A New Version of my Paper “Between Walras and Marshall: Menger’s Third Way” Is Now Available on SSRN

Last week I reposted a revised version of a blogpost from last November, which was a revised section from my paper “Between Walras and Marshall: Menger’s Third Way.” That paper was presented at a conference in September 2021 marking the 100th anniversary of Menger’s death. I have now completed my revision of the entire paper, and the new version is now posted on SSRN.

Here is the link to the new version, and here is the abstract of the paper:

Neoclassical economics is bifurcated between Marshall’s partial-equilibrium and Walras’s general-equilibrium. Neoclassical theory having failed to explain the Great Depression, Keynes proposed a theory of involuntary unemployment, later subsumed under the neoclassical synthesis of Keynesian and Walrasian theories. Lacking suitable microfoundations, that synthesis collapsed. But Walrasian theory provides no account of how equilibrium is achieved. Marshallian partial-equilibrium analysis offered a more plausible account of how general equilibrium is reached. But presuming that all markets, but the one being analyzed, are already in equilibrium, Marshallian partial equilibrium, like Walrasian general equilibrium, begs the question of how equilibrium is attained. A Mengerian approach to circumvent this conceptual impasse, relying in part on a critique of Franklin Fisher’s analysis of the stability of general equilibrium, is proposed.

Commnets, criticisms and suggestions are welcomed and encouraged.

An Updated Version of my Paper “Robert Lucas and the Pretense of Science” Has Been Posted on SSRN

I have just submitted the paper to the European Journal of the History of Economic Thought. The updated version is not substantively different from the previous version, but I have cut some marginally relevant material and made what I hope are editorial improvements. Here’s a link to the new version.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4260708

Any comments, questions, criticisms or suggestions would be greatly appreciated.

I hope to post a revised version of my paper “Between Walras and Marshall: Menger’s Third Way” on SSRN within the next week or two. In my previous post I copied a revision of the section on Franklin Fisher’s important book Disequilibrium Foundations of Equilibrium Economics.

Franklin Fisher on the Disequilibrium Foundations of Economics and the Stability of General Equilibrium Redux

Last November I posted a revised section of a paper I’m now working on an earlier version of which is posted on SSRN. I have now further revised the paper and that section in particular, so I’m posting the current version of that section in hopes of receiving further comments, criticisms, and suggestions before I submit the paper to a journal. So I will be very grateful to all those who respond, and will try not to be too cranky in my replies.

I         Fisher’s model and the No Favorable Surprise Assumption

Unsuccessful attempts to prove, under standard neoclassical assumptions, the stability of general equilibrium led Franklin Fisher (1983 [Disequilibrium Foundations of Equilibrium Economics) to suggest an alternative approach to proving stability. based on three assumptions: (1) trading occurs at disequilibrium prices (in contrast to the standard assumption that no trading takes place until a new equilibrium is found with prices being adjusted under a tatonnement process); (2) all unsatisfied transactors — either unsatisfied demanders or unsatisfied suppliers — in any disequilibrated market are either all on the demand side or all on the supply side of that market; (3) the “no favorable surprises” (NFS) assumption previously advanced by Hahn (1978 [“On Non-Walrasian Equilibria”).

At the starting point of a disequilibrium process, some commodities would be in excess demand, some in excess supply, and, perhaps, some in equilibrium. Let Zi denote the excess demand for any commodity, i ranging from 1 to n; let commodities in excess demand be numbered from 1 to k, commodities initially in equilibrium numbered from k+1 to m, and commodities in excess supply numbered from m+1 to n. Thus, by assumption, no agent had an excess supply of commodities numbered from 1 to k, no agent had an excess demand for commodities numbered from m+1 to n, and no agent had either an excess demand or excess supply for commodities numbered between k+1 and m.[1]

Fisher argued that in disequilibrium, with prices, not necessarily uniform across all trades, rising in markets with excess demand and falling in markets with excess supply, and not changing in markets with zero excess demand, the sequence of adjustments would converge on an equilibrium price vector. Every agent would form plans to transact conditional on expectations of the prices at which it planned purchases or sales, either spot for forward, could be executed.[2] Because unsuccessful demanders and suppliers would respond to failed attempts to execute planned trades by raising the prices offered, or reducing the prices accepted, prices for goods or services in excess demand would rise, and would fall for goods and services in excess supply. Insofar as agents successfully execute their plans, prices for commodities in excess demand would rise and prices for commodities in excess supply would fall.

