Archive for the 'Robert Clower' Category

Say’s (and Walras’s) Law Revisited

Update (6/18/2019): The current draft of my paper is now available on SSRN. Here is a link.

The annual meeting of the History of Economics Society is coming up in two weeks. It will be held at Columbia University at New York, and I will be presenting an unpublished paper of mine “Say’s Law and the Classical Theory of Depressions.” I began writing this paper about 20 years ago, but never finished it. My thinking about Say’s Law goes back to my first paper on classical monetary theory, and I have previously written blog-posts about Say’s Law (here and here). And more recently I realized that in a temporary-equilibrium framework, both Say’s Law and Walras’s Law, however understood, may be violated.

Here’s the abstract from my paper:

Say’s Law occupies a prominent, but equivocal, position in the history of economics, having been the object of repeated controversies about its meaning and significance since it was first propounded early in the nineteenth century. It has been variously defined, and arguments about its meaning and validity have not reached consensus about what was being attacked or defended. This paper proposes a unifying interpretation of Say’s Law based on the idea that the monetary sector of an economy with a competitively supplied money involves at least two distinct markets not just one. Thus, contrary to the Lange-Patinkin interpretation of Say’s Law, an excess supply or demand for money does not necessarily imply an excess supply or demand for goods in a Walrasian GE model. Beyond modifying the standard interpretation of the inconsistency between Say’s Law and a monetary economy, the paper challenges another standard interpretation of Say’s Law as being empirically refuted by the existence of lapses from full employment and economic depressions. Under the alternative interpretation, originally suggested by Clower and Leijonhufvud and by Hutt, Say’s Law provides a theory whereby disequilibrium in one market, causing the amount actually supplied to fall short of what had been planned to be supplied, reduces demand in other markets, initiating a cumulative process of shrinking demand and supply. This cumulative process of contracting supply is analogous to the Keynesian multiplier whereby a reduction in demand initiates a cumulative process of declining demand. Finally, it is shown that in a temporary-equilibrium context, Walras’s Law (and a fortiori Say’ Law) may be violated.

Here is the Introduction of my paper.

I. Introduction

Say’s Law occupies a prominent, but uncertain, position in the history of economics, having been the object of repeated controversies since the early nineteenth century. Despite a formidable secondary literature, the recurring controversies still demand a clear resolution. Say’s Law has been variously defined, and arguments about its meaning and validity have failed to achieve any clear consensus about just what is being defended or attacked. So, I propose in this paper to reconsider Say’s Law in a way that is faithful in spirit to how it was understood by its principal architects, J. B. Say, James Mill, and David Ricardo as well as their contemporary critics, and to provide a conceptual framework within which to assess the views of subsequent commentators.

In doing so, I hope to dispel perhaps the oldest and certainly the most enduring misunderstanding about Say’s Law: that it somehow was meant to assert that depressions cannot occur, or that they are necessarily self-correcting if market forces are allowed to operate freely. As I have tried to suggest with the title of this paper, Say’s Law was actually an element of Classical insights into the causes of depressions. Indeed, a version of the same idea expressed by Say’s Law implicitly underlies those modern explanations of depressions that emphasize coordination failures, though Say’s Law actually conveys an additional insight missing from most modern explanations.

The conception of Say’s Law articulated in this paper bears a strong resemblance to what Clower (1965, 1967) and Leijonhufvud (1968, 1981) called Say’s Principle. However, their artificial distinction between Say’s Law and Say’s Principle suggests a narrower conception and application of Say’s principle than, I believe, is warranted.  Moreover, their apparent endorsement of the idea that the validity of Say’s Law somehow depends in a critical way on the absence of money implied a straightforward misinterpretation of Say’s Law earlier propounded by, among other, Hayek, Lange and Patinkin in which only what became known as Walras’s Law and not Say’s Law is a logically necessary property of a general-equilibrium system. Finally, it is appropriate to note at the outset that, in most respects, the conception of Say’s Law for which I shall be arguing was anticipated in a quirky, but unjustly neglected, work by Hutt (1975) and by the important, and similarly neglected, work of Earl Thompson (1974).

