Archive for the 'Axel Leijonfuvud' Category

Hayek and Temporary Equilibrium

In my three previous posts (here, here, and here) about intertemporal equilibrium, I have been emphasizing that the defining characteristic of an intertemporal equilibrium is that agents all share the same expectations of future prices – or at least the same expectations of those future prices on which they are basing their optimizing plans – over their planning horizons. At a given moment at which agents share the same expectations of future prices, the optimizing plans of the agents are consistent, because none of the agents would have any reason to change his optimal plan as long as price expectations do not change, or are not disappointed as a result of prices turning out to be different from what they had been expected to be.

The failure of expected prices to be fulfilled would therefore signify that the information available to agents in forming their expectations and choosing optimal plans conditional on their expectations had been superseded by newly obtained information. The arrival of new information can thus be viewed as a cause of disequilibrium as can any difference in information among agents. The relationship between information and equilibrium can be expressed as follows: differences in information or differences in how agents interpret information leads to disequilibrium, because those differences lead agents to form differing expectations of future prices.

Now the natural way to generalize the intertemporal equilibrium model is to allow for agents to have different expectations of future prices reflecting their differences in how they acquire, or in how they process, information. But if agents have different information, so that their expectations of future prices are not the same, the plans on which agents construct their subjectively optimal plans will be inconsistent and incapable of implementation without at least some revisions. But this generalization seems incompatible with the equilibrium of optimal plans, prices and price expectations described by Roy Radner, which I have identified as an updated version of Hayek’s concept of intertemporal equilibrium.

The question that I want to explore in this post is how to reconcile the absence of equilibrium of optimal plans, prices, and price expectations, with the intuitive notion of market clearing that we use to analyze asset markets and markets for current delivery. If markets for current delivery and for existing assets are in equilibrium in the sense that prices are adjusting in those markets to equate demand and supply in those markets, how can we understand the idea that  the optimizing plans that agents are seeking to implement are mutually inconsistent?

The classic attempt to explain this intermediate situation which partially is and partially is not an equilibrium, was made by J. R. Hicks in 1939 in Value and Capital when he coined the term “temporary equilibrium” to describe a situation in which current prices are adjusting to equilibrate supply and demand in current markets even though agents are basing their choices of optimal plans to implement over time on different expectations of what prices will be in the future. The divergence of the price expectations on the basis of which agents choose their optimal plans makes it inevitable that some or all of those expectations won’t be realized, and that some, or all, of those agents won’t be able to implement the optimal plans that they have chosen, without at least some revisions.

In Hayek’s early works on business-cycle theory, he argued that the correct approach to the analysis of business cycles must be analyzed as a deviation by the economy from its equilibrium path. The problem that he acknowledged with this approach was that the tools of equilibrium analysis could be used to analyze the nature of the equilibrium path of an economy, but could not easily be deployed to analyze how an economy performs once it deviates from its equilibrium path. Moreover, cyclical deviations from an equilibrium path tend not to be immediately self-correcting, but rather seem to be cumulative. Hayek attributed the tendency toward cumulative deviations from equilibrium to the lagged effects of monetary expansion which cause cumulative distortions in the capital structure of the economy that lead at first to an investment-driven expansion of output, income and employment and then later to cumulative contractions in output, income, and employment. But Hayek’s monetary analysis was never really integrated with the equilibrium analysis that he regarded as the essential foundation for a theory of business cycles, so the monetary analysis of the cycle remained largely distinct from, if not inconsistent with, the equilibrium analysis.

I would suggest that for Hayek the Hicksian temporary-equilibrium construct would have been the appropriate theoretical framework within which to formulate a monetary analysis consistent with equilibrium analysis. Although there are hints in the last part of The Pure Theory of Capital that Hayek was thinking along these lines, I don’t believe that he got very far, and he certainly gave no indication that he saw in the Hicksian method the analytical tool with which to weave the two threads of his analysis.

I will now try to explain how the temporary-equilibrium method makes it possible to understand  the conditions for a cumulative monetary disequilibrium. I make no attempt to outline a specifically Austrian or Hayekian theory of monetary disequilibrium, but perhaps others will find it worthwhile to do so.

As I mentioned in my previous post, agents understand that their price expectations may not be realized, and that their plans may have to be revised. Agents also recognize that, given the uncertainty underlying all expectations and plans, not all debt instruments (IOUs) are equally reliable. The general understanding that debt – promises to make future payments — must be evaluated and assessed makes it profitable for some agents to specialize in in debt assessment. Such specialists are known as financial intermediaries. And, as I also mentioned previously, the existence of financial intermediaries cannot be rationalized in the ADM model, because, all contracts being made in period zero, there can be no doubt that the equilibrium exchanges planned in period zero will be executed whenever and exactly as scheduled, so that everyone’s promise to pay in time zero is equally good and reliable.

For our purposes, a particular kind of financial intermediary — banks — are of primary interest. The role of a bank is to assess the quality of the IOUs offered by non-banks, and select from the IOUs offered to them those that are sufficiently reliable to be accepted by the bank. Once a prospective borrower’s IOU is accepted, the bank exchanges its own IOU for the non-bank’s IOU. No non-bank would accept a non-bank’s IOU, at least not on terms as favorable as those on which the bank offers in accepting an IOU. In return for the non-bank IOU, the bank credits the borrower with a corresponding amount of its own IOUs, which, because the bank promises to redeem its IOUs for the numeraire commodity on demand, is generally accepted at face value.

