Posts Tagged 'J. R. Hicks'

Hicks on Temporary Equilibrium

Published January 23, 2025 Arrow-Debrew-McKenzie model , Carl Menger , expectations , Friedman , intertemporal equilibrium , J. R. Hicks , macroeconomics , rational expectations , rational expectations equilibrium , Robert Clower , temporary equilibrium 4 Comments
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J. R. Hicks, who introduced the concept of intertemporal equilibrium to English-speaking economists in Value and Capital, was an admirer of Carl Menger, one of the three original Marginal Revolutionaries, crediting Menger in particular for having created an economic theory in time (see his “Time in Economics” in Collected Essays on Economic Theory, vol. II). The goal of grounding economic theory in time inspired many of Hicks’s theoretical contributions, including his exposition of intertemporal equilibrium in Value and Capital which was based on the idea of temporary equilibrium.

Recognizing that (full) intertemporal equilibrium requires all current markets to clear and all agents to share correct expectations of the future prices on which their plans depend, Hicks used temporary equilibrium to describe a sequence of intermediate positions of an economy moving toward or away from (full) intertemporal equilibrium. This was done by positing discrete weekly time periods in which economic activity–production, consumption, buying and selling–occurs during the week at equilibrium prices, prices being set on Monday followed by economic activity at Monday’s prices until start of a new week. This modeling strategy allowed Hicks to embed a quasi-static supply and demand analysis within his intertemporal equilibrium model, the week serving as a time period short enough to allow a conditions, including agents’ expectations, to be plausibly held constant until the following week. Demarcating a short period in which conditions remain constant simplifies the analysis by allowing changes conditions to change once a week. A static weekly analysis is transformed into a dynamic analysis by way of goods and assets held from week to week and by recognizing that agents’ plans to buy and sell depend not only on current prices but on expected future prices.

Weekly price determination assumes that all desired purchases and sales, at Monday’s prices, can be executed, i.e., that markets clear. But market-clearing in temporary equilibrium, involves an ambiguity not present in static equilibrium in which agents’ decision depend only on current prices. Unlike a static model. in which changes in demand and supply are permanent, and no intertemporal substitution occurs, intertemporal substitution both in supply and in demand do occur in a temporary-equilibrium model, so that transitory changes in the demand for, and supply of, goods and assets held from week to week do occur. Distinguishing between desired and undesired (unplanned, involuntary) inventory changes is difficult without knowledge of agents’ plans and the expectations on which their plans depend. Because Monday prices may differ from the prices that agents had expected, some agents may be unable to execute their prior plans to buy and sell.

Some agents may make only minor plan adjustments; others may have to make significant adjustments, and some even scrapping plans that became unviable. The disappointment of expectations likely also causes some or all previously held expectations to be revised. The interaction between expected and realized prices in a temporary-equilibrium model clearly resembles how, according to Menger, the current values of higher-order goods are imputed from the expected prices of the lower-order goods into which those higher-order goods will be transformed.

Hicks never fully developed his temporary equilibrium method (See DeVroey, 2006, “The Temporary Equilibrium Method: Hicks against Hicks”), eventually replacing the market-clearing assumption of what he called a flex-price model for a fix-price disequilibrium model. Hicks had two objections to his temporary-equilibrium method: a) that changes in industrial organization, e.g., the vertical integration of large industrial firms into distribution and retailing, rendered flex-price models increasingly irrelevant to modern economies, and b) that in many markets (especially the labor market) a week is too short for the adjustments necessary for markets to clear. Hicks’s dissatisfaction with temporary equilibrium was reinforced by the apparent inconsistency between flex-price models and the Keynesian model to which, despite his criticisms, he remained attached.

DeVroey rejected Hicks’s second reason for dissatisfaction with his creation, showing it to involve a confusions between logical time (i.e., a sequence of temporal events of unspecified duration) and real time (i.e, the temporal duration of those events). The temporary-equilibrium model pertains to both logical and real time. The function of “Mondays” was to telescope flexible market-clearing price adjustments into a discrete logical time period wherein all the information relevant to price determination is brought to bear. Calling that period a “day” serves no purpose other than to impart the fictitious appearance of realism to an artifact. Whether price determination is telescoped into an instant or a day does not matter.

As for the first reason, DeVroey observed that Hicks’s judgment that flex-price models became irrelevant owing to changes in industrial organization are neither empirically compelling, the stickiness of some prices having always been recognized, nor theoretically necessary. The temporary equilibrium analysis was not meant to be a realistic description of price determination, but as a framework for understanding how a competitive economic system responds to displacements from equilibrium. Hicks seemed to conclude that the assumption of market-clearing rendered temporary-equilibrium models unable to account for high unemployment and other stylized facts related to macroeconomic cycles. But, as noted above, market-clearing in temporary equilibrium does preclude unplanned (aka involuntary) inventory accumulation and unplanned intertemporal labor substitution (aka involuntary unemployment).

Hicks’s seeming confusion about his own idea is hard to understand. In criticizing temporary equilibrium as an explanation of how a competitive economic system operates, he lost sight of the distinction that he had made between disequilibrium as markets failing to clear at a given time and disequilibrium as the absence of intertemporal equilibrium in which mutually consistent optimized plans can be executed by independent agents.