Fisher reduced this informal analysis to a formal model in which stability could be proved, at least under standard neoclassical assumptions augmented by plausible assumptions about the adjustment process. Stability of equilibrium is proved by defining some function (V) of the endogenous variables of the model (x1, . . ., xn, t) and showing that the function satisfies the Lyapounov stability conditions: V ≥ 0, dV/dt ≤ 0, and dV/dt = 0 in equilibrium. Fisher defined V as the sum of the expected utilities of households plus the expected profits of firms, all firm profits being distributed to households in equilibrium. Fisher argued that, under the NFS assumption, the expected utility of agents would decline as prices are adjusted when agents fail to execute their planned transactions, disappointed buyers raising the prices offered and disappointed sellers lowering the prices accepted. These adjustments would reduce the expected utility or profit from those transactions, and in equilibrium no further adjustment would be needed and the Lyapounov conditions satisfied. The combination of increased prices for goods purchased and decreased prices for goods sold implies that, with no favorable surprises, dV/dt would be negative until an equilibrium, in which all planned transactions are executed, is reached, so that the sum of expected utility and expected profit is stabilized, confirming the stability of the disequilibrium arbitrage process.

II         Two Problems with the No Favorable Surprise Assumption

Acknowledging that the NFS assumption is ad hoc, not a deep property of rationality implied by standard neoclassical assumptions, Fisher (1983, p. 87) justified the assumption on the pragmatic grounds. “It may well be true,” he wrote,

that an economy of rational agents who understand that there is disequilibrium and act on arbitrage opportunities is driven toward equilibrium, but not if these agents continually perceive new previously unanticipated opportunities for further arbitrage. The appearance of such new and unexpected opportunities will generally disturb the system until they are absorbed.

Such opportunities can be of different kinds. The most obvious sort is the appearance of unforeseen technological developments – the unanticipated development of new products or processes. There are other sorts of new opportunities as well. An unanticipated change in tastes or the development of new uses for old products is one; the discovery of new sources of raw materials another. Further, efficiency improvements in firms are not restricted to technological developments. The discovery of a more efficient mode of internal organization or of a better way of marketing can also present a new opportunity.

Because favorable surprises following the displacement of a prior equilibrium would potentially violate the Lyapounov condition that V be non-increasing, the NFS assumption allows it to be proved that arbitrage of price differences leads to convergence on a new equilibrium. It is not, of course, only favorable surprises that can cause instability, inasmuch as the Lyapounov function must be non-negative as well as non-increasing, and a sufficiently large unfavorable surprise would violate the non-negativity condition.[3]

However, acknowledging the unrealism of the NFS assumption and its conflation of exogenous surprises with those that are endogenous, Fisher (pp. 90-91) argued that proving stability under the NFS assumption is still significant, because, if stability could not be proved under the assumption of no surprises of any kind, it likely could not be proved “under the more interesting weaker assumption” of No Exogenous Favorable Surprises.

The NFS assumption suffers from two problems deeper than Fisher acknowledged. First, it reckons only with equilibrating adjustments in current prices when trading is possible in both spot and forward markets for all goods and services, so that spot and forward prices for each commodity and service are being continuously arbitraged in his setup. Second, he does not take explicit account of interactions between markets of the sort that motivate Lipsey and Lancaster’s (1956 [“Tbe General Theory of Second Best) general theory of the second best.

          A. Semi-complete markets

Fisher does not introduce trading in state-contingent markets, so his model might be described as semi-complete. Because all traders have the choice, when transacting to engage, in either a spot or a forward transaction, depending on their liquidity position, so that when spot and forward trades are occurring for the same product or service, the ratio of those prices, reflecting own commodity interest rates, are constrained by arbitrage to match money interest rate. In an equilibrium, both spot and forward prices must adjusted so that the arbitrage relationships between spot and forward prices for all commodities and services in which both spot and forward prices are occurring is satisfied and all agents are able to execute the trads that they wish to make at the prices they expected when planning those purchases. In other words, an equilibrium requires that all agents that are actually trading commodities or services in which both spot and forward trades are occurring concurrently must share the same expectations of future prices. Otherwise, agents with differing expectations would have an incentive to switch from trading spot to forward or vice versa.

