demand. That is the essence of competitive rivalry. Obviously, not every firm could succeed in such a strategy, but some firms, presumably those with a cost advantage, or a willingness to accept a reduced profit margin, could expand, thereby forcing marginal firms out of the market.

Workers seem to me to have the characteristics of type-one firms, while most actual businesses seem to resemble type-two firms. So what I am suggesting is that the inability of workers to take over the jobs of co-workers (the analog of output expansion by a firm) when faced with the prospect of a layoff means that a powerful incentive operating in non-labor markets for price cutting in response to reduced demand is not present in labor markets. A firm faced with the prospect of being terminated by a customer whose demand for the firm’s product has fallen may offer significant concessions to retain the customer’s business, especially if it can, in the process, gain an increased share of the customer’s business. A worker facing the prospect of a layoff cannot offer his employer a similar deal. And requiring a workforce of many workers, the employer cannot generally avoid the morale-damaging effects of a wage cut on his workforce by replacing current workers with another set of workers at a lower wage than the old workers were getting.

I think that what I wrote four years ago is clearly right, identifying an important reason for wage stickiness. But there’s also another reason that I didn’t mention then, but whose importance has since come to appear increasingly significant to me, especially as a result of writing and rewriting my paper “Hayek, Hicks, Radner and three concepts of intertemporal equilibrium.”

If you are unemployed because the demand for your employer’s product has gone down, and your employer, planning to reduce output, is laying off workers no longer needed, how could you, as an individual worker, unconstrained by a union collective-bargaining agreement or by a minimum-wage law, persuade your employer not to lay you off? Could you really keep your job by offering to accept a wage cut — no matter how big? If you are being laid off because your employer is reducing output, would your offer to work at a lower wage cause your employer to keep output unchanged, despite a reduction in demand? If not, how would your offer to take a pay cut help you keep your job? Unless enough workers are willing to accept a big enough wage cut for your employer to find it profitable to maintain current output instead of cutting output, how would your own willingness to accept a wage cut enable you to keep your job?

Now, if all workers were to accept a sufficiently large wage cut, it might make sense for an employer not to carry out a planned reduction in output, but the offer by any single worker to accept a wage cut certainly would not cause the employer to change its output plans. So, if you are making an independent decision whether to offer to accept a wage cut, and other workers are making their own independent decisions about whether to accept a wage cut, would it be rational for you or any of them to accept a wage cut? Whether it would or wouldn’t might depend on what each worker was expecting other workers to do. But certainly given the expectation that other workers are not offering to accept a wage cut, why would it make any sense for any worker to be the one to offer to accept a wage cut? Would offering to accept a wage cut, increase the likelihood that a worker would be one of the lucky ones chosen not to be laid off? Why would offering to accept a wage cut that no one else was offering to accept, make the worker willing to work for less appear more desirable to the employer than the others that wouldn’t accept a wage cut? One reaction by the employer might be: what’s this guy’s problem?

Combining this way of looking at the incentives workers have to offer to accept wage reductions to keep their jobs with my argument in my post of four years ago, I now am inclined to suggest that unemployment as such provides very little incentive for workers and employers to cut wages. Price cutting in periods of excess supply is often driven by aggressive price cutting by suppliers with large unsold inventories. There may be lots of unemployment, but no one is holding a large stock of unemployed workers, and no is in a position to offer low wages to undercut the position of those currently employed at  nominal wages that, arguably, are too high.

That’s not how labor markets operate. Labor markets involve matching individual workers and individual employers more or less one at a time. If nominal wages fall, it’s not because of an overhang of unsold labor flooding the market; it’s because something is changing the expectations of workers and employers about what wage will be offered by employers, and accepted by workers, for a particular kind of work. If the expected wage is too high, not all workers willing to work at that wage will find employment; if it’s too low, employers will not be able to find as many workers as they would like to hire, but the situation will not change until wage expectations change. And the reason that wage expectations change is not because the excess demand for workers causes any immediate pressure for nominal wages to rise.

The further point I would make is that the optimal responses of workers and the optimal responses of their employers to a recessionary reduction in demand, in which the employers, given current input and output prices, are planning to cut output and lay off workers, are mutually interdependent. While it is, I suppose, theoretically possible that if enough workers decided to immediately offer to accept sufficiently large wage cuts, some employers might forego plans to lay off their workers, there are no obvious market signals that would lead to such a response, because such a response would be contingent on a level of coordination between workers and employers and a convergence of expectations about future outcomes that is almost unimaginable.

One can’t simply assume that it is in the independent self-interest of every worker to accept a wage cut as soon as an employer perceives a reduced demand for its product, making the current level of output unprofitable. But unless all, or enough, workers decide to accept a wage cut, the optimal response of the employer is still likely to be to cut output and lay off workers. There is no automatic mechanism by which the market adjusts to demand shocks to achieve the set of mutually consistent optimal decisions that characterizes a full-employment market-clearing equilibrium. Market-clearing equilibrium requires not merely isolated price and wage cuts by individual suppliers of inputs and final outputs, but a convergence of expectations about the prices of inputs and outputs that will be consistent with market clearing. And there is no market mechanism that achieves that convergence of expectations.