In the next section, I offer a restatement of the Classical conception of Say’s Law. That conception was indeed based on the insight that, in the now familiar formulation, supply creates its own demand. But to grasp how this insight was originally understood, one must first understand the problem for which Say’s Law was proposed as a solution. The problem concerns the relationship between a depression and a general glut of all goods, but it has two aspects. First, is a depression in some sense caused by a general glut of all goods? Second, is a general glut of all goods logically conceivable in a market economy? In section three, I shall consider the Classical objections to Say’s Law and the responses offered by the Classical originators of the doctrine in reply to those objections. In section four, I discuss the modern objections offered to Say’s Law, their relation to the earlier objections, and the validity of the modern objections to the doctrine. In section five, I re-examine the Classical doctrine, relating it explicitly to a theory of depressions characterized by “inadequate aggregate demand.” I also elaborate on the subtle, but important, differences between my understanding of Say’s Law and what Clower and Leijonhufvud have called Say’s Principle. In section six, I show that when considered in the context of a temporary-equilibrium model in there is an incomplete set of forward and state-contingent markets, not even Walras’s Law, let alone Say’s Law, is logically necessary property of the model. An understanding of the conditions in which neither Walras’s Law nor Say’s Law is satisfied provides an important insight into financial crises and the systemic coordination failures that are characteristic of the deep depression to which they lead.

And here are the last two sections of the paper.

VI. Say’s Law Violated

            I have just argued that Clower, Leijonhufvud and Hutt explained in detail how the insight provided by Say’s Law into the mechanism whereby disturbances causing disequilibrium in one market or sector can be propagated and amplified into broader and deeper economy-wide disturbances and disequilibria. I now want to argue that by relaxing the strict Walrasian framework in which since Lange (1942) articulated Walras’s Law and Say’s Law, it is possible to show conditions under which neither Walras’s Law nor Say’s Law is satisfied.

            I relax the Walrasian framework by assuming that there is not a complete set of forward and state-contingent markets in which future transactions can be undertaken in the present. Because there a complete set of markets in which future prices are determined and visible to everyone, economic agents must formulate their intertemporal plans for production and consumption relying not only on observed current prices, but also on their expectations of currently unobservable future prices. As already noted, the standard proof of Walras’s Law and a fortiori of Say’s Law (or Identity) are premised on the assumption that all agents make their decisions about purchases and sales on their common knowledge of all prices.

            Thus, in the temporary-equilibrium framework, economic agents make their production and consumption decisions not on the basis of their common knowledge of future market prices common, but on their own conjectural expectations of those prices, expectations that may, or may not, be correct, and may, or may not, be aligned with the expectations of other agents. Unless the agents’ expectations of future prices are aligned, the expectations of some, or all, agents must be disappointed, and the plans to buy and sell formulated based on those expectations will have to be revised, or abandoned, once agents realize that their expectations were incorrect.

            Consider a simple two-person, two-good, two-period model in which agents make plans based on current prices observed in period 1 and their expectations of what prices will be in period 2. Given price expectations for period 2, period-1 prices are determined in a tatonnement process, so that no trading occurs until a temporary- equilibrium price vector for period 1 is found. Assume, further, that price expectations for period 2 do not change in the course of the tatonnement. Once a period-1 equilibrium price vector is found, the two budget constraints subject to which the agents make their optimal decisions, need not have the same values for expected prices in period 2, because it is not assumed that the period-2 price expectations of the two agents are aligned. Because the proof of Walras’s Law depends on agents basing their decisions to buy and sell each commodity on prices for each commodity in each period that are common to both agents, Walras’s Law cannot be proved unless the period-2 price expectations of both agents are aligned.

            The implication of the potential violation of Walras’s Law is that when actual prices turn out to be different from what they were expected to be, economic agents who previously assumed obligations that are about to come due may be unable to discharge those obligations. In standard general-equilibrium models, the tatonnement process assures that no trading takes place unless equilibrium prices have been identified. But in a temporary-equilibrium model, when decisions to purchase and sell are based not on equilibrium prices, but on actual prices that may not have been expected, the discharge of commitments is not certain.

            Of course, if Walras’s Law cannot be proved, neither can Say’s Law. Supply cannot create demand when the insolvency of economic agents obstructs mutually advantageous transactions between agents when some agents have negative net worth. The negative net worth of some agents can be transmitted to other agents holding obligations undertaken by agents whose net worth has become negative.

            Moreover, because the private supply of a medium of exchange by banks depends on the value of money-backing assets held by banks, the monetary system may cease to function in an economy in which the net worth of agents whose obligations are held banks becomes negative. Thus, the argument made in section IV.A for the validity of Say’s Law in the Identity sense breaks down once a sufficient number of agents no longer have positive net worth.

VII.      Conclusion

            My aim in this paper has been to explain and clarify a number of the different ways in which Say’s Law has been understood and misunderstood. A fair reading of the primary and secondary literature allows one to understand that many of the criticisms of Say’s Law have been not properly understood the argument that Say’s Law was either intended or could be reasonably interpreted to have said. Indeed, Say’s Law, properly understood, can actually help one understand the cumulative process of economic contraction whose existence supposedly proved its invalidity. However, I have also been able to show that there are plausible conditions in which a sufficiently serious financial breakdown, associated with financial crises in which substantial losses of net worth lead to widespread and contagious insolvency, when even Walras’s Law, and a fortiori Say’s Law, no longer hold. Understanding how Say’s Law may be violated may thus help in understanding the dynamics of financial crises and the cumulative systemic coordination failures of deep depressions.