Thus, bank debt functions as a medium of exchange even as it enables non-bank agents to make current expenditures they could not have made otherwise if they can demonstrate to the bank that they are sufficiently likely to repay the loan in the future at agreed upon terms. Such borrowing and repayments are presumably similar to the borrowing and repayments that would occur in the ADM model unmediated by any financial intermediary. In assessing whether a prospective borrower will repay a loan, the bank makes two kinds of assessments. First, does the borrower have sufficient income-earning capacity to generate enough future income to make the promised repayments that the borrower would be committing himself to make? Second, should the borrower’s future income, for whatever reason, turn out to be insufficient to finance the promised repayments, does the borrower have collateral that would allow the bank to secure repayment from the collateral offered as security? In making both kinds of assessments the bank has to form an expectation about the future — the future income of the borrower and the future value of the collateral.

In a temporary-equilibrium context, the expectations of future prices held by agents are not the same, so the expectations of future prices of at least some agents will not be accurate, and some agents won’tbe able to execute their plans as intended. Agents that can’t execute their plans as intended are vulnerable if they have incurred future obligations based on their expectations of future prices that exceed their repayment capacity given the future prices that are actually realized. If they have sufficient wealth — i.e., if they have asset holdings of sufficient value — they may still be able to repay their obligations. However, in the process they may have to sell assets or reduce their own purchases, thereby reducing the income earned by other agents. Selling assets under pressure of obligations coming due is almost always associated with selling those assets at a significant loss, which is precisely why it usually preferable to finance current expenditure by borrowing funds and making repayments on a fixed schedule than to finance the expenditure by the sale of assets.

Now, in adjusting their plans when they observe that their price expectations are disappointed, agents may respond in two different ways. One type of adjustment is to increase sales or decrease purchases of particular goods and services that they had previously been planning to purchase or sell; such marginal adjustments do not fundamentally alter what agents are doing and are unlikely to seriously affect other agents. But it is also possible that disappointed expectations will cause some agents to conclude that their previous plans are no longer sustainable under the conditions in which they unexpectedly find themselves, so that they must scrap their old plans replacing them with completely new plans instead. In the latter case, the abandonment of plans that are no longer viable given disappointed expectations may cause other agents to conclude that the plans that they had expected to implement are no longer profitable and must be scrapped.

When agents whose price expectations have been disappointed respond with marginal adjustments in their existing plans rather than scrapping them and replacing them with new ones, a temporary equilibrium with disappointed expectations may still exist and that equilibrium may be reached through appropriate price adjustments in the markets for current delivery despite the divergent expectations of future prices held by agents. Operation of the price mechanism may still be able to achieve a reconciliation of revised but sub-optimal plans. The sub-optimal temporary equilibrium will be inferior to the allocation that would have resulted had agents all held correct expectations of future prices. Nevertheless, given a history of incorrect price expectations and misallocations of capital assets, labor, and other factors of production, a sub-optimal temporary equilibrium may be the best feasible outcome.

But here’s the problem. There is no guarantee that, when prices turn out to be very different from what they were expected to be, the excess demands of agents will adjust smoothly to changes in current prices. A plan that was optimal based on the expectation that the price of widgets would be $500 a unit may well be untenable at a price of $120 a unit. When realized prices are very different from what they had been expected to be, those price changes can lead to discontinuous adjustments, violating a basic assumption — the continuity of excess demand functions — necessary to prove the existence of an equilibrium. Once output prices reach some minimum threshold, the best response for some firms may be to shut down, the excess demand for the product produced by the firm becoming discontinuous at the that threshold price. The firms shutting down operations may be unable to repay loans they had obligated themselves to repay based on their disappointed price expectations. If ownership shares in firms forced to cease production are held by households that have predicated their consumption plans on prior borrowing and current repayment obligations, the ability of those households to fulfill their obligations may be compromised once those firms stop paying out the expected profit streams. Banks holding debts incurred by firms or households that borrowers cannot service may find that their own net worth is reduced sufficiently to make the banks’ own debt unreliable, potentially causing a breakdown in the payment system. Such effects are entirely consistent with a temporary-equilibrium model if actual prices turn out to be very different from what agents had expected and upon which they had constructed their future consumption and production plans.

Sufficiently large differences between expected and actual prices in a given period may result in discontinuities in excess demand functions once prices reach critical thresholds, thereby violating the standard continuity assumptions on which the existence of general equilibrium depends under the fixed-point theorems that are the lynchpin of modern existence proofs. C. J. Bliss made such an argument in a 1983 paper (“Consistent Temporary Equilibrium” in the volume Modern Macroeconomic Theory edited by  J. P. Fitoussi) in which he also suggested, as I did above, that the divergence of individual expectations implies that agents will not typically regard the debt issued by other agents as homogeneous. Bliss therefore posited the existence of a “Financier” who would subject the borrowing plans of prospective borrowers to an evaluation process to determine if the plan underlying the prospective loan sought by a borrower was likely to generate sufficient cash flow to enable the borrower to repay the loan. The role of the Financier is to ensure that the plans that firms choose are based on roughly similar expectations of future prices so that firms will not wind up acting on price expectations that must inevitably be disappointed.

I am unsure how to understand the function that Bliss’s Financier is supposed to perform. Presumably the Financier is meant as a kind of idealized companion to the Walrasian auctioneer rather than as a representation of an actual institution, but the resemblance between what the Financier is supposed to do and what bankers actually do is close enough to make it unclear to me why Bliss chose an obviously fictitious character to weed out business plans based on implausible price expectations rather than have the role filled by more realistic characters that do what their real-world counterparts are supposed to do. Perhaps Bliss’s implicit assumption is that real-world bankers do not constrain the expectations of prospective borrowers sufficiently to suggest that their evaluation of borrowers would increase the likelihood that a temporary equilibrium actually exists so that only an idealized central authority could impose sufficient consistency on the price expectations to make the existence of a temporary equilibrium likely.