So, this brings me back to Keynes and the idea of sticky wages as the key to explaining cyclical fluctuations in output and employment. Keynes writes at the beginning of chapter 19 of the General Theory.

For the classical theory has been accustomed to rest the supposedly self-adjusting character of the economic system on an assumed fluidity of money-wages; and, when there is rigidity, to lay on this rigidity the blame of maladjustment.

A reduction in money-wages is quite capable in certain circumstances of affording a stimulus to output, as the classical theory supposes. My difference from this theory is primarily a difference of analysis. . . .

The generally accept explanation is . . . quite a simple one. It does not depend on roundabout repercussions, such as we shall discuss below. The argument simply is that a reduction in money wages will, cet. par. Stimulate demand by diminishing the price of the finished product, and will therefore increase output, and will therefore increase output and employment up to the point where  the reduction which labour has agreed to accept in its money wages is just offset by the diminishing marginal efficiency of labour as output . . . is increased. . . .

It is from this type of analysis that I fundamentally differ.

[T]his way of thinking is probably reached as follows. In any given industry we have a demand schedule for the product relating the quantities which can be sold to the prices asked; we have a series of supply schedules relating the prices which will be asked for the sale of different quantities. .  . and these schedules between them lead up to a further schedule which, on the assumption that other costs are unchanged . . . gives us the demand schedule for labour in the industry relating the quantity of employment to different levels of wages . . . This conception is then transferred . . . to industry as a whole; and it is supposed, by a parity of reasoning, that we have a demand schedule for labour in industry as a whole relating the quantity of employment to different levels of wages. It is held that it makes no material difference to this argument whether it is in terms of money-wages or of real wages. If we are thinking of real wages, we must, of course, correct for changes in the value of money; but this leaves the general tendency of the argument unchanged, since prices certainly do not change in exact proportion to changes in money wages.

If this is the groundwork of the argument . . ., surely it is fallacious. For the demand schedules for particular industries can only be constructed on some fixed assumption as to the nature of the demand and supply schedules of other industries and as to the amount of aggregate effective demand. It is invalid, therefore, to transfer the argument to industry as a whole unless we also transfer our assumption that the aggregate effective demand is fixed. Yet this assumption amount to an ignoratio elenchi. For whilst no one would wish to deny the proposition that a reduction in money-wages accompanied by the same aggregate demand as before will be associated with an increase in employment, the precise question at issue is whether the reduction in money wages will or will not be accompanied by the same aggregate effective demand as before measured in money, or, at any rate, measured by an aggregate effective demand which is not reduced in full proportion to the reduction in money-wages. . . But if the classical theory is not allowed to extend by analogy its conclusions in respect of a particular industry to industry as a whole, it is wholly unable to answer the question what effect on employment a reduction in money-wages will have. For it has no method of analysis wherewith to tackle the problem. (General Theory, pp. 257-60)

Keynes’s criticism here is entirely correct. But I would restate slightly differently. Standard microeconomic reasoning about preferences, demand, cost and supply is partial-equilbriium analysis. The focus is on how equilibrium in a single market is achieved by the adjustment of the price in a single market to equate the amount demanded in that market with amount supplied in that market.

Supply and demand is a wonderful analytical tool that can illuminate and clarify many economic problems, providing the key to important empirical insights and knowledge. But supply-demand analysis explicitly – but too often without realizing its limiting implications – assumes that other prices and incomes in other markets are held constant. That assumption essentially means that the market – i.e., the demand, cost and supply curves used to represent the behavioral characteristics of the market being analyzed – is small relative to the rest of the economy, so that changes in that single market can be assumed to have a de minimus effect on the equilibrium of all other markets. (The conditions under which such an assumption could be justified are themselves not unproblematic, but I am now assuming that those problems can in fact be assumed away at least in many applications. And a good empirical economist will have a good instinctual sense for when it’s OK to make the assumption and when it’s not OK to make the assumption.)

So, the underlying assumption of microeconomics is that the individual markets under analysis are very small relative to the whole economy. Why? Because if those markets are not small, we can’t assume that the demand curves, cost curves, and supply curves end up where they started. Because a high price in one market may have effects on other markets and those effects will have further repercussions that move the very demand, cost and supply curves that were drawn to represent the market of interest. If the curves themselves are unstable, the ability to predict the final outcome is greatly impaired if not completely compromised.

The working assumption of the bread and butter partial-equilibrium analysis that constitutes econ 101 is that markets have closed borders. And that assumption is not always valid. If markets have open borders so that there is a lot of spillover between and across markets, the markets can only be analyzed in terms of broader systems of simultaneous equations, not the simplified solutions that we like to draw in two-dimensional space corresponding to intersections of stable supply curves with stable supply curves.

What Keynes was saying is that it makes no sense to draw a curve representing the demand of an entire economy for labor or a curve representing the supply of labor of an entire economy, because the underlying assumption of such curves that all other prices are constant cannot possibly be satisfied when you are drawing a demand curve and a supply curve for an input that generates more than half the income earned in an economy.