The point that I want to emphasize here is that, insofar as equilibration can be shown to occur in Fisher’s arbitrage model, it depends on the ability of agents to choose between purchasing spot or forward, thereby creating a market mechanism whereby agents’ expectations of future prices to be reconciled along with the adjustment of current prices (either spot or forward) to allow agents to execute their plans to transact. Equilibrium depends not only on the adjustment of current prices to equilibrium levels for spot transactions but on the adjustment of expectations of future spot prices to equilibrium levels. Unlike the market feedback on current prices in current markets conveyed by unsatisfied demanders and suppliers, inconsistencies in agents’ notional plans for future transactions convey no discernible feedback without a broad array of forward or futures markets in which those expectations are revealed and reconciled. Without such feedback on expectations, a plausible account of how expectations of future prices are equilibrated cannot — except under implausibly extreme assumptions — easily be articulated.[4] Nor can the existence of a temporary equilibrium of current prices in current markets, beset by agents’ inconsistent and conflicting expectations, be taken for granted under standard assumptions. And even if a temporary equilibrium exists, it cannot, under standard assumptions, be shown to be optimal (Arrow and Hahn, 1971, 136-51).

            B          Market interactions and the theory of second-best

Second, in Fisher’s account, price changes occur when transactors cannot execute their desired transactions at current prices, those price changes then creating arbitrage opportunities that induce further price changes. Fisher’s stability argument hinges on defining a Lyapounov function in which the prices of goods in excess demand rise as frustrated demanders offer increased prices and prices of goods in excess supply fall as disappointed suppliers accept reduced prices.

But the argument works only if a price adjustment in one market caused by a previous excess demand or excess supply does not simultaneously create excess demands or supplies in markets not previously in disequilibrium or further upset the imbalance between supply and demand in markets already in disequilibrium.

To understand why Fisher’s ad hoc assumptions do not guarantee that the Lyapounov function he defined will be continuously non-increasing, consider the famous Lipsey and Lancaster (1956) second-best theorem, according to which, if one optimality condition in an economic model is unsatisfied because a relevant variable is constrained, the second-best solution, rather than satisfy the other unconstrained optimum conditions, involves revision of at least some of the unconstrained optimum conditions.

Contrast Fisher’s statement of the No Favorable Surprise assumption with how Lipsey and Lancaster (1956, 11) described the import of their theorem.

From this theorem there follows the important negative corollary that there is no a priori way to judge as between various situations in which some of the Paretian optimum conditions are fulfilled while others are not. Specifically, it is not true that a situation in which more, but not all, of the optimum conditions are fulfilled is necessarily, or is even likely to be, superior to a situation in which fewer are fulfilled. It follows, therefore, that in a situation in which there exist many constraints which prevent the fulfilment of the Paretian optimum conditions the removal of any one constraint may affect welfare or efficiency either by raising it, by lowering it, or by leaving it unchanged.

The general theorem of the second best states that if one of the Paretian optimum conditions cannot be fulfilled a second-best optimum situation is achieved only by departing from all other optimum conditions. It is important to note that in general, nothing can be said about the direction or the magnitude of the secondary departures from optimum conditions made necessary by the original non-fulfillment of one condition.

Although Lipsey and Lancaster were not referring to the adjustment process following the displacement of a prior equilibrium, their discussion implies that the stability of an adjustment process depends on the specific sequence of adjustments in that process, inasmuch as each successive price adjustment, aside from its immediate effect on the particular market in which the price adjusts, transmits feedback effects to related markets. A price adjustment in one market may increase, decrease, or leave unchanged, the efficiency of other markets, and the equilibrating tendency of a price adjustment in one market may be offset by indirect disequilibrating tendencies in other markets. When a price adjustment in one market indirectly reduces efficiency in other markets, the resulting price adjustments may well trigger further indirect efficiency reductions.