But from the perspective of positive macroeconomic and business-cycle theory, explicitly introducing banks that simultaneously provide an economy with a medium of exchange – either based on convertibility into a real commodity or into a fiat base money issued by the monetary authority – while intermediating between ultimate borrowers and ultimate lenders seems to be a promising way of modeling a dynamic economy that sometimes may — and sometimes may not — function at or near a temporary equilibrium.

We observe economies operating in the real world that sometimes appear to be functioning, from a macroeconomic perspective, reasonably well with reasonably high employment, increasing per capita output and income, and reasonable price stability. At other times, these economies do not function well at all, with high unemployment and negative growth, sometimes with high rates of inflation or with deflation. Sometimes, these economies are beset with financial crises in which there is a general crisis of solvency, and even apparently solvent firms are unable to borrow. A macroeconomic model should be able to account in some way for the diversity of observed macroeconomic experience. The temporary equilibrium paradigm seems to offer a theoretical framework capable of accounting for this diversity of experience and for explaining at least in a very general way what accounts for the difference in outcomes: the degree of congruence between the price expectations of agents. When expectations are reasonably consistent, the economy is able to function at or near a temporary equilibrium which is likely to exist. When expectations are highly divergent, a temporary equilibrium may not exist, and even if it does, the economy may not be able to find its way toward the equilibrium. Price adjustments in current markets may be incapable of restoring equilibrium inasmuch as expectations of future prices must also adjust to equilibrate the economy, there being no market mechanism by which equilibrium price expectations can be adjusted or restored.

This, I think, is the insight underlying Axel Leijonhufvud’s idea of a corridor within which an economy tends to stay close to an equilibrium path. However if the economy drifts or is shocked away from its equilibrium time path, the stabilizing forces that tend to keep an economy within the corridor cease to operate at all or operate only weakly, so that the tendency for the economy to revert back to its equilibrium time path is either absent or disappointingly weak.

The temporary-equilibrium method, it seems to me, might have been a path that Hayek could have successfully taken in pursuing the goal he had set for himself early in his career: to reconcile equilibrium-analysis with a theory of business cycles. Why he ultimately chose not to take this path is a question that, for now at least, I will leave to others to try to answer.

The Free Market Economy Is Awesome and Fragile

Scott Sumner’s three most recent posts (here, here, and here)have been really great, and I’ld like to comment on all of them. I will start with a comment on his post discussing whether the free market economy is stable; perhaps I will get around to the other two next week. Scott uses a 2009 paper by Robert Hetzel as the starting point for his discussion. Hetzel distinguishes between those who view the stabilizing properties of price adjustment as being overwhelmed by real instabilities reflecting fluctuations in consumer and entrepreneurial sentiment – waves of optimism and pessimism – and those who regard the economy as either perpetually in equilibrium (RBC theorists) or just usually in equilibrium (Monetarists) unless destabilized by monetary shocks. Scott classifies himself, along with Hetzel and Milton Friedman, in the latter category.

Scott then brings Paul Krugman into the mix:

Friedman, Hetzel, and I all share the view that the private economy is basically stable, unless disturbed by monetary shocks. Paul Krugman has criticized this view, and indeed accused Friedman of intellectual dishonesty, for claiming that the Fed caused the Great Depression. In Krugman’s view, the account in Friedman and Schwartz’s Monetary History suggests that the Depression was caused by an unstable private economy, which the Fed failed to rescue because of insufficiently interventionist monetary policies. He thinks Friedman was subtly distorting the message to make his broader libertarian ideology seem more appealing.

This is a tricky topic for me to handle, because my own view of what happened in the Great Depression is in one sense similar to Friedman’s – monetary policy, not some spontaneous collapse of the private economy, was what precipitated and prolonged the Great Depression – but Friedman had a partial, simplistic and distorted view of how and why monetary policy failed. And although I believe Friedman was correct to argue that the Great Depression did not prove that the free market economy is inherently unstable and requires comprehensive government intervention to keep it from collapsing, I think that his account of the Great Depression was to some extent informed by his belief that his own simple k-percent rule for monetary growth was a golden bullet that would ensure economic stability and high employment.

I’d like to first ask a basic question: Is this a distinction without a meaningful difference? There are actually two issues here. First, does the Fed always have the ability to stabilize the economy, or does the zero bound sometimes render their policies impotent?  In that case the two views clearly do differ. But the more interesting philosophical question occurs when not at the zero bound, which has been the case for all but one postwar recession. In that case, does it make more sense to say the Fed caused a recession, or failed to prevent it?

Here’s an analogy. Someone might claim that LeBron James is a very weak and frail life form, whose legs will cramp up during basketball games without frequent consumption of fluids. Another might suggest that James is a healthy and powerful athlete, who needs to drink plenty of fluids to perform at his best during basketball games. In a sense, both are describing the same underlying reality, albeit with very different framing techniques. Nonetheless, I think the second description is better. It is a more informative description of LeBron James’s physical condition, relative to average people.

By analogy, I believe the private economy in the US is far more likely to be stable with decent monetary policy than is the economy of Venezuela (which can fall into depression even with sufficiently expansionary monetary policy, or indeed overly expansionary policies.)