But the problem is even deeper than just the inability to draw a curve that meaningfully represents the demand of an entire economy for labor. The assumption that you can model a transition from one point on the curve to another point on the curve is simply untenable, because not only is the assumption that other variables are being held constant untenable and self-contradictory, the underlying assumption that you are starting from an equilibrium state is never satisfied when you are trying to analyze a situation of unemployment – at least if you have enough sense not to assume that economy is starting from, and is not always in, a state of general equilibrium.

So, Keynes was certainly correct to reject the naïve transfer of partial equilibrium theorizing from its legitimate field of applicability in analyzing the effects of small parameter changes on outcomes in individual markets – what later came to be known as comparative statics – to macroeconomic theorizing about economy-wide disturbances in which the assumptions underlying the comparative-statics analysis used in microeconomics are clearly not satisfied. That illegitimate transfer of one kind of theorizing to another has come to be known as the demand for microfoundations in macroeconomic models that is the foundational methodological principle of modern macroeconomics.

The principle, as I have been arguing for some time, is illegitimate for a variety of reasons. And one of those reasons is that microeconomics itself is based on the macroeconomic foundational assumption of a pre-existing general equilibrium, in which all plans in the entire economy are, and will remain, perfectly coordinated throughout the analysis of a particular parameter change in a single market. Once you relax the assumption that all, but one, markets are in equilibrium, the discipline imposed by the assumption of the rationality of general equilibrium and comparative statics is shattered, and a different kind of theorizing must be adopted to replace it.

The search for that different kind of theorizing is the challenge that has always faced macroeconomics. Despite heroic attempts to avoid facing that challenge and pretend that macroeconomics can be built as if it were microeconomics, the search for a different kind of theorizing will continue; it must continue. But it would certainly help if more smart and creative people would join in that search.

Hu McCulloch Figures out (More or Less) the Great Depression

Last week Houston McCulloch, one of the leading monetary economists of my generation, posted an  insightful and thoughtful discussion of the causes of the Great Depression with which I largely, though not entirely, agree. Although Scott Sumner has already commented on Hu’s discussion, I also wanted to weigh in with some of my comments. Here is how McCulloch sets up his discussion.

Understanding what caused the Great Depression of 1929-39 and why it persisted so long has been fairly characterized by Ben Bernanke as the “Holy Grail of Macroeconomics.” The fear that the financial crisis of 2008 would lead to a similar Depression induced the Fed to use its emergency powers to bail out failing firms and to more than quadruple the monetary base, while Congress authorized additional bailouts and doubled the national debt. Could the Great Recession have taken a similar turn had these extreme measures not been taken?

Economists have often blamed the Depression on U.S. monetary policy or financial institutions.  Friedman and Schwartz (1963) famously argued that a spontaneous wave of runs against fragile fractional reserve banks led to a rise in the currency/deposit ratio. The Fed failed to offset the resulting fall in the money multiplier with base expansion, leading to a disastrous 24% deflation from 1929 to 1933. Through the short-run Phillips curve effect (Friedman 1968), this in turn led to a surge in unemployment to 22.5% by 1932.

The Debt-Deflation theory of Irving Fisher, and later Ben Bernanke (1995), takes the deflation as given, and blames the severity of the disruption on the massive bankruptcies that were caused by the increased burden of nominal indebtedness.  Murray Rothbard (1963) uses the “Austrian” business cycle theory of Ludwig von Mises and F.A. Hayek to blame the downturn on excessive domestic credit expansion by the Fed during the 1920s that disturbed the intertemporal structure of production (cf. McCulloch 2014).

My own view, after pondering the problem for many decades, is that indeed the Depression was monetary in origin, but that the ultimate blame lies not with U.S. domestic monetary and financial policy during the 1920s and 30s. Rather, the massive deflation was an inevitable consequence of Europe’s departure from the gold standard during World War I —  and its bungled and abrupt attempt to return to gold in the late 1920s.

I agree with every word of this introductory passage, so let’s continue.

In brief, the departure of the European belligerents from gold in 1914 massively reduced the global demand for gold, leading to the inflation of prices in terms of gold — and, therefore, in terms of currencies like the U.S. dollar which were convertible to gold at a fixed parity. After the war, Europe initially postponed its return to gold, leading to a plateau of high prices during the 1920s that came to be perceived as the new normal. In the late 1920s, there was a scramble to return to the pre-war gold standard, with the inevitable consequence that commodity prices — in terms of gold, and therefore in terms of the dollar — had to return to something approaching their 1914 level.

The deflation was thus inevitable, but was made much more harmful by its postponement and then abruptness. In retrospect, the UK could have returned to its pre-war parity with far less pain by emulating the U.S. post-Civil War policy of freezing the monetary base until the price level gradually fell to its pre-war level. France should not have over-devalued the franc, and then should have monetized its gold influx rather than acting as a global gold sink. Gold reserve ratios were unnecessarily high, especially in France.