But beyond DeVroey’s criticisms of Hicks’s reasons for dissatisfaction with his temporary-equilibrium model, a more serious problem with Hicks’s own understanding of the temporary-equilibrium model is that he treated agents’ expectations as exogenous parameters within the model rather than as equilibrating variables. Here is how Hicks described the parametric nature of agents’ price expectations.

The effect of actual prices on price expectations is capable of further analysis; but even here we can give no simple rule. Even if autonomous variations are left out of account, there are still two things to consider: the influence of present prices and influence of past prices. These act in very different ways, and so it makes a great deal of difference which influence is the stronger.

Since past prices are past, they are, with respect to the current situation, simply data; if their influence is completely dominant, price-expectations can be treated as data too. This is the case we began by considering; the change in the current price does not disturb price-expectations, it is treated as quite temporary. But as soon as past prices cease to be completely dominant, we have to allow for some influence of current prices on expectations. Even so, that influence may have some various degrees of intensity, and work in various different ways.

It does not seem possible to carry general economic analysis of this matter any further; all we can do here is to list a number of possible cases. A list will be more useful if it is systematic; let us therefore introduce a measure for the reaction we are studying. If we neglect the possibility that a change in the current price of X may affect to a different extent the price of X expected to rule at different future dates, and if we also neglect the possibility that it may affect the expected future prices of other commodities or factors (both of which are serious omissions), then we may classify cases according to the elasticity of expectations. (Value and Capital. 2d ed., pp. 204-05).

When Hicks wrote Value and Capital, and for more than three decades thereafter, treating expectations as exogenous variables was routine, except when economists indulged the admittedly fanciful assumption of perfect foresight. It was not until the rational-expectations revolution that expectations came to be viewed as equilibrating. In almost all of Milton Friedman’s theorizing about expectations, for example, his assumption was that expectations are adaptive, Even in his famous explication of the natural-rate hypothesis, Friedman (1968: “The Role of Monetary Policy”) assumed that expectations are adaptive to prior experience, which corresponds to the elasticity of expectations being less than unity. Hicks failed to understand that expectations are formed endogenously by agents, not parametrically by the model, and that endogenous process may sometimes bring the system closer to, and sometimes further from, equilibrium.

Consider Hicks’s analysis of a change in the price of one commodity, given a fixed interest rate, an endogenous money supply and unit-elastic price expectations, .

Suppose that the rate of interest . . . is taken as given, while the price of one commodity (X) rises by 5 per cent. If the system is to be perfectly stable, this rise should induce an excess supply of X, however many . . . repercussions through other markets we allow for. Now what are the changes in prices which will restore equality between supply and demand in the markets for other commodities? If we consider some other markets only, we get results which do not differ very much from those to which we have been accustomed; the stability of the system survives these tests without difficulty. But when we consider the repercussions on all other markets . . . then we seem to move into a different world. Equilibrium can only be restored  in the other commodity markets if the prices of the other commodities are unchanged, and the price ratios between all current prices and all expected prices are unchanged (since elasticities of expectations are unity), and (ex hypothesi) rates of interest are unchanged—then there is no opportunity for substitution anywhere. The demands and supplies for all goods and services will be unchanged. Being equal before, they will be equal still. It is a general proportional rise in prices which restores equilibrium in the other commodity markets; but it fails to produce an excess supply over demand in the market for the first commodity X. So far as the commodity markets taken alone are concerned, the system behaves like Wicksell’s system. It is in ‘neutral equilibrium’; that is to say, it can be in equilibrium at any level of money prices. [Hicks’s footnote here is as follows: The reader will have noticed that this argument depends upon the assumption that the system of relative prices is uniquely determined. I do not feel many qualms about this assumption myself. If it is  not justified anything may happen.]

If elasticities of expectations are generally greater than unity, so that people interpret a change in prices, not merely as an indication that they will go on changing in the same direction, then a rise in all prices by so much per cent (with constant rate of interest) will make demands generally greater than supplies, so that the rise in prices will continue. A system with elasticities of expectations greater than unity, and constant rate of interest, is definitely unstable. 

Technically, then, the case where elasticities of expectations ae equal to unity marks the dividing line between stability and instability. But its own stability is of a very questionable sort. A slight disturbance will be sufficient to make it pass over into instability.1 (Id., pp. 254-55).

Of course, to view price expectations as equilibrating variables does not imply that price expectations do equilibrate; it means that expectations adjust endogenously as agents obtain new information and that, if agents’ expectations are correct, intertemporal equilibrium will result. Current prices are also equilibrating variables, but, contrary to the rational-expectations postulate, expectations are only potentially, not necessarily, equilibrating. Whether expectations equilibrate or disequilibrate is an empirical question that does not admit of an a priori answer.

Hicks was correct that, owing to the variability of expectations, the outcomes of a temporary-equilibrium model are indeterminate and that unstable outcomes tend to follow from unstable expectations. What he did not do was identify the role of disappointed expectations in the coordination failures that cause severe macroeconomic downturns. Disappointed expectations likely lead to or coincide with monetary disturbances, but contrary to Clower (1965: “The Keynesian Counterrevolution: A Theoretical Appraisal”), monetary exchange is not the only, or even the primary, cause of disruptive expectational disappointments.

In the complex trading networks unerlying modern economies susceptible to macroeconomic disturbances, credit is an essential element of commercial relationships. Most commerce is conducted by way of credit; only small amounts of legal commerce is by immediate transfer of legal-tender cash or currency. In the imaginary world described by the ADM model, no credit is needed or used, because transactions are validated by the Walrasian auctioneer before trading starts.