I like Scott’s LeBron James analogy, but I have two problems with it. First, although LeBron James is a great player, he’s not perfect. Sometimes, even he messes up. When he messes up, it may not be his fault, in the sense that, with better information or better foresight – say, a little more rest in the second quarter – he might have sunk the game-winning three-pointer at the buzzer. Second, it’s one thing to say that a monetary shock caused the Great Depression, but maybe we just don’t know how to avoid monetary shocks. LeBron can miss shots, so can the Fed. Milton Friedman certainly didn’t know how to avoid monetary shocks, because his pet k-percent rule, as F. A. Hayek shrewdly observed, was a simply a monetary shock waiting to happen. And John Taylor certainly doesn’t know how to avoid monetary shocks, because his pet rule would have caused the Fed to raise interest rates in 2011 with possibly devastating consequences. I agree that a nominal GDP level target would have resulted in a monetary policy superior to the policy the Fed has been conducting since 2008, but do I really know that? I am not sure that I do. The false promise held out by Friedman was that it is easy to get monetary policy right all the time. It certainly wasn’t the case for Friedman’s pet rule, and I don’t think that there is any monetary rule out there that we can be sure will keep us safe and secure and fully employed.

But going beyond the LeBron analogy, I would make a further point. We just have no theoretical basis for saying that the free-market economy is stable. We can prove that, under some assumptions – and it is, to say the least, debatable whether the assumptions could properly be described as reasonable – a model economy corresponding to the basic neoclassical paradigm can be solved for an equilibrium solution. The existence of an equilibrium solution means basically that the neoclassical model is logically coherent, not that it tells us much about how any actual economy works. The pieces of the puzzle could all be put together in a way so that everything fits, but that doesn’t mean that in practice there is any mechanism whereby that equilibrium is ever reached or even approximated.

The argument for the stability of the free market that we learn in our first course in economics, which shows us how price adjusts to balance supply and demand, is an argument that, when every market but one – well, actually two, but we don’t have to quibble about it – is already in equilibrium, price adjustment in the remaining market – if it is small relative to the rest of the economy – will bring that market into equilibrium as well. That’s what I mean when I refer to the macrofoundations of microeconomics. But when many markets are out of equilibrium, even the markets that seem to be equilibrium (with amounts supplied and demanded equal) are not necessarily in equilibrium, because the price adjustments in other markets will disturb the seeming equilibrium of the markets in which supply and demand are momentarily equal. So there is not necessarily any algorithm, either in theory or in practice, by which price adjustments in individual markets would ever lead the economy into a state of general equilibrium. If we believe that the free market economy is stable, our belief is therefore not derived from any theoretical proof of the stability of the free market economy, but simply on an intuition, and some sort of historical assessment that free markets tend to work well most of the time. I would just add that, in his seminal 1937 paper, “Economics and Knowledge,” F. A. Hayek actually made just that observation, though it is not an observation that he, or most of his followers – with the notable and telling exceptions of G. L. S. Shackle and Ludwig Lachmann – made a big fuss about.

Axel Leijonhufvud, who is certainly an admirer of Hayek, addresses the question of the stability of the free-market economy in terms of what he calls a corridor. If you think of an economy moving along a time path, and if you think of the time path that would be followed by the economy if it were operating at a full-employment equilibrium, Leijonjhufvud’s corridor hypothesis is that the actual time path of the economy tends to revert to the equilibrium time path as long as deviations from the equilibrium are kept within certain limits, those limits defining the corridor. However, if the economy, for whatever reasons (exogenous shocks or some other mishaps) leaves the corridor, the spontaneous equilibrating tendencies causing the actual time path to revert back to the equilibrium time path may break down, and there may be no further tendency for the economy to revert back to its equilibrium time path. And as I pointed out recently in my post on Earl Thompson’s “Reformulation of Macroeconomic Theory,” he was able to construct a purely neoclassical model with two potential equilibria, one of which was unstable so that a shock form the lower equilibrium would lead either to a reversion to the higher-level equilibrium or to downward spiral with no endogenous stopping point.

Having said all that, I still agree with Scott’s bottom line: if the economy is operating below full employment, and inflation and interest rates are low, there is very likely a problem with monetary policy.

Roger and Me

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.

Aggregate Demand and Coordination Failures

Regular readers of this blog may have noticed that I have been writing less about monetary policy and more about theory and methodology than when I started blogging a little over three years ago. Now one reason for that is that I’ve already said what I want to say about policy, and, since I get bored easily, I look for new things to write about. Another reason is that, at least in the US, the economy seems to have reached a sustainable growth path that seems likely to continue for the near to intermediate term. I think that monetary policy could be doing more to promote recovery, and I wish that it would, but unfortunately, the policy is what it is, and it will continue more or less in the way that Janet Yellen has been saying it will. Falling oil prices, because of increasing US oil output, suggest that growth may speed up slightly even as inflation stays low, possibly even falling to one percent or less. At least in the short-term, the fall in inflation does not seem like a cause for concern. A third reason for writing less about monetary policy is that I have been giving a lot of thought to what it is that I dislike about the current state of macroeconomics, and as I have been thinking about it, I have been writing about it.

In thinking about what I think is wrong with modern macroeconomics, I have been coming back again and again, though usually without explicit attribution, to an idea that was impressed upon me as an undergrad and grad student by Axel Leijonhufvud: that the main concern of macroeconomics ought to be with failures of coordination. A Swede, trained in the tradition of the Wicksellian Stockholm School, Leijonhufvud immersed himself in the study of the economics of Keynes and Keynesian economics, while also mastering the Austrian literature, and becoming an admirer of Hayek, especially Hayek’s seminal 1937 paper, “Economics and Knowledge.”

In discussing Keynes, Leijonhufvud focused on two kinds of coordination failures.