Here is where I start to quibble a bit with Hu, mainly about the importance of Britain’s 1925 resumption of convertibility at the prewar parity with the dollar. Largely owing to Keynes’s essay “The Economic Consequences of Mr. Churchill,” in which Keynes berated Churchill for agreeing to the demands of the City and to the advice of the British Treasury advisers (including Ralph Hawtrey), on whom he relied despite Keynes’s attempt to convince him otherwise, to quickly resume gold convertibility at the prewar dollar parity, warning of the devastating effects of the subsequent deflation on British industry and employment, much greater significance has been attributed to the resumption of convertibility than it actually had on the subsequent course of events. Keynes’s analysis of the deflationary effect of the resumption was largely correct, but the effect turned out to be milder than he anticipated. Britain had already undergone a severe deflation in the early 1920s largely as a result of the American deflation. Thus by 1925, Britain had already undergone nearly 5 years of continuous deflation that brought the foreign exchange value of sterling to within 10 percent of the prewar dollar parity. The remaining deflation required to enable sterling to appreciate another 10 percent was not trivial, but by 1925 most of the deflationary pain had already been absorbed. Britain was able to sustain further mild deflation for the next four years till mid-1929 even as the British economy grew and unemployment declined gradually. The myth that Britain was mired in a continuous depression after the resumption of convertibility in 1925 has no basis in the evidence. Certainly, a faster recovery would have been desirable, and Hawtrey consistently criticized the Bank of England for keeping Bank Rate at 5% even with deflation in the 1-2% range.

The US Federal Reserve was somewhat accommodative in the 1925-28 period, but could have easily been even more accommodative. As McCulloch correctly notes it was really France, which undervalued the franc when it restored convertibility in 1928, and began accumulating gold in record quantities that became the primary destabilizing force in the world economy. Britain was largely an innocent bystander.

However, given that the U.S. had a fixed exchange rate relative to gold and no control over Europe’s misguided policies, it was stuck with importing the global gold deflation — regardless of its own domestic monetary policies. The debt/deflation problem undoubtedly aggravated the Depression and led to bank failures, which in turn increased the currency/deposit ratio and compounded the situation. However, a substantial portion of the fall in the U.S. nominal money stock was to be expected as a result of the inevitable deflation — and therefore was the product, rather than the primary cause, of the deflation. The anti-competitive policies of the Hoover years and FDR’s New Deal (Rothbard 1963, Ohanian 2009) surely aggravated and prolonged the Depression, but were not the ultimate cause.

Actually, the Fed, holding 40% of the world’s gold reserves in 1929, could have eased pressure on the world gold market by allowing an efflux of gold to accommodate the French demand for gold. However, instead of taking an accommodative stance, the Fed, seized by dread of stock-market speculation, kept increasing short-term interest rates, thereby attracting gold into the United States instead of allowing gold to flow out, increasing pressure on the world gold market and triggering the latent deflationary forces that until mid-1929 had been kept at bay. Anti-competitive policies under Hoover and under FDR were certainly not helpful, but those policies, as McCulloch recognizes, did not cause the collapse of output between 1929 and 1933.

Contemporary economists Ralph Hawtrey, Charles Rist, and Gustav Cassel warned throughout the 1920s that substantial deflation, in terms of gold and therefore the dollar, would be required to sustain a return to anything like the 1914 gold standard.[1]  In 1928, Cassel actually predicted that a global depression was imminent:

The post-War superfluity of gold is, however, of an entirely temporary character, and the great problem is how to meet the growing scarcity of gold which threatens the world both from increased demand and from diminished supply. We must solve this problem by a systematic restriction of the monetary demand for gold. Only if we succeed in doing this can we hope to prevent a permanent fall in the general price level and a prolonged and world-wide depression which would inevitably be connected with such a fall in prices [as quoted by Johnson (1997, p. 55)].

As early as 1919 both Hawtrey and Cassel had warned that a global depression would follow an attempt to restore the gold standard as it existed before World War I. To avoid such a deflation it was necessary to limit the increase in the monetary demand for gold. Hawtrey and Cassel therefore proposed shifting to a gold exchange standard in which gold coinage would not be restored and central banks would hold non-gold foreign exchange reserves rather than gold bullion. The 1922 Genoa Resolutions were largely inspired by the analysis of Hawtrey and Cassel, and those resolutions were largely complied with until France began its insane gold accumulation policy in 1928 just as the Fed began tightening monetary policy to suppress stock-market speculation, thereby triggering, more or less inadvertently, an almost equally massive inflow of gold into the US. (On Hawtrey and Cassel, see my paper with Ron Batchelder.)

McCulloch has a very interesting discussion of the role of the gold standard as a tool of war finance, which reminds me of Earl Thompson’s take on the gold standard, (“Gold Standard: Causes and Consequences”) that Earl contributed to a volume I edited, Business Cycles and Depressions: An Encyclopedia. To keep this post from growing inordinately long, and because it’s somewhat tangential to McCulloch’s larger theme, I won’t comment on that part of McCulloch’s discussion.

The Gold Exchange Standard

After the war, in order to stay on gold at $20.67 an ounce, with Europe off gold, the U.S. had to undo its post-1917 inflation. The Fed achieved this by raising the discount rate on War Bonds, beginning in late 1919, inducing banks to repay their corresponding loans. The result was a sharp 16% fall in the price level from 1920 to 1922. Unemployment rose from 3.0% in 1919 to 8.7% in 1921. However, nominal wages fell quickly, and unemployment was back to 4.8% by 1923, where it remained until 1929.[3]

The 1920-22 deflation thus brought the U.S. price level into equilibrium, but only in a world with Europe still off gold. Restoring the full 1914 gold standard would have required going back to approximately the 1914 value of gold in terms of commodities, and therefore the 1914 U.S. price level, after perhaps extrapolating for a continuation of the 1900-1914 “gold inflation.”