But in the real world, trades are not validated in advance, agents relying instead on the credit-worthiness of counterparties. Establishing the creditworthiness of counterparties is costly, so specialists (financial intermediaries) emerge to guage traders’ creditworthiness. It is the possibility of expectational disappointment, which are excluded a priori from the ADM general-equilibrium model, that creates both a demand for, and a supply of, credit money, not vice versa. At times, this had been done directly, but it is overwhelmingly done by intermediaries whose credit worthiness is well and widely recognized. Intermediaries exchange their highly credible debt for the less well or less widely recognized debts of individual agents. The debt of some these financial intermediaries may then circulate as generally acceptable media of exchange.

But what constitutes creditworthiness depends on the expectations of those that judge the creditworthiness of an individual or a firm. The creditworthiness of agents depends on the value of assets that they hold, their liabilities, and their expected income streams and cash flows. Loss of income or depreciation of assets reduces agents’ creditworthiness.

Expectational disappointments always impair the creditworthiness of agents whose expectations have been disappointed, their expected income streams having been reduced or their assets depreciated. Insofar as financial intermediaries have accepted the liabilities of individuals or businesses suffering expectational disappointment, those financial intermediaries may find that their own creditworthiness has been impaired. Because the foundation of the profitability of a financial intermediary is its creditworthiness in the eyes of the general public, the impairment of creditworthiness is a potentially catastrophic event for a financial intermediary.

The interconnectedness of economic and especially financial networks implies that impairments of creditworthiness in any substantial part of an economic system may be transmitted quickly to other parts of the system. Such expectational shocks are common, but, under some circumstances, the shocks may not only be transmitted, they may be amplified, leading to a systemic crisis.

Because expectational disappointments and disturbances are ruled out by hypothesis in the ADM model, we cannot hope to gain insight into such events from the standard ADM model. It was precisely Hicks’s temporary equilibrium model that provided the tools for such an analysis, but, unfortunately those tools remain underemployed.

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1 To be clear, the assumption of unit elasticity of expectations means that agents conclude that any observed price change is permanent. If agents believe that an observed price change is permanent, they must conclude that, to restore equilibrium relative prices, all other prices must change proportionately. Hicks therefore posited that, rather than use their understanding, given their information, of the causes of the price change, agents automatically extrapolate any observed price change to all other prices. Such mechanistic expectations are hard to rationalize, but Hicks’s reasoning entails that inference.

Krugman on Mr. Keynes and the Moderns

Published July 28, 2021 A. C. Pigou , D. H. Robertson , Frederick Lavington , gold standard , Gustav Cassel , Keynes , Paul Krugman , R. G. Hawtrey , Robert Barro , Scott Sumner , sticky prices , Uncategorized 10 Comments
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UPDATE: Re-upping this slightly revised post from July 11, 2011

Paul Krugman recently gave a lecture “Mr. Keynes and the Moderns” (a play on the title of the most influential article ever written about The General Theory, “Mr. Keynes and the Classics,” by another Nobel laureate J. R. Hicks) at a conference in Cambridge, England commemorating the publication of Keynes’s General Theory 75 years ago. Scott Sumner and Nick Rowe, among others, have already commented on his lecture. Coincidentally, in my previous posting, I discussed the views of Sumner and Krugman on the zero-interest lower bound, a topic that figures heavily in Krugman’s discussion of Keynes and his relevance for our current difficulties. (I note in passing that Krugman credits Brad Delong for applying the term “Little Depression” to those difficulties, a term that I thought I had invented, but, oh well, I am happy to share the credit with Brad).

In my earlier posting, I mentioned that Keynes’s, slightly older, colleague A. C. Pigou responded to the zero-interest lower bound in his review of The General Theory. In a way, the response enhanced Pigou’s reputation, attaching his name to one of the most famous “effects” in the history of economics, but it made no dent in the Keynesian Revolution. I also referred to “the layers upon layers of interesting personal and historical dynamics lying beneath the surface of Pigou’s review of Keynes.” One large element of those dynamics was that Keynes chose to make, not Hayek or Robbins, not French devotees of the gold standard, not American laissez-faire ideologues, but Pigou, a left-of-center social reformer, who in the early 1930s had co-authored with Keynes a famous letter advocating increased public-works spending to combat unemployment, the main target of his immense rhetorical powers and polemical invective.  The first paragraph of Pigou’s review reveals just how deeply Keynes’s onslaught had wounded Pigou.

When in 1919, he wrote The Economic Consequences of the Peace, Mr. Keynes did a good day’s work for the world, in helping it back towards sanity. But he did a bad day’s work for himself as an economist. For he discovered then, and his sub-conscious mind has not been able to forget since, that the best way to win attention for one’s own ideas is to present them in a matrix of sarcastic comment upon other people. This method has long been a routine one among political pamphleteers. It is less appropriate, and fortunately less common, in scientific discussion.  Einstein actually did for Physics what Mr. Keynes believes himself to have done for Economics. He developed a far-reaching generalization, under which Newton’s results can be subsumed as a special case. But he did not, in announcing his discovery, insinuate, through carefully barbed sentences, that Newton and those who had hitherto followed his lead were a gang of incompetent bunglers. The example is illustrious: but Mr. Keynes has not followed it. The general tone de haut en bas and the patronage extended to his old master Marshall are particularly to be regretted. It is not by this manner of writing that his desire to convince his fellow economists is best promoted.