First, there is a problem in the labor market. If there is unemployment because the real wage is too high, an individual worker can’t solve the problem by offering to accept a reduced nominal wage. Suppose the price of output is $1 a unit and the wage is $10 a day, but the real wage consistent with full employment is $9 a day, meaning that producers choose to produce less output than they would produce if the real wage were lower, thus hiring fewer workers than they would if the real wage were lower than it is. If an individual worker offers to accept a wage of $9 a day, but other workers continue to hold out for $10 a day, it’s not clear that an employer would want to hire the worker who offers to work for $9 a day. If employers are not hiring additional workers because they can’t cover the cost of the additional output produced with the incremental revenue generated by the added output, the willingness of one worker to work for $9 a day is not likely to make a difference to the employer’s output and hiring decisions. It is not obvious what sequence of transactions would result in an increase in output and employment when the real wage is above the equilibrium level. There are complex feedback effects from a change, so that the net effect of making those changes in a piecemeal fashion is unpredictable, even though there is a possible full-employment equilibrium with a real wage of $9 a day. If the problem is that real wages in general are too high for full employment, the willingness of an individual worker to accept a reduced wage from a single employer does not fix the problem.

In the standard competitive model, there is a perfect market for every commodity in which every transactor is assumed to be able to buy and sell as much as he wants. But the standard competitive model has very little to say about the process by which those equilibrium prices are arrived at. And a typical worker is never faced with that kind of choice posited in the competitive model: an impersonal uniform wage at which he can decide how many hours a day or week or year he wants to work at that uniform wage. Under those circumstances, Keynes argued that the willingness of some workers to accept wage cuts in order to gain employment would not significantly increase employment, and might actually have destabilizing side-effects. Keynes tried to make this argument in the framework of an equilibrium model, though the nature of the argument, as Don Patinkin among others observed, was really better suited to a disequilibrium framework. Unfortunately, Keynes’s argument was subsequently dumbed down to a simple assertion that wages and prices are sticky (especially downward).

Second, there is an intertemporal problem, because the interest rate may be stuck at a rate too high to allow enough current investment to generate the full-employment level of spending given the current level of the money wage. In this scenario, unemployment isn’t caused by a real wage that is too high, so trying to fix it by wage adjustment would be a mistake. Since the source of the problem is the rate of interest, the way to fix the problem would be to reduce the rate of interest. But depending on the circumstances, there may be a coordination failure: bear speculators, expecting the rate of interest to rise when it falls to abnormally low levels, prevent the rate of interest from falling enough to induce enough investment to support full employment. Keynes put too much weight on bear speculators as the source of the intertemporal problem; Hawtrey’s notion of a credit deadlock would actually have been a better way to go, and nowadays, when people speak about a Keynesian liquidity trap, what they really have in mind is something closer to Hawtreyan credit deadlock than to the Keynesian liquidity trap.

Keynes surely deserves credit for identifying and explaining two possible sources of coordination failures, failures affecting the macroeconomy, because interest rates and wages, though they actually come in many different shapes and sizes, affect all markets and are true macroeconomic variables. But Keynes’s analysis of those coordination failures was far from being fully satisfactory, which is not surprising; a theoretical pioneer rarely provides a fully satisfactory analysis, leaving lots of work for successors.

But I think that Keynes’s theoretical paradigm actually did lead macroeconomics in the wrong direction, in the direction of a highly aggregated model with a single output, a bond, a medium of exchange, and a labor market, with no explicit characterization of the production technology. (I.e., is there one factor or two, and if two how is the price of the second factor determined? See, here, here, here, and here my discussion of Earl Thompson’s “A Reformulation of Macroeconomic Theory,” which I hope at some point to revisit and continue.)

Why was it the wrong direction? Because, the Keynesian model (both Keynes’s own version and the Hicksian IS-LM version of his model) ruled out the sort of coordination problems that might arise in a multi-product, multi-factor, intertemporal model in which total output depends in a meaningful way on the meshing of the interdependent plans, independently formulated by decentralized decision-makers, contingent on possibly inconsistent expectations of the future. In the over-simplified and over-aggregated Keynesian model, the essence of the coordination problem has been assumed away, leaving only a residue of the actual problem to be addressed by the model. The focus of the model is on aggregate expenditure, income, and output flows, with no attention paid to the truly daunting task of achieving sufficient coordination among the independent decision makers to allow total output and income to closely approximate the maximum sustainable output and income that the system could generate in a perfectly coordinated state, aka full intertemporal equilibrium.

This way of thinking about macroeconomics led to the merging of macroeconomics with neoclassical growth theory and to the routine and unthinking incorporation of aggregate production functions in macroeconomic models, a practice that is strictly justified only in a single-output, two-factor model in which the value of capital is independent of the rate of interest, so that the havoc-producing effects of reswitching and capital-reversal can be avoided. Eventually, these models were taken over by modern real-business-cycle theorists, who dogmatically rule out any consideration of coordination problems, while attributing all observed output and employment fluctuations to random productivity shocks. If one thinks of macroeconomics as an attempt to understand coordination failures, the RBC explanation of output and employment fluctuations is totally backwards; productivity fluctuations, like fluctuations in output and employment, are the not the results of unexplained random disturbances, they are the symptoms of coordination failures. That’s it, eureka! Solve the problem by assuming that it does not exist.

If you are thinking that this seems like an Austrian critique of the Keynesian model or the Keynesian approach, you are right; it is an Austrian critique. But it has nothing to do with stereotypical Austrian policy negativism; it is a critique of the oversimplified structure of the Keynesian model, which foreshadowed the reduction ad absurdum or modern real-business-cycle theory, which has nearly banished the idea of coordination failures from modern macroeconomics. The critique is not about the lack of a roundabout capital structure; it is about the narrow scope for inconsistencies in production and consumption plans.