This is basically right except that I don’t think it makes sense to refer to the US price level as being in equilibrium in 1922. Holding 40% of the world’s monetary gold reserves, the US was in a position to determine the value of gold at whatever level it wanted. To call the particular level at which the US decided to stabilize the value of gold in 1922 an equilibrium is not based on any clear definition of equilibrium that I can identify.

However, the European countries did not seriously try to get back on gold until the second half of the 1920s. The Genoa Conference of 1922 recognized that prices were too high for a full gold standard, but instead tried to put off the necessary deflation with an unrealistic “Gold Exchange Standard.” Under that system, only the “gold center” countries, the U.S. and UK, would hold actual gold reserves, while other central banks would be encouraged to hold dollar or sterling reserves, which in turn would only be fractionally backed by gold. The Gold Exchange Standard sounded good on paper, but unrealistically assumed that the rest of the world would permanently kowtow to the financial supremacy of New York and London.

There is an argument to be made that the Genoa Resolutions were unrealistic in the sense that they assumed that countries going back on the gold standard would be willing to forego the holding of gold reserves to a greater extent than they were willing to. But to a large extent, this was the result of systematically incorrect ideas about how the gold standard worked before World War I and how the system could work after World War I, not of any inherent or necessary properties of the gold standard itself. Nor was the assumption that the rest of the world would permanently kowtow to the financial supremacy of New York and London all that unrealistic when considered in the light of how readily, before World War I, the rest of the world kowtowed to the financial supremacy of London.

In 1926, under Raymond Poincaré, France stabilized the franc after a 5:1 devaluation. However, it overdid the devaluation, leaving the franc undervalued by about 25%, according to The Economist (Johnson 1997, p. 131). Normally, under the specie flow mechanism, this would have led to a rapid accumulation of international reserves accompanied by monetary expansion and inflation, until the price level caught up with purchasing power parity. But instead, the Banque de France sterilized the reserve influx by reducing its holdings of government and commercial credit, so that inflation did not automatically stop the reserve inflow. Furthermore, it often cashed dollar and sterling reserves for gold, again contrary to the Gold Exchange Standard.  The Banking Law of 1928 made the new exchange rate, as well as the gold-only policy, official. By 1932, French gold reserves were 80% of currency and sight deposits (Irwin 2012), and France had acquired 28.4% of world gold reserves — even though it accounted for only 6.6% of world manufacturing output (Johnson 1997, p. 194). This “French Gold Sink” created even more deflationary pressure on gold, and therefore dollar prices, than would otherwise have been expected.

Here McCulloch is unintentionally displaying some of the systematically incorrect ideas about how the gold standard worked that I referred to above. McCulloch is correct that the franc was substantially undervalued when France restored convertibility in 1928. But under the gold standard, the French price level would automatically adjust to the world price level regardless of what happened to the French money supply. However, the Bank of France, partly because it was cashing in the rapidly accumulating foreign exchange reserves for gold as French exports were rising and its imports falling given the low internal French price level, and partly because it was legally barred from increasing the supply of banknotes by open-market operations, was accumulating gold both actively and passively. With no mechanism for increasing the quantity of banknotes in France, a balance of payment of surplus was the only mechanism by which an excess demand for money could be accommodated. It was not an inflow of gold that was being sterilized (sterilization being a misnomer reflecting a confusion about the direction of causality) it was the lack of any domestic mechanism for increasing the quantity of banknotes that caused an inflow of gold. Importing gold was the only means by which an excess domestic demand for banknotes could be satisfied.

The Second Post-War Deflation

By 1931, French gold withdrawals forced Germany to adopt exchange controls, and Britain to give up convertibility altogether. However, these countries did not then disgorge their remaining gold, but held onto it in the hopes of one day restoring free convertibility. Meanwhile, after having been burned by the Bank of England’s suspension, the “Gold Bloc” countries — Belgium, Netherlands and Switzerland — also began amassing gold reserves in earnest, raising their share of world gold reserves from 4.2% in June 1930 to 11.1% two years later (Johnson 1997, p. 194). Despite the dollar’s relatively strong position, the Fed also contributed to the problem by raising its gold coverage ratio to over 75% by 1930, well in excess of the 40% required by law (Irwin 2012, Fig. 5).

The result was a second post-war deflation as the value of gold, and therefore of the dollar, in terms of commodities, abruptly caught up with the greatly increased global demand for gold. The U.S. price level fell 24.0% between 1929 and 1933, with deflation averaging 6.6% per year for 4 years in a row. Unemployment shot up to 22.5% by 1932.

By 1933, the U.S. price level was still well above its 1914 level. However, if the “gold inflation” of 1900-1914 is extrapolated to 1933, as in Figure 3, the trend comes out to almost the 1933 price level. It therefore appears that the U.S. price level, if not its unemployment rate, was finally near its equilibrium under a global gold standard with the dollar at $20.67 per ounce, and that further deflation was probably unnecessary.[4]

Once again McCulloch posits an equilibrium price level under a global gold standard. The mistake is in assuming that there is a fixed monetary demand for gold, which is an assumption completely without foundation. The monetary demand for gold is not fixed. The greater the monetary demand for gold the higher the equilibrium real value of gold and the lower the price level in terms of gold. The equilibrium price level is a function of the monetary demand for gold.