Krugman acknowledges Keynes’s shady scholarship (“I know that there’s dispute about whether Keynes was fair in characterizing the classical economists in this way”), only to absolve him of blame. He then uses Keynes’s example to attack “modern economists” who deny that a failure of aggregate demand can cause of mass unemployment, offering up John Cochrane and Niall Ferguson as examples, even though Ferguson is a historian not an economist.

Krugman also addresses Robert Barro’s assertion that Keynes’s explanation for high unemployment was that wages and prices were stuck at levels too high to allow full employment, a problem easily solvable, in Barro’s view, by monetary expansion. Although plainly annoyed by Barro’s attempt to trivialize Keynes’s contribution, Krugman never addresses the point squarely, preferring instead to justify Keynes’s frustration with those (conveniently nameless) “classical economists.”

Keynes’s critique of the classical economists was that they had failed to grasp how everything changes when you allow for the fact that output may be demand-constrained.

Not so, as I pointed out in my first post. Frederick Lavington, an even more orthodox disciple than Pigou of Marshall, had no trouble understanding that “the inactivity of all is the cause of the inactivity of each.” It was Keynes who failed to see that the failure of demand was equally a failure of supply.

They mistook accounting identities for causal relationships, believing in particular that because spending must equal income, supply creates its own demand and desired savings are automatically invested.

Supply does create its own demand when economic agents succeed in executing their plans to supply; it is when, owing to their incorrect and inconsistent expectations about future prices, economic agents fail to execute their plans to supply, that both supply and demand start to contract. Lavington understood that; Pigou understood that. Keynes understood it, too, but believing that his new way of understanding how contractions are caused was superior to that of his predecessors, he felt justified in misrepresenting their views, and attributing to them a caricature of Say’s Law that they would never have taken seriously.

And to praise Keynes for understanding the difference between accounting identities and causal relationships that befuddled his predecessors is almost perverse, as Keynes’s notorious confusion about whether the equality of savings and investment is an equilibrium condition or an accounting identity was pointed out by Dennis Robertson, Ralph Hawtrey and Gottfried Haberler within a year after The General Theory was published. To quote Robertson:

(Mr. Keynes’s critics) have merely maintained that he has so framed his definition that Amount Saved and Amount Invested are identical; that it therefore makes no sense even to inquire what the force is which “ensures equality” between them; and that since the identity holds whether money income is constant or changing, and, if it is changing, whether real income is changing proportionately, or not at all, this way of putting things does not seem to be a very suitable instrument for the analysis of economic change.

It just so happens that in 1925, Keynes, in one of his greatest pieces of sustained, and almost crushing sarcasm, The Economic Consequences of Mr. Churchill, offered an explanation of high unemployment exactly the same as that attributed to Keynes by Barro. Churchill’s decision to restore the convertibility of sterling to gold at the prewar parity meant that a further deflation of at least 10 percent in wages and prices would be necessary to restore equilibrium.  Keynes felt that the human cost of that deflation would be intolerable, and held Churchill responsible for it.

Of course Keynes in 1925 was not yet the Keynes of The General Theory. But what historical facts of the 10 years following Britain’s restoration of the gold standard in 1925 at the prewar parity cannot be explained with the theoretical resources available in 1925? The deflation that began in England in 1925 had been predicted by Keynes. The even worse deflation that began in 1929 had been predicted by Ralph Hawtrey and Gustav Cassel soon after World War I ended, if a way could not be found to limit the demand for gold by countries, rejoining the gold standard in aftermath of the war. The United States, holding 40 percent of the world’s monetary gold reserves, might have accommodated that demand by allowing some of its reserves to be exported. But obsession with breaking a supposed stock-market bubble in 1928-29 led the Fed to tighten its policy even as the international demand for gold was increasing rapidly, as Germany, France and many other countries went back on the gold standard, producing the international credit crisis and deflation of 1929-31. Recovery came not from Keynesian policies, but from abandoning the gold standard, thereby eliminating the deflationary pressure implicit in a rapidly rising demand for gold with a more or less fixed total supply.

Keynesian stories about liquidity traps and Monetarist stories about bank failures are epiphenomena obscuring rather than illuminating the true picture of what was happening.  The story of the Little Depression is similar in many ways, except the source of monetary tightness was not the gold standard, but a monetary regime that focused attention on rising price inflation in 2008 when the appropriate indicator, wage inflation, had already started to decline.

Roger and Me

Published April 29, 2015 Axel Leijonfuvud , expectations , rational expectations , Roger Farmer , search theories , temporary equilibrium 2 Comments
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Last week Roger Farmer wrote a post elaborating on a comment that he had left to my post on Price Stickiness and Macroeconomics. Roger’s comment is aimed at this passage from my post:

[A]lthough price stickiness is a sufficient condition for inefficient macroeconomic fluctuations, it is not a necessary condition. It is entirely possible that even with highly flexible prices, there would still be inefficient macroeconomic fluctuations. And the reason why price flexibility, by itself, is no guarantee against macroeconomic contractions is that macroeconomic contractions are caused by disequilibrium prices, and disequilibrium prices can prevail regardless of how flexible prices are.