I will soon be posting the paper on SSRN. When it’s posted I will post a link to an update to this post.



Who’s Afraid of Say’s Law?

There’s been a lot of discussion about Say’s Law in the blogosphere lately, some of it finding its way into the comments section of my recent post “What Does Keynesisan Mean,” in which I made passing reference to Keynes’s misdirected tirade against Say’s Law in the General Theory. Keynes wasn’t the first economist to make a fuss over Say’s Law. It was a big deal in the nineteenth century when Say advanced what was then called the Law of the Markets, pointing out that the object of all production is, in the end, consumption, so that all productive activity ultimately constitutes a demand for other products. There were extended debates about whether Say’s Law was really true, with Say, Ricardo, James and John Stuart Mill all weighing on in favor of the Law, and Malthus and the French economist J. C. L. de Sismondi arguing against it. A bit later, Karl Marx also wrote at length about Say’s Law, heaping his ample supply of scorn upon Say and his Law. Thomas Sowell’s first book, I believe drawn from the doctoral dissertation he wrote under George Stigler, was about the classical debates about Say’s Law.

The literature about Say’s Law is too vast to summarize in a blog post. Here’s my own selective take on it.

Say was trying to refute a certain kind of explanation of economic crises, and what we now would call cyclical or involuntary unemployment, an explanation attributing such unemployment to excess production for which income earners don’t have enough purchasing power in their pockets to buy. Say responded that the reason why income earners had supplied the services necessary to produce the available output was to earn enough income to purchase the output. This is the basic insight behind the famous paraphrase (I don’t know if it was Keynes’s paraphrase or someone else’s) of Say’s Law — supply creates its own demand. If it were instead stated as products or services are supplied only because the suppliers want to buy other products or services, I think that it would be more in sync than the standard formulation with Say’s intent. Another way to think about Say’s Law is as a kind of conservation law.

There were two famous objections made to Say’s Law: first, current supply might be offered in order to save for future consumption, and, second, current supply might be offered in order to add to holdings of cash. In either case, there could be current supply that is not matched by current demand for output, so that total current demand would be insufficient to generate full employment. Both these objections are associated with Keynes, but he wasn’t the first to make either of them. The savings argument goes back to the nineteenth century, and the typical response was that if there was insufficient current demand, because the desire to save had increased, the public deciding to reduce current expenditures on consumption, the shortfall in consumption demand would lead to an increase in investment demand driven by falling interest rates and rising asset prices. In the General Theory, Keynes proposed an argument about liquidity preference and a potential liquidity trap, suggesting a reason why the necessary adjustment in the rate of interest would not necessarily occur.

Keynes’s argument about a liquidity trap was and remains controversial, but the argument that the existence of money implies that Say’s Law can be violated was widely accepted. Indeed, in his early works on business-cycle theory, F. A. Hayek made the point, seemingly without embarrassment or feeling any need to justify it at length, that the existence of money implied a disconnect between overall supply and overall demand, describing money as a kind of loose joint in the economic system. This argument, apparently viewed as so trivial or commonplace by Hayek that he didn’t bother proving it or citing authority for it, was eventually formalized by the famous market-socialist economist (who, for a number of years was a tenured professor at that famous bastion of left-wing economics the University of Chicago) Oskar Lange who introduced a distinction between Walras’s Law and Say’s Law (“Say’s Law: A Restatement and Criticism”).

Walras’s Law says that the sum of all excess demands and excess supplies, evaluated at any given price vector, must identically equal zero. The existence of a budget constraint makes this true for each individual, and so, by the laws of arithmetic, it must be true for the entire economy. Essentially, this was a formalization of the logic of Say’s Law. However, Lange showed that Walras’s Law reduces to Say’s Law only in an economy without money. In an economy with money, Walras’s Law means that there could be an aggregate excess supply of all goods at some price vector, and the excess supply of goods would be matched by an equal excess demand for money. Aggregate demand would be deficient, and the result would be involuntary unemployment. Thus, according to Lange’s analysis, Say’s Law holds, as a matter of necessity, only in a barter economy. But in an economy with money, an excess supply of all real commodities was a logical possibility, which means that there could be a role for some type – the choice is yours — of stabilization policy to ensure that aggregate demand is sufficient to generate full employment. One of my regular commenters, Tom Brown, asked me recently whether I agreed with Nick Rowe’s statement: “the goal of good monetary policy is to try to make Say’s Law true.” I said that I wasn’t sure what the statement meant, thereby avoiding the need to go into a lengthy explanation about why I am not quite satisfied with that way of describing the goal of monetary policy.