The 1929-33 deflation was much more destructive than the 1920-22 deflation, in large part because it followed a 7-year “plateau” of relatively stable prices that lulled the credit and labor markets into thinking that the higher price level was the new norm — and that gave borrowers time to accumulate substantial nominal debt. In 1919-1920, on the other hand, the newly elevated price level seemed abnormally high and likely to come back down in the near future, as it had after 1812 and 1865.

This is correct, and I fully agree.

How It Could Have been Different

In retrospect, the UK could have successfully gotten itself back on gold with far less disruption simply by emulating the U.S. post-Civil War policy of freezing the monetary base at its war-end level, and then letting the economy grow into the money supply with a gradual deflation. This might have taken 14 years, as in the U.S. between 1865-79, or even longer, but it would have been superior to the economic, social, and political turmoil that the UK experienced. After the pound rose to its pre-war parity of $4.86, the BOE could have begun gradually buying gold reserves with new liabilities and even redeeming those liabilities on demand for gold, subject to reserve availability. Once reserves reached say 20% of its liabilities, it could have started to extend domestic credit to the government and the private sector through the banks, while still maintaining convertibility. Gold coins could even have been circulated, as demanded.

Again, I reiterate that, although the UK resumption was more painful for Britain than it need have been, the resumption had little destabilizing effect on the international economy. The UK did not have a destabilizing effect on the world economy until the September 1931 crisis that caused Britain to leave the gold standard.

If the UK and other countries had all simply devalued in proportion to their domestic price levels at the end of the war, they could have returned to gold quicker, and with less deflation. However, given that a country’s real demand for money — and therefore its demand for real gold reserves — depends only on the real size of the economy and its net gold reserve ratio, such policies would not have reduced the ultimate global demand for gold or lessened the postwar deflation in countries that remained on gold at a fixed parity.

This is an important point. Devaluation was a way of avoiding an overvalued currency and the relative deflation that a single country needed to undergo. But the main problem facing the world in restoring the gold standard was not the relative deflation of countries with overvalued currencies but the absolute deflation associated with an increased world demand for gold across all countries. Indeed, it was France, the country that did devalue that was the greatest source of increased demand for gold owing to its internal monetary policies based on a perverse gold standard ideology.

In fact, the problem was not that gold was “undervalued” (as Johnson puts it) or that there was a “shortage” of gold (as per Cassel and others), but that the price level in terms of gold, and therefore dollars, was simply unsustainably high given Europe’s determination to return to gold. In any event, it was inconceivable that the U.S. would have devalued in 1922, since it had plenty of gold, had already corrected its price level to the world situation with the 1920-22 deflation, and did not have the excuse of a banking crisis as in 1933.

I think that this is totally right. It was not the undervaluation of individual currencies that was the problem, it was the increase in the demand for gold associated with the simultaneous return of many countries to the gold standard. It is also a mistake to confuse Cassel’s discussion of gold shortage, which he viewed as a long-term problem, with the increase in gold demand associated with returning to the gold standard which was the cause of sudden deflation starting in 1929 as a result of the huge increase in gold demand by the Bank of France, a phenomenon that McCulloch mentions early on in his discussion but does not refer to again.

Keynes and the Fisher Equation

The history of economics society is holding its annual meeting in Chicago from Friday June 15 to Sunday June 17. Bringing together material from a number of posts over the past five years or so about Keynes and the Fisher equation and Fisher effect, I will be presenting a new paper called “Keynes and the Fisher Equation.” Here is the abstract of my paper.

One of the most puzzling passages in the General Theory is the attack (GT p. 142) on Fisher’s 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.” Keynes’s attack on the real/nominal distinction is puzzling on its own terms, inasmuch as the distinction is a straightforward and widely accepted distinction that was hardly unique to Fisher, and was advanced as a fairly obvious proposition by many earlier economists including Marshall. What makes Keynes’s criticism even more problematic is that Keynes’s own celebrated theorem in the Tract on Monetary Reform about covered interest arbitrage is merely an application of Fisher’s reasoning in Appreciation and Interest. Moreover, Keynes endorsed Fisher’s distinction in the Treatise on Money. But even more puzzling is that Keynes’s analysis in Chapter 17 demonstrates that in equilibrium the return on alternative assets must reflect their differences in their expected rates of appreciation. Thus Keynes, himself, in the General Theory endorsed the essential reasoning underlying the distinction between real and the money rates of interest. The solution to the puzzle lies in understanding the distinction between the relationships between the real and nominal rates of interest at a moment in time and the effects of a change in expected rates of appreciation that displaces an existing equilibrium and leads to a new equilibrium. Keynes’s criticism of the Fisher effect must be understood in the context of his criticism of the idea of a unique natural rate of interest implicitly identifying the Fisherian real rate with a unique natural rate.

And here is the concluding section of my paper.