Here’s Roger’s comment:

I have a somewhat different take. I like Lucas’ insistence on equilibrium at every point in time as long as we recognize two facts. 1. There is a continuum of equilibria, both dynamic and steady state and 2. Almost all of them are Pareto suboptimal.

I made the following reply to Roger’s comment:

Roger, I think equilibrium at every point in time is ok if we distinguish between temporary and full equilibrium, but I don’t see how there can be a continuum of full equilibria when agents are making all kinds of long-term commitments by investing in specific capital. Having said that, I certainly agree with you that expectational shifts are very important in determining which equilibrium the economy winds up at.

To which Roger responded:

I am comfortable with temporary equilibrium as the guiding principle, as long as the equilibrium in each period is well defined. By that, I mean that, taking expectations as given in each period, each market clears according to some well defined principle. In classical models, that principle is the equality of demand and supply in a Walrasian auction. I do not think that is the right equilibrium concept.

Roger didn’t explain – at least not here, he probably has elsewhere — exactly why he doesn’t think equality of demand and supply in a Walrasian auction is not the right equilibrium concept. But I would be interested in hearing from him why he thinks equality of supply and demand is not the right equilibrium concept. Perhaps he will clarify his thinking for me.

Hicks wanted to separate ‘fix price markets’ from ‘flex price markets’. I don’t think that is the right equilibrium concept either. I prefer to use competitive search equilibrium for the labor market. Search equilibrium leads to indeterminacy because there are not enough prices for the inputs to the search process. Classical search theory closes that gap with an arbitrary Nash bargaining weight. I prefer to close it by making expectations fundamental [a proposition I have advanced on this blog].

I agree that the Hicksian distinction between fix-price markets and flex-price markets doesn’t cut it. Nevertheless, it’s not clear to me that a Thompsonian temporary-equilibrium model in which expectations determine the reservation wage at which workers will accept employment (i.e, the labor-supply curve conditional on the expected wage) doesn’t work as well as a competitive search equilibrium in this context.

Once one treats expectations as fundamental, there is no longer a multiplicity of equilibria. People act in a well defined way and prices clear markets. Of course ‘market clearing’ in a search market may involve unemployment that is considerably higher than the unemployment rate that would be chosen by a social planner. And when there is steady state indeterminacy, as there is in my work, shocks to beliefs may lead the economy to one of a continuum of steady state equilibria.

There is an equilibrium for each set of expectations (with the understanding, I presume, that expectations are always uniform across agents). The problem that I see with this is that there doesn’t seem to be any interaction between outcomes and expectations. Expectations are always self-fulfilling, and changes in expectations are purely exogenous. But in a classic downturn, the process seems to be cumulative, the contraction seemingly feeding on itself, causing a spiral of falling prices, declining output, rising unemployment, and increasing pessimism.

That brings me to the second part of an equilibrium concept. Are expectations rational in the sense that subjective probability measures over future outcomes coincide with realized probability measures? That is not a property of the real world. It is a consistency property for a model.

Yes; I agree totally. Rational expectations is best understood as a property of a model, the property being that if agents expect an equilibrium price vector the solution of the model is the same equilibrium price vector. It is not a substantive theory of expectation formation, the model doesn’t posit that agents correctly foresee the equilibrium price vector, that’s an extreme and unrealistic assumption about how the world actually works, IMHO. The distinction is crucial, but it seems to me that it is largely ignored in practice.

And yes: if we plop our agents down into a stationary environment, their beliefs should eventually coincide with reality.

This seems to me a plausible-sounding assumption for which there is no theoretical proof, and in view of Roger’s recent discussion of unit roots, dubious empirical support.

If the environment changes in an unpredictable way, it is the belief function, a primitive of the model, that guides the economy to a new steady state. And I can envision models where expectations on the transition path are systematically wrong.

I need to read Roger’s papers about this, but I am left wondering by what mechanism the belief function guides the economy to a steady state? It seems to me that the result requires some pretty strong assumptions.

The recent ‘nonlinearity debate’ on the blogs confuses the existence of multiple steady states in a dynamic model with the existence of multiple rational expectations equilibria. Nonlinearity is neither necessary nor sufficient for the existence of multiplicity. A linear model can have a unique indeterminate steady state associated with an infinite dimensional continuum of locally stable rational expectations equilibria. A linear model can also have a continuum of attracting points, each of which is an equilibrium. These are not just curiosities. Both of these properties characterize modern dynamic equilibrium models of the real economy.

I’m afraid that I don’t quite get the distinction that is being made here. Does “multiple steady states in a dynamic model” mean multiple equilibria of the full Arrow-Debreu general equilibrium model? And does “multiple rational-expectations equilibria” mean multiple equilibria conditional on the expectations of the agents? And I also am not sure what the import of this distinction is supposed to be.

My further question is, how does all of this relate to Leijonhfuvud’s idea of the corridor, which Roger has endorsed? My own understanding of what Axel means by the corridor is that the corridor has certain stability properties that keep the economy from careening out of control, i.e. becoming subject to a cumulative dynamic process that does not lead the economy back to the neighborhood of a stable equilibrium. But if there is a continuum of attracting points, each of which is an equilibrium, how could any of those points be understood to be outside the corridor?

Anyway, those are my questions. I am hoping that Roger can enlighten me.