I think that Leijonhufvud almost 40 years ago was getting at this point when he wrote the following paragraph near toward end of his book on Keynes.

The unclear mix of statics and dynamics [in the General Theory] would seem to be main reason for later muddles. One cannot assume that what went wrong was simply that Keynes slipped up here and there in his adaptation of standard tools, and that consequently, if we go back and tinker a little more with the Marshallian toolbox his purposes will be realized. What is required, I believe, is a systematic investigation from the standpoint of the information problems stressed in this study, of what elements of the static theory of resource allocation can without further ado be utilized in the analysis of dynamic and historical systems. This, of course, would be merely a first step: the gap yawns very wide between the systematic and rigorous modern analysis of the stability of simple, “featureless,” pure exchange systems and Keynes’ inspired sketch of the income-constrained process in a monetary exchange-cum production system. But even for such a first step, the prescription cannot be to “go back to Keynes.” If one must retrace some step of past developments in order to get on the right track – and that is probably advisable – my own preference is to go back to Hayek. Hayek’s Gestalt-conception of what happens during business cycles, it has been generally agreed, was much less sound that Keynes’. As an unhappy consequence, his far superior work on the fundamentals of the problem has not received the attention it deserves. (pp. 401-02)

I don’t think that we actually need to go back to Hayek, though “Economics and Knowledge” should certainly be read by every macroeconomist, but we do need to get a clearer understanding of the potential for breakdowns in economic activity to be caused by inconsistent expectations, especially when expectations are themselves mutually dependent and reinforcing. Because expectations are mutually interdependent, they are highly susceptible to network effects. Network effects produce tipping points, tipping points can lead to catastrophic outcomes. Just wanted to share that with you. Have a nice day.

Never Reason from a Disequilibrium

One of Scott Sumner’s many contributions as a blogger has been to show over and over and over again how easy it is to lapse into fallacious economic reasoning by positing a price change and then trying to draw inferences about the results of the price change. The problem is that a price change doesn’t just happen; it is the result of some other change. There being two basic categories of changes (demand and supply) that can affect price, there are always at least two possible causes for a given price change. So, until you have specified the antecedent change responsible for the price change under consideration, you can’t work out the consequences of the price change.

In this post, I want to extend Scott’s insight in a slightly different direction, and explain how every economic analysis has to begin with a statement about the initial conditions from which the analysis starts. In particular, you need to be clear about the equilibrium position corresponding to the initial conditions from which you are starting. If you posit some change in the system, but your starting point isn’t an equilibrium, you have no way of separating out the adjustment to the change that you are imposing on the system from the change the system would be undergoing simply to reach the equilibrium toward which it is already moving, or, even worse, from the change the system would be undergoing if its movement is not toward equilibrium.

Every theoretical analysis in economics properly imposes a ceteris paribus condition. Unfortunately, the ubiquitous ceteris paribus condition comes dangerously close to rendering economic theory irrefutable, except perhaps in a statistical sense, because empirical refutations of the theory can always be attributed to changes, abstracted from only in the theory, but not in the real world of our experience. An empirical model with a sufficient number of data points may be able to control for the changes in conditions that the theory holds constant, but the underlying theory is a comparison of equilibrium states (comparative statics), and it is quite a stretch to assume that the effects of perpetual disequilibrium can be treated as nothing but white noise. Austrians are right to be skeptical of econometric analysis; so was Keynes, for that matter. But skepticism need not imply nihilism.

Let me try to illustrate this principle by applying it to the Keynesian analysis of involuntary unemployment. In the General Theory Keynes argued that if adequate demand is deficient, the likely result is an equilibrium with involuntary unemployment. The “classical” argument that Keynes disputed was that, in principle at least, involuntary unemployment could not persist, because unemployed workers, if only they would accept reduced money wages, would eventually find employment. Keynes denied that involuntary unemployment could not persist, arguing that if workers did accept reduced money wages, the wage reductions would not get translated into reduced real wages. Instead, falling nominal wages would induce employers to cut prices by roughly the same percentage as the reduction in nominal wages, leaving real wages more or less unchanged, thereby nullifying the effectiveness of nominal-wage cuts, and, instead, fueling a vicious downward spiral of prices and wages.

In making this argument, Keynes didn’t dispute the neoclassical proposition that, with a given capital stock, the marginal product of labor declines as employment increases, implying that real wages have to fall for employment to be increased. His argument was about the nature of the labor-supply curve, labor supply, in Keynes’s view, being a function of both the real and the nominal wage, not, as in the neoclassical theory, only the real wage. Under Keynes’s “neoclassical” analysis, the problem with nominal-wage cuts is that they don’t do the job, because they lead to corresponding price cuts. The only way to reduce unemployment, Keynes insisted, is to raise the price level. With nominal wages constant, an increased price level would achieve the real-wage cut necessary for employment to be increased. And this is precisely how Keynes defined involuntary unemployment: the willingness of workers to increase the amount of labor actually supplied in response to a price level increase that reduces their real wage.

Interestingly, in trying to explain why nominal-wage cuts would fail to increase employment, Keynes suggested that the redistribution of income from workers to entrepreneurs associated with reduced nominal wages would tend to reduce consumption, thereby reducing, not increasing, employment. But if that is so, how is it that a reduced real wage, achieved via inflation, would increase employment? Why would the distributional effect of a reduced nominal, but unchanged real, wage be more adverse to employment han a reduced real wage, achieved, with a fixed nominal wage, by way of a price-level increase?