Thus, in adjustment processes involving interrelated markets, a price change in one market can indeed cause a favorable surprises in one or more other markets by indirectly causing net increases in utility through feedback effects on other markets.

III        Conclusion

Consider a macroeconomic equilibrium satisfying all optimality conditions between marginal rates of substitution in production and consumption and relative prices. If that equilibrium is subjected to a macoreconomic disturbance affecting all, or most, individual markets, thereby changing all optimality conditions corresponding to the prior equilibrium, the new equilibrium will likely entail a different set of optimality conditions. While systemic optimality requires price adjustments to satisfy all the optimality conditions, actual price adjustments occur sequentially, in piecemeal fashion, with prices changing market by market or firm by firm, price changes occurring as agents perceive demand or cost changes. Those changes need not always induce equilibrating adjustments, nor is the arbitraging of price differences necessarily equilibrating when, under suboptimal conditions, prices have generally deviated from their equilibrium values. 

Smithian invisible-hand theorems are of little relevance in explaining the transition to a new equilibrium following a macroeconomic disturbance, because, in this context, the invisible-hand theorem begs the relevant question by assuming that the equilibrium price vector has been found. When all markets are in disequilibrium, moving toward equilibrium in one market has repercussions on other markets, and the simple story of how price adjustment in response to a disequilibrium in that market alone restores equilibrium breaks down, because market conditions in every market depend on market conditions in every other market. So, unless all optimality conditions are satisfied simultaneously, there is no assurance that piecemeal adjustments will bring the system closer to an optimal, or even a second-best, state.

If my interpretation of the NFS assumption is correct, Fisher’s stability results may provide support for Leijonhufvud’s (1973 “Effective Demand Failures”) suggestion that there is a corridor of stability around an equilibrium time path within which, under normal circumstances, an economy will not be displaced too far from path, so that an economy, unless displaced outside that corridor, will revert, more or less on its own, to its equilibrium path.[5]

Leijonhufvud attributed such resilience to the holding of buffer stocks of inventories of goods, holdings of cash and the availability of credit lines enabling agents to operate normally despite disappointed expectations. If negative surprises persist, agents will be unable to add to, or draw from, inventories indefinitely, or to finance normal expenditures by borrowing or drawing down liquid assets. Once buffer stocks are exhausted, the stabilizing properties of the economy have been overwhelmed by the destabilizing tendencies, income-constrained agents cut expenditures, as implied by the Keynesian multiplier analysis, triggering a cumulative contraction, and rendering a spontaneous recovery without compensatory fiscal or monetary measures, impossible.

But my critique of Fisher’s NFS assumption suggests other, perhaps deeper, reasons why displacements of equilibrium may not be self-correcting, such displacements may invalidate previously held expectations, and in the absence of a dense array of forward and futures markets, there is likely no market mechanism that would automatically equilibrate unsettled and inconsistent expectations. In such an environment, price adjustments in current spot markets may cause price adjustments that, under the logic of the Lipsey-Lancaster second-best theorem may in fact be welfare-diminishing rather than welfare-enhancing and may therefore not equilibrate, but only further disequilibrate the macroeconomy.


[1] Fisher’s stability analysis was conducted in the context of complete markets in which all agents could make transactions for future delivery at prices agreed on in the present. Thus, for Fisher arbitrage means that agents choose between contracting for future delivery or waiting to transact until later based on their expectations of whether the forward price now is more or less than the expected future price. In equilibrium, expectations of future prices are correct so that agents are indifferent between making forward transactions of waiting to make spot transactions unless liquidity considerations dictate a preference for selling forward now or postponing buying till later.

[2] Fisher assumed that, for every commodity or service, transactions can be made either spot or forward. When Fisher spoke of arbitrage, he was referring to the decisions of agents whether to transact spot or forward given the agent’s expectations of the spot price at the time of planned exchange, the forward prices adjusting so that, with no transactions costs, agents are indifferent, at the margin, between transacting spot or forward, given their expectations of the future spot price.

[3] It was therefore incorrect for Fisher (1983, 88) to assert: “we can hope to show that  that the continued presence new opportunities is a necessary condition for instability — for continued change,” inasmuch as