CAUTION Accounting Identity Handle with Care

Published February 11, 2015 accounting identities , Hawtrey , Keynes , R. G. Lipsey , Scott Sumner 17 Comments
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About three years ago, early in my blogging career, I wrote a series of blog posts (most or all aimed at Scott Sumner) criticizing him for an argument in a blog post about the inefficacy of fiscal stimulus that relied on the definitional equality of savings and investment. Here’s the statement I found objectionable.

Wren-Lewis seems to be . . . making a simple logical error (which is common among Keynesians.)  He equates “spending” with “consumption.”  But the part of income not “spent” is saved, which means it’s spent on investment projects.  Remember that S=I, indeed saving is defined as the resources put into investment projects.  So the tax on consumers will reduce their ability to save and invest.

I’m not going to quote any further from that discussion. If you’re interested here are links to the posts that I wrote (here, here, here, here, here, and this one in which I made an argument so obviously false that, in my embarrassment, I felt like giving up blogging, and this one in which I managed to undo, at least partially, the damage of the self-inflicted wound). But, probably out of exhaustion, that discussion came to an inconclusive end, and Scott and I went on with our lives with no hard feelings.

Well, in a recent post, Scott has again invoked the savings-equals-investment identity, so I am going to have to lodge another protest, even though I thought that, aside from his unfortunate reference to the savings-investment identity, his post made a lot of sense. So I am going to raise the issue one more time – we have had three years to get over our last discussion – hoping that I can now convince Scott to stop using accounting identities to make causal statements.

Scott begins by discussing the simplest version of the income-expenditure model (aka the Keynesian cross or 45-degree model), while treating it, as did Keynes, as if it were interchangeable with the national-accounting identities:

In the standard national income accounting, gross domestic income equals gross domestic output.  In the simplest model of all (with no government or trade) you have the following identity:

NGDI = C + S = C + I = NGDP  (it also applies to RGDI and RGDP)

Because these two variables are identical, any model that explains one will, ipso facto, explain the other.

There is a lot of ground to cover in these few lines. First of all, there are actually three relevant variables — income, output, and expenditure – not just two. Second aggregate income is not really the same thing as consumption and savings. Aggregate income is constituted by the aggregate earnings of all factors of production. However, an accounting identity assures us that all factor incomes accruing to factors of production, which are all ultimately owned by the households providing services to business firms, must be disposed of either by being spent on consumption or by being saved. Aggregate expenditure is different from aggregate income; expenditure is constituted not by the earnings of households, but by their spending on consumption and by the spending of businesses on investment, the purchase of durable equipment not physically embodied in output sold to households or other businesses. Aggregate expenditure is very close to but not identical with aggregate output. They can differ, because not all output is sold, some of it being retained within the firm as work in progress or as inventory. However, in an equilibrium situation in which variables were unchanging, aggregate income, expenditure and output would all be equal.

The equality of these three variables can be thought of as a condition of macroeconomic equilibrium. When a macroeconomic system is not in equilibrium, aggregate factor incomes are not equal to aggregate expenditure or to aggregate output. The inequality between factor incomes and expenditure induces further adjustments in spending and earnings ultimately leading to an equilibrium in which equality between those variables is restored.

So what Scott should have said is that because NGDI and NGDP are equal in equilibrium, any model that explains one will, ipso facto, explain the other, because the equality between the two is the condition for finding a solution to the model. It therefore follows that savings and investment are absolutely not the same thing. Savings is the portion of household earnings from providing factor services that is not spent on consumption. Investment is what business firms spend on plant and equipment. The two magnitudes are obviously not the same, and they do not have to be equal. However, equality between savings and investment is, like the equality between income and expenditure, a condition for macroeconomic equilibrium. In an economy not in equilibrium, savings does not equal investment. But the inequality between savings and investment induces adjustments that, in a stable macroeconomic system, move the economy toward equilibrium. Back to Scott:

Nonetheless, I think if we focus on NGDI we are more likely to be able to think clearly about macro issues.  Consider the recent comment left by Doug:

Regarding Investment, changes in private investment are the single biggest dynamic in the business cycle. While I may be 1/4 the size of C in terms of the contribution to spending, it is 6x more volatile. The economy doesn’t slip into recession because of a fluctuation in Consumption. Changes in Investment drive AD.

This is probably how most people look at things, but in my view it’s highly misleading. Monetary policy drives AD, and AD drives investment. This is easier to explain if we think in terms of NGDI, not NGDP.  Tight money reduces NGDI.  That means the sum of nominal consumption and nominal saving must fall, by the amount that NGDI declines.  What about real income?  If wages are sticky, then as NGDI declines, hours worked will fall, and real income will decline.

So far we have no reason to assume that C or S will fall at a different rate than NGDI. But if real income falls for temporary reasons (the business cycle), then the public will typically smooth consumption.  Thus if NGDP falls by 4%, consumption might fall by 2% while saving might fall by something like 10%.  This is a prediction of the permanent income hypothesis.  And of course if saving falls much more sharply than gross income, investment will also decline sharply, because savings is exactly equal to investment.

First, I observe that consumption smoothing and the permanent-income hypothesis are irrelevant to the discussion, because Scott does not explain where any of his hypothetical numbers come from or how they are related. Based on commenter Doug’s suggestion that savings is ¼ the size of consumption, one could surmise that a 4% reduction in NGDP and a 2% reduction in consumption imply a marginal propensity to consumer of 0.4. Suppose that consumption did not change at all (consumption smoothing to the max), then savings, bearing the entire burden of adjustment, would fall through the floor. What would that imply for the new equilibrium of NGDI? In the standard Keynesian model, a zero marginal propensity to consume would imply a smaller effect on NGDP from a given shock than you get with an MPC of 0.4.