There are at least two problems with Lange’s formulation of Say’s Law. The first was pointed out by Clower and Leijonhufvud in their wonderful paper (“Say’s Principle: What It Means and Doesn’t Mean” reprinted here and here) on what they called Say’s Principle in which they accepted Lange’s definition of Say’s Law, while introducing the alternative concept of Say’s Principle as the supply-side analogue of the Keynesian multiplier. The key point was to note that Lange’s analysis was based on the absence of trading at disequilibrium prices. If there is no trading at disequilibrium prices, because the Walrasian auctioneer or clearinghouse only processes information in a trial-and-error exercise aimed at discovering the equilibrium price vector, no trades being executed until the equilibrium price vector has been discovered (a discovery which, even if an equilibrium price vector exists, may not be made under any price-adjustment rule adopted by the auctioneer, rational expectations being required to “guarantee” that an equilibrium price vector is actually arrived at, sans auctioneer), then, indeed, Say’s Law need not obtain in notional disequilibrium states (corresponding to trial price vectors announced by the Walrasian auctioneer or clearinghouse). The insight of Clower and Leijonhufvud was that in a real-time economy in which trading is routinely executed at disequilibrium prices, transactors may be unable to execute the trades that they planned to execute at the prevailing prices. But when planned trades cannot be executed, trading and output contract, because the volume of trade is constrained by the lesser of the amount supplied and the amount demanded.

This is where Say’s Principle kicks in; If transactors do not succeed in supplying as much as they planned to supply at prevailing prices, then, depending on the condition of their balances sheets, and the condition of credit markets, transactors may have to curtail their demands in subsequent periods; a failure to supply as much as had been planned last period will tend reduce demand in this period. If the “distance” from equilibrium is large enough, the demand failure may even be amplified in subsequent periods, rather than damped. Thus, Clower and Leijonhufvud showed that the Keynesian multiplier was, at a deep level, really just another way of expressing the insight embodied in Say’s Law (or Say’s Principle, if you insist on distinguishing what Say meant from Lange’s reformulation of it in terms of Walrasian equilibrium).

I should add that, as I have mentioned in an earlier post, W. H. Hutt, in a remarkable little book, clarified and elaborated on the Clower-Leijonhufvud analysis, explaining how Say’s Principle was really implicit in many earlier treatments of business-cycle phenomena. The only reservation I have about Hutt’s book is that he used it to wage an unnecessary polemical battle against Keynes.

At about the same time that Clower and Leijonhufvud were expounding their enlarged view of the meaning and significance of Say’s Law, Earl Thompson showed that under “classical” conditions, i.e., a competitive supply of privately produced bank money (notes and deposits) convertible into gold, Say’s Law in Lange’s narrow sense, could also be derived in a straightforward fashion. The demonstration followed from the insight that when bank money is competitively issued, it is accomplished by an exchange of assets and liabilities between the bank and the bank’s customer. In contrast to the naïve assumption of Lange (adopted as well by his student Don Patinkin in a number of important articles and a classic treatise) that there is just one market in the monetary sector, there are really two markets in the monetary sector: a market for money supplied by banks and a market for money-backing assets. Thus, any excess demand for money would be offset not, as in the Lange schema, by an excess supply of goods, but by an excess supply of money-backing services. In other words, the public can increase their holdings of cash by giving their IOUs to banks in exchange for the IOUs of the banks, the difference being that the IOUs of the banks are money and the IOUs of customers are not money, but do provide backing for the money created by banks. The market is equilibrated by adjustments in the quantity of bank money and the interest paid on bank money, with no spillover on the real sector. With no spillover from the monetary sector onto the real sector, Say’s Law holds by necessity, just as it would in a barter economy.

A full exposition can be found in Thompson’s original article. I summarized and restated its analysis of Say’s Law in my 1978 1985 article on classical monetary theory and in my book Free Banking and Monetary Reform. Regrettably, I did not incorporate the analysis of Clower and Leijonhufvud and Hutt into my discussion of Say’s Law either in my article or in my book. But in a world of temporary equilibrium, in which future prices are not correctly foreseen by all transactors, there are no strict intertemporal budget constraints that force excess demands and excess supplies to add up to zero. In short, in such a world, things can get really messy, which is where the Clower-Leijonhufvud-Hutt analysis can be really helpful in sorting things out.

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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