Keynes’s explanation for all this is confused. In chapter 19, where he makes the argument that money-wage cuts can’t eliminate involuntary unemployment, he presents a variety of reasons why nominal-wage cuts are ineffective, and it is usually not clear at what level of theoretical abstraction he is operating, and whether he is arguing that nominal-wage cuts would not work even in principle, or that, although nominal-wage cuts might succeed in theory, they would inevitably fail in practice. Even more puzzling, It is not clear whether he thinks that real wages have to fall to achieve full employment or that full employment could be restored by an increase in aggregate demand with no reduction in real wages. In particular, because Keynes doesn’t start his analysis from a full-employment equilibrium, and doesn’t specify the shock that moves the economy off its equilibrium position, we can only guess whether Keynes is talking about a shock that had reduced labor productivity or (more likely) a shock to entrepreneurial expectations (animal spirits) that has no direct effect on labor productivity.

There was a rhetorical payoff for Keynes in maintaining that ambiguity, because he wanted to present a “general theory” in which full employment is a special case. Keynes therefore emphasized that the labor market is not self-equilibrating by way of nominal-wage adjustments. That was a perfectly fine and useful insight: when the entire system is out of kilter; there is no guarantee that just letting the free market set prices will bring everything back into place. The theory of price adjustment is fundamentally a partial-equilibrium theory that isolates the disequiibrium of a single market, with all other markets in (approximate) equilibrium. There is no necessary connection between the adjustment process in a partial-equilibrium setting and the adjustment process in a full-equilibrium setting. The stability of a single market in disequilibrium does not imply the stability of the entire system of markets in disequilibrium. Keynes might have presented his “general theory” as a theory of disequilibrium, but he preferred (perhaps because he had no other tools to work with) to spell out his theory in terms of familiar equilibrium concepts: savings equaling investment and income equaling expenditure, leaving it ambiguous whether the failure to reach a full-employment equilibrium is caused by a real wage that is too high or an interest rate that is too high. Axel Leijonhufvud highlights the distinction between a disequilibrium in the real wage and a disequilibrium in the interest rate in an important essay “The Wicksell Connection” included in his book Information and Coordination.

Because Keynes did not commit himself on whether a reduction in the real wage is necessary for equilibrium to be restored, it is hard to assess his argument about whether, by accepting reduced money wages, workers could in fact reduce their real wages sufficiently to bring about full employment. Keynes’s argument that money-wage cuts accepted by workers would be undone by corresponding price cuts reflecting reduced production costs is hardly compelling. If the current level of money wages is too high for firms to produce profitably, it is not obvious why the reduced money wages paid by entrepreneurs would be entirely dissipated by price reductions, with none of the cost decline being reflected in increased profit margins. If wage cuts do increase profit margins, that would encourage entrepreneurs to increase output, potentially triggering an expansionary multiplier process. In other words, if the source of disequilibrium is that the real wage is too high, the real wage depending on both the nominal wage and price level, what is the basis for concluding that a reduction in the nominal wage would cause a change in the price level sufficient to keep the real wage at a disequilibrium level? Is it not more likely that the price level would fall no more than required to bring the real wage back to the equilibrium level consistent with full employment? The question is not meant as an expression of policy preference; it is a question about the logic of Keynes’s analysis.

Interestingly, present-day opponents of monetary stimulus (for whom “Keynesian” is a term of extreme derision) like to make a sort of Keynesian argument. Monetary stimulus, by raising the price level, reduces the real wage. That means that monetary stimulus is bad, as it is harmful to workers, whose interests, we all know, is the highest priority – except perhaps the interests of rentiers living off the interest generated by their bond portfolios — of many opponents of monetary stimulus. Once again, the logic is less than compelling. Keynes believed that an increase in the price level could reduce the real wage, a reduction that, at least potentially, might be necessary for the restoration of full employment.

But here is my question: why would an increase in the price level reduce the real wage rather than raise money wages along with the price level. To answer that question, you need to have some idea of whether the current level of real wages is above or below the equilibrium level. If unemployment is high, there is at least some reason to think that the equilibrium real wage is less than the current level, which is why an increase in the price level would be expected to cause the real wage to fall, i.e., to move the actual real wage in the direction of equilibrium. But if the current real wage is about equal to, or even below, the equilibrium level, then why would one think that an increase in the price level would not also cause money wages to rise correspondingly? It seems more plausible that, in the absence of a good reason to think otherwise, that inflation would cause real wages to fall only if real wages are above their equilibrium level.

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.

Macroeconomic Science and Meaningful Theorems

Greg Hill has a terrific post on his blog, providing the coup de grace to Stephen Williamson’s attempt to show that the way to increase inflation is for the Fed to raise its Federal Funds rate target. Williamson’s problem, Hill points out is that he attempts to derive his results from relationships that exist in equilibrium. But equilibrium relationships in and of themselves are sterile. What we care about is how a system responds to some change that disturbs a pre-existing equilibrium.

Williamson acknowledged that “the stories about convergence to competitive equilibrium – the Walrasian auctioneer, learning – are indeed just stories . . . [they] come from outside the model” (here).  And, finally, this: “Telling stories outside of the model we have written down opens up the possibility for cheating. If everything is up front – written down in terms of explicit mathematics – then we have to be honest. We’re not doing critical theory here – we’re doing economics, and we want to be treated seriously by other scientists.”

This self-conscious scientism on Williamson’s part is not just annoyingly self-congratulatory. “Hey, look at me! I can write down mathematical models, so I’m a scientist, just like Richard Feynman.” It’s wildly inaccurate, because the mere statement of equilibrium conditions is theoretically vacuous. Back to Greg:

The most disconcerting thing about Professor Williamson’s justification of “scientific economics” isn’t its uncritical “scientism,” nor is it his defense of mathematical modeling. On the contrary, the most troubling thing is Williamson’s acknowledgement-cum-proclamation that his models, like many others, assume that markets are always in equilibrium.