It seems to me that Scott is simply positing numbers and performing calculations independently of any model, and then tells us that the numbers have to to be what he says they are because of an accounting identity. That does not seem like an assertion not an argument, or, maybe like reasoning from a price change. Scott is trying to make an inference about how the world operates from an accounting identity between two magnitudes. The problem is that the two magnitudes are variables in an economic model, and their values are determined by the interaction of all the variables in the model. Just because you can solve the model mathematically by using the equality of two variables as an equilibrium condition does not entitle you to posit a change in one and then conclude that the other must change by the same amount. You have to show how the numbers you have posited are derived from the model.

If two variables are really identical, rather than just being equal in equilibrium, then they are literally the same thing, and you can’t draw any inference about the real world from the fact that they are equal, there being no possible state of the world in which they are not equal. It is only because savings and investment are not the same thing, and because in some states of the world they are not equal, that we can make any empirical statement about what the world is like when savings and investment are equal. Back to Scott:

This is where Keynesian economics has caused endless confusion.  Keynesians don’t deny that (ex post) less saving leads to less investment, but they think this claim is misleading, because (they claim) an attempt by the public to save less will boost NGDP, and this will lead to more investment (and more realized saving.)  In their model when the public attempts to save less (ex ante), it may well end up saving more (ex post.)

I agree that Keynesian economics has caused a lot of confusion about savings and investment, largely because Keynes, who, as a philosopher and a mathematician, should have known better, tied himself into knots by insisting that savings and investment are identical, while at the same time saying that their equality was brought about, not by variations in the rate of interest, but by variations in income. Hawtrey, Robertson, and Haberler, among others, pointed out the confusion, but Keynes never seemed to grasp the point. Textbook treatments of national-income accounting and the simple Keynesian cross still don’t seem to have figured this out. But despite his disdain for Keynesian economics, Scott still has to figure it out, too. The best place to start is Richard Lipsey’s classic article “The Foundations of the Theory of National Income: An Analysis of Some Fundamental Errors” (a gated link is available here).

Scott begins by sayings that Keynesians don’t deny that (ex post) less saving leads to less investment. I don’t understand that assertion at all; Keynesians believe that a desired increase in savings, if desired savings exceeded investment, leads to a decrease in income that reduces saving. But the abortive attempt to increase savings has no effect on investment unless you posit an investment function (AKA an accelerator) that includes income as an independent variable. The accelerator was later added to the basic Keynesian model Hicks and others in order to generate cyclical fluctuations in income and employment, but non-Keynesians like Ralph Hawtrey had discussed the accelerator model long before Keynes wrote the General Theory. Scott then contradicts himself in the next sentence by saying that Keynesians believe that by attempting to save less, the public may wind up saving more. Again this result relies on the assumption of an accelerator-type investment function, which is a non-Keynesian assumption. In the basic Keynesian model investment is determined by entrepreneurial expectations. An increase (decrease) in thrift will be self-defeating, because in the new equilibrium income will have fallen (risen) sufficiently to reduce (increase) savings back to the fixed amount of investment entrepreneurs planned to undertake, entrepreneurial expectations being held fixed over the relevant time period.

I more or less agree with the rest of Scott’s post, but Scott seems to have the same knee-jerk negative reaction to Keynes and Keynesians that I have to Friedman and Friedmanians. Maybe it’s time for both of us to lighten up a bit. Anyway in honor of Scott’s recent appoint to the Ralph Hawtrey Chair of Monetary Policy at the Mercatus Center at George Mason University, I will just close with this quotation from Ralph Hawtrey’s review of the General Theory (chapter 7 of Hawtrey’s Capital and Employment) about Keynes’s treatment of savings and investment as identically equal.

[A]n essential step in [Keynes’s] train of reasoning is the proposition that investment and saving are necessarily equal. That proposition Mr. Keynes never really establishes; he evades the necessity doing so by defining investment and saving as different names for the same thing. He so defines income to be the same thing as output, and therefore, if investment is the excess of output over consumption, and saving is the excess of income over consumption, the two are identical. Identity so established cannot prove anything. The idea that a tendency for investment and saving to become different has to be counteracted by an expansion or contraction of the total of incomes is an absurdity; such a tendency cannot strain the economic system, it can only strain Mr. Keynes’s vocabulary.

Temporary Equilibrium One More Time

Published September 23, 2014 expectations , intertemporal equilibrium , IS-LM , J. R. Hicks , Paul Krugman , rational expectations , temporary equilibrium 2 Comments
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It’s always nice to be noticed, especially by Paul Krugman. So I am not upset, but in his response to my previous post, I don’t think that Krugman quite understood what I was trying to convey. I will try to be clearer this time. It will be easiest if I just quote from his post and insert my comments or explanations.

Glasner is right to say that the Hicksian IS-LM analysis comes most directly not out of Keynes but out of Hicks’s own Value and Capital, which introduced the concept of “temporary equilibrium”.