Keynes’s criticisms of the Fisher effect, especially the facile assumption that changes in inflation expectations are reflected mostly, if not entirely, in nominal interest rates – an assumption for which neither Fisher himself nor subsequent researchers have found much empirical support – were grounded in well-founded skepticism that changes in expected inflation do not affect the real interest rate. A Fisherian analysis of an increase in expected deflation at the zero lower bound shows that the burden of the adjustment must be borne by an increase in the real interest rate. Of course, such a scenario might be dismissed as a special case, which it certainly is, but I very much doubt that it is the only assumptions leading to the conclusion that a change in expected inflation or deflation affects the real as well as the nominal interest rate.

Although Keynes’s criticism of the Fisher equation (or more precisely against the conventional simplistic interpretation) was not well argued, his intuition was sound. And in his contribution to the Fisher festschrift, Keynes (1937b) correctly identified the two key assumptions leading to the conclusion that changes in inflation expectations are reflected entirely in nominal interest rates: (1) a unique real equilibrium and (2) the neutrality (actually superneutrality) of money. Keynes’s intuition was confirmed by Hirshleifer (1970, 135-38) who derived the Fisher equation as a theorem by performing a comparative-statics exercise in a two-period general-equilibrium model with money balances, when the money stock in the second period was increased by an exogenous shift factor k. The price level in the second period increases by a factor of k and the nominal interest rate increases as well by a factor of k, with no change in the real interest rate.

But typical Keynesian and New Keynesian macromodels based on the assumption of no capital or a single capital good drastically oversimplify the analysis, because those highly aggregated models assume that the determination of the real interest rate takes place in a single market. The market-clearing assumption invites the conclusion that the rate of interest, like any other price, is determined by the equality of supply and demand – both of which are functions of that price — in  that market.

The equilibrium rate of interest, as C. J. Bliss (1975) explains in the context of an intertemporal general-equilibrium analysis, is not a price; it is an intertemporal rate of exchange characterizing the relationships between all equilibrium prices and expected equilibrium prices in the current and future time periods. To say that the interest rate is determined in any single market, e.g., a market for loanable funds or a market for cash balances, is, at best, a gross oversimplification, verging on fallaciousness. The interest rate or term structure of interest rates is a reflection of the entire intertemporal structure of prices, so a market for something like loanable funds cannot set the rate of interest at a level inconsistent with that intertemporal structure of prices without disrupting and misaligning that structure of intertemporal price relationships. The interest rates quoted in the market for loanable funds are determined and constrained by those intertemporal price relationships, not the other way around.

In the real world, in which current prices, future prices and expected future prices are not and almost certainly never are in an equilibrium relationship with each other, there is always some scope for second-order variations in the interest rates transacted in markets for loanable funds, but those variations are still tightly constrained by the existing intertemporal relationships between current, future and expected future prices. Because the conditions under which Hirshleifer derived his theorem demonstrating that changes in expected inflation are fully reflected in nominal interest rates are not satisfied, there is no basis for assuming that a change in expected inflation affect only nominal interest rates with no effect on real rates.

There are probably a huge range of possible scenarios of how changes in expected inflation could affect nominal and real interest rates. One should not disregard the Fisher equation as one possibility, it seems completely unwarranted to assume that it is the most plausible scenario in any actual situation. If we read Keynes at the end of his marvelous Chapter 17 in the General Theory in which he remarks that he has abandoned the belief he had once held in the existence of a unique natural rate of interest, and has come to believe that there are really different natural rates corresponding to different levels of unemployment, we see that he was indeed, notwithstanding his detour toward a pure liquidity preference theory of interest, groping his way toward a proper understanding of the Fisher equation.

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)

Because Keynes believed that an increased in the expected future price level implies an increase in the marginal efficiency of capital, it follows that an increase in expected inflation under conditions of less than full employment would increase investment spending and employment, thereby raising the real rate of interest as well the nominal rate. Cottrell (1994) has attempted to make an argument along such lines within a traditional IS-LM framework. I believe that, in a Fisherian framework, my argument points in a similar direction.

 

What Hath Merkel Wrought?

In my fifth month of blogging in November 2011, I wrote a post which I called “The Economic Consequences of Mrs. Merkel.” The title, as I explained, was inspired by J. M. Keynes’s famous essay “The Economic Consequences of Mr. Churchill,” which eloquently warned that Britain was courting disaster by restoring the convertibility of sterling into gold at the prewar parity of $4.86 to the pound, the dollar then being the only major currency convertible into gold. The title of Keynes’s essay, in turn, had been inspired by Keynes’s celebrated book The Economic Consequences of the Peace about the disastrous Treaty of Versailles, which accurately foretold the futility of imposing punishing war reparations on Germany.

In his essay, Keynes warned that by restoring the prewar parity, Churchill would force Britain into an untenable deflation at a time when more than 10% of the British labor force was unemployed (i.e., looking for, but unable to find, a job at prevailing wages). Keynes argued that the deflation necessitated by restoration of the prewar parity would impose an intolerable burden of continued and increased unemployment on British workers.