Why is this assumption a problem?  Because, as Arrow, Debreu, and others demonstrated a half-century ago, the conditions required for general equilibrium are unimaginably stringent.  And no one who’s not already ensconced within Williamson’s camp is likely to characterize real-world economies as always being in equilibrium or quickly converging upon it.  Thus, when Williamson responds to a question about this point with, “Much of economics is competitive equilibrium, so if this is a problem for me, it’s a problem for most of the profession,” I’m inclined to reply, “Yes, Professor, that’s precisely the point!”

Greg proceeds to explain that the Walrasian general equilibrium model involves the critical assumption (implemented by the convenient fiction of an auctioneer who announces prices and computes supply and demand at that prices before allowing trade to take place) that no trading takes place except at the equilibrium price vector (where the number of elements in the vector equals the number of prices in the economy). Without an auctioneer there is no way to ensure that the equilibrium price vector, even if it exists, will ever be found.

Franklin Fisher has shown that decisions made out of equilibrium will only converge to equilibrium under highly restrictive conditions (in particular, “no favorable surprises,” i.e., all “sudden changes in expectations are disappointing”).  And since Fisher has, in fact, written down “the explicit mathematics” leading to this conclusion, mustn’t we conclude that the economists who assume that markets are always in equilibrium are really the ones who are “cheating”?

An alternative general equilibrium story is that learning takes place allowing the economy to converge on a general equilibrium time path over time, but Greg easily disposes of that story as well.

[T]he learning narrative also harbors massive problems, which come out clearly when viewed against the background of the Arrow-Debreu idealized general equilibrium construction, which includes a complete set of intertemporal markets in contingent claims.  In the world of Arrow-Debreu, every price in every possible state of nature is known at the moment when everyone’s once-and-for-all commitments are made.  Nature then unfolds – her succession of states is revealed – and resources are exchanged in accordance with the (contractual) commitments undertaken “at the beginning.”

In real-world economies, these intertemporal markets are woefully incomplete, so there’s trading at every date, and a “sequence economy” takes the place of Arrow and Debreu’s timeless general equilibrium.  In a sequence economy, buyers and sellers must act on their expectations of future events and the prices that will prevail in light of these outcomes.  In the limiting case of rational expectations, all agents correctly forecast the equilibrium prices associated with every possible state of nature, and no one’s expectations are disappointed. 

Unfortunately, the notion that rational expectations about future prices can replace the complete menu of Arrow-Debreu prices is hard to swallow.  Frank Hahn, who co-authored “General Competitive Analysis” with Kenneth Arrow (1972), could not begin to swallow it, and, in his disgorgement, proceeded to describe in excruciating detail why the assumption of rational expectations isn’t up to the job (here).  And incomplete markets are, of course, but one departure from Arrow-Debreu.  In fact, there are so many more that Hahn came to ridicule the approach of sweeping them all aside, and “simply supposing the economy to be in equilibrium at every moment of time.”

Just to pile on, I would also point out that any general equilibrium model assumes that there is a given state of knowledge that is available to all traders collectively, but not necessarily to each trader. In this context, learning means that traders gradually learn what the pre-existing facts are. But in the real world, knowledge increases and evolves through time. As knowledge changes, capital — both human and physical — embodying that knowledge becomes obsolete and has to be replaced or upgraded, at unpredictable moments of time, because it is the nature of new knowledge that it cannot be predicted. The concept of learning incorporated in these sorts of general equilibrium constructs is a travesty of the kind of learning that characterizes the growth of knowledge in the real world. The implications for the existence of a general equilibrium model in a world in which knowledge grows in an unpredictable way are devastating.

Greg aptly sums up the absurdity of using general equilibrium theory (the description of a decentralized economy in which the component parts are in a state of perfect coordination) as the microfoundation for macroeconomics (the study of decentralized economies that are less than perfectly coordinated) as follows:

What’s the use of “general competitive equilibrium” if it can’t furnish a sturdy, albeit “external,” foundation for the kind of modeling done by Professor Williamson, et al?  Well, there are lots of other uses, but in the context of this discussion, perhaps the most important insight to be gleaned is this: Every aspect of a real economy that Keynes thought important is missing from Arrow and Debreu’s marvelous construction.  Perhaps this is why Axel Leijonhufvud, in reviewing a state-of-the-art New Keynesian DSGE model here, wrote, “It makes me feel transported into a Wonderland of long ago – to a time before macroeconomics was invented.”

To which I would just add that nearly 70 years ago, Paul Samuelson published his magnificent Foundations of Economic Analysis, a work undoubtedly read and mastered by Williamson. But the central contribution of the Foundations was the distinction between equilibrium conditions and what Samuelson (owing to the influence of the still fashionable philosophical school called logical positivism) mislabeled meaningful theorems. A mere equilibrium condition is not the same as a meaningful theorem, but Samuelson showed how a meaningful theorem can be mathematically derived from an equilibrium condition. The link between equilibrium conditions and meaningful theorems was the foundation of economic analysis. Without a mathematical connection between equilibrium conditions and meaningful theorems analogous to the one provided by Samuelson in the Foundations, claims to have provided microfoundations for macroeconomics are, at best, premature.

Leijonhufvud on Friedman

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

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

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

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

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

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

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

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

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

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

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

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


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.

Enter your email address to follow this blog and receive notifications of new posts by email.

Join 1,389 other followers

Follow Uneasy Money on WordPress.com