Actually, that’s not what I was trying to say. I wasn’t making any explicit connection between Hicks’s temporary-equilibrium concept from Value and Capital and the IS-LM model that he introduced two years earlier in his paper on Keynes and the Classics. Of course that doesn’t mean that the temporary equilibrium method isn’t connected to the IS-LM model; one would need to do a more in-depth study than I have done of Hicks’s intellectual development to determine how much IS-LM was influenced by Hicks’s interest in intertemporal equilibrium and in the method of temporary equilibrium as a way of analyzing intertemporal issues.

This involves using quasi-static methods to analyze a dynamic economy, not because you don’t realize that it’s dynamic, but simply as a tool. In particular, V&C discussed at some length a temporary equilibrium in a three-sector economy, with goods, bonds, and money; that’s essentially full-employment IS-LM, which becomes the 1937 version with some price stickiness. I wrote about that a long time ago.

Now I do think that it’s fair to say that the IS-LM model was very much in the spirit of Value and Capital, in which Hicks deployed an explicit general-equilibrium model to analyze an economy at a Keynesian level of aggregation: goods, bonds, and money. But the temporary-equilibrium aspect of Value and Capital went beyond the Keynesian analysis, because the temporary equilibrium analysis was explicitly intertemporal, all agents formulating plans based on explicit future price expectations, and the inconsistency between expected prices and actual prices was explicitly noted, while in the General Theory, and in IS-LM, price expectations were kept in the background, making an appearance only in the discussion of the marginal efficiency of capital.

So is IS-LM really Keynesian? I think yes — there is a lot of temporary equilibrium in The General Theory, even if there’s other stuff too. As I wrote in the last post, one key thing that distinguished TGT from earlier business cycle theorizing was precisely that it stopped trying to tell a dynamic story — no more periods, forced saving, boom and bust, instead a focus on how economies can stay depressed. Anyway, does it matter? The real question is whether the method of temporary equilibrium is useful.

That is precisely where I think Krugman’s grasp on the concept of temporary equilibrium is slipping. Temporary equilibrium is indeed about periods, and it is explicitly dynamic. In my previous post I referred to Hicks’s discussion in Capital and Growth, about 25 years after writing Value and Capital, in which he wrote

The Temporary Equilibrium model of Value and Capital, also, is “quasi-static” [like the Keynes theory] – in just the same sense. The reason why I was contented with such a model was because I had my eyes fixed on Keynes.

As I read this passage now — and it really bothered me when I read it as I was writing my previous post — I realize that what Hicks was saying was that his desire to conform to the Keynesian paradigm led him to compromise the integrity of the temporary equilibrium model, by forcing it to be “quasi-static” when it really was essentially dynamic. The challenge has been to convert a “quasi-static” IS-LM model into something closer to the temporary-equilibrium method that Hicks introduced, but did not fully execute in Value and Capital.

What are the alternatives? One — which took over much of macro — is to do intertemporal equilibrium all the way, with consumers making lifetime consumption plans, prices set with the future rationally expected, and so on. That’s DSGE — and I think Glasner and I agree that this hasn’t worked out too well. In fact, economists who never learned temporary-equiibrium-style modeling have had a strong tendency to reinvent pre-Keynesian fallacies (cough-Say’s Law-cough), because they don’t know how to think out of the forever-equilibrium straitjacket.

Yes, I agree! Rational expectations, full-equilibrium models have turned out to be a regression, not an advance. But the way I would make the point is that the temporary-equilibrium method provides a sort of a middle way to do intertemporal dynamics without presuming that consumption plans and investment plans are always optimal.

What about disequilibrium dynamics all the way? Basically, I have never seen anyone pull this off. Like the forever-equilibrium types, constant-disequilibrium theorists have a remarkable tendency to make elementary conceptual mistakes.

Again, I agree. We can’t work without some sort of equilibrium conditions, but temporary equilibrium provides a way to keep the discipline of equilibrium without assuming (nearly) full optimality.

Still, Glasner says that temporary equilibrium must involve disappointed expectations, and fails to take account of the dynamics that must result as expectations are revised.

Perhaps I was unclear, but I thought I was saying just the opposite. It’s the “quasi-static” IS-LM model, not temporary equilibrium, that fails to take account of the dynamics produced by revised expectations.

I guess I’d say two things. First, I’m not sure that this is always true. Hicks did indeed assume static expectations — the future will be like the present; but in Keynes’s vision of an economy stuck in sustained depression, such static expectations will be more or less right.

Again, I agree. There may be self-fulfilling expectations of a low-income, low-employment equilibrium. But I don’t think that that is the only explanation for such a situation, and certainly not for the downturn that can lead to such an equilibrium.

Second, those of us who use temporary equilibrium often do think in terms of dynamics as expectations adjust. In fact, you could say that the textbook story of how the short-run aggregate supply curve adjusts over time, eventually restoring full employment, is just that kind of thing. It’s not a great story, but it is the kind of dynamics Glasner wants — and it’s Econ 101 stuff.

Again, I agree. It’s not a great story, but, like it or not, the story is not a Keynesian story.

So where does this leave us? I’m not sure, but my impression is that Krugman, in his admiration for the IS-LM model, is trying too hard to identify IS-LM with the temporary-equilibrium approach, which I think represented a major conceptual advance over both the Keynesian model and the IS-LM representation of the Keynesian model. Temporary equilibrium and IS-LM are not necessarily inconsistent, but I mainly wanted to point out that the two aren’t the same, and shouldn’t be conflated.

About Me

David Glasner
Washington, DC

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

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

Follow me on Twitter @david_glasner

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