But, as it turned out, Churchill’s decision turned out to be less disastrous than Keynes had feared. The resulting deflation was quite mild, wages in nominal terms were roughly stable, and real output and employment grew steadily with unemployment gradually falling under 10% by 1928. The deflationary shock that Keynes had warned against turned out to be less severe than Keynes had feared because the U.S. Federal Reserve, under the leadership of Benjamin Strong, President of the New York Fed, the de facto monetary authority of the US and the world, followed a policy that allowed a slight increase in the world price level in terms of dollars, thereby moderating the deflationary effect on Britain of restoring the prewar sterling/dollar exchange rate.

Thanks to Strong’s enlightened policy, the world economy continued to expand through 1928. I won’t discuss the sequence of events in 1928 and 1929 that led to the 1929 stock market crash, but those events had little, if anything, to do with Churchill’s 1925 decision. I’ve discussed the causes of the 1929 crash and the Great Depression in many other places including my 2011 post about Mrs. Merkel, so I will skip the 1929 story in this post.

The point that I want to make is that even though Keynes’s criticism of Churchill’s decision to restore the prewar dollar/sterling parity was well-taken, the dire consequences that Keynes foretold, although they did arrive a few years thereafter, were not actually caused by Churchill’s decision, but by decisions made in Paris and New York, over which Britain may have had some influence, but little, if any, control.

What I want to discuss in this post is how my warnings about potential disaster almost six and a half years ago have turned out. Here’s how I described the situation in November 2011:

Fast forward some four score years to today’s tragic re-enactment of the deflationary dynamics that nearly destroyed European civilization in the 1930s. But what a role reversal! In 1930 it was Germany that was desperately seeking to avoid defaulting on its obligations by engaging in round after round of futile austerity measures and deflationary wage cuts, causing the collapse of one major European financial institution after another in the annus horribilis of 1931, finally (at least a year after too late) forcing Britain off the gold standard in September 1931. Eighty years ago it was France, accumulating huge quantities of gold, in Midas-like self-satisfaction despite the economic wreckage it was inflicting on the rest of Europe and ultimately itself, whose monetary policy was decisive for the international value of gold and the downward course of the international economy. Now, it is Germany, the economic powerhouse of Europe dominating the European Central Bank, which effectively controls the value of the euro. And just as deflation under the gold standard made it impossible for Germany (and its state and local governments) not to default on its obligations in 1931, the policy of the European Central Bank, self-righteously dictated by Germany, has made default by Greece and now Italy and at least three other members of the Eurozone inevitable. . . .

If the European central bank does not soon – and I mean really soon – grasp that there is no exit from the debt crisis without a reversal of monetary policy sufficient to enable nominal incomes in all the economies in the Eurozone to grow more rapidly than does their indebtedness, the downward spiral will overtake even the stronger European economies. (I pointed out three months ago that the European crisis is a NGDP crisis not a debt crisis.) As the weakest countries choose to ditch the euro and revert back to their own national currencies, the euro is likely to start to appreciate as it comes to resemble ever more closely the old deutschmark. At some point the deflationary pressures of a rising euro will cause even the Germans, like the French in 1935, to relent. But one shudders at the economic damage that will be inflicted until the Germans come to their senses. Only then will we be able to assess the full economic consequences of Mrs. Merkel.

Greece did default, but the European Community succeeded in imposing draconian austerity measures on Greece, while Italy, Spain, France, and Portugal, which had all been in some danger, managed to avoid default. That they did so is due first to the enormous cost that would have be borne by a country in the Eurozone to extricate itself from the Eurozone and reinstitute its own national currency and second to the actions taken by Mario Draghi, who succeeded Jean Claude Trichet as President of the European Central Bank in November 2011. If monetary secession from the eurozone were less fraught, surely Greece and perhaps other countries would have chosen that course rather than absorb the continuing pain of remaining in the eurozone.

But if it were not for a decisive change in policy by Draghi, Greece and perhaps other countries would have been compelled to follow that uncharted and potentially catastrophic path. But, after assuming leadership of the ECB, Draghi immediately reversed the perverse interest-rate hikes imposed by his predecessor and, even more crucially, announced in July 2012 that the ECB “is ready to do whatever it takes to preserve the Euro. And believe me, it will be enough.” Draghi’s reassurance that monetary easing would be sufficient to avoid default calmed markets, alleviated market pressure driving up interest rates on debt issued by those countries.

But although Draghi’s courageous actions to ease monetary policy in the face of German disapproval avoided a complete collapse, the damage inflicted by Mrs. Merkel’s ferocious anti-inflation policy did irreparable damage, not only on Greece, but, by deepening the European downturn and delaying and suppressing the recovery, on the rest of the European community, inflaming anti-EU, populist nationalism in much of Europe that helped fuel the campaign for Brexit in the UK and has inspired similar anti-EU movements elsewhere in Europe and almost prevented Mrs. Merkel from forming a government after the election a few months ago.

Mrs. Merkel is perhaps the most impressive political leader of our time, and her willingness to follow a humanitarian policy toward refugees fleeing the horrors of war and persecution showed an extraordinary degree of political courage and personal decency that ought to serve as a model for other politicians to emulate. But that admirable legacy will be forever tarnished by the damage she inflicted on her own country and the rest of the EU by her misguided battle against the phantom threat of inflation.


About Me

David Glasner
Washington, DC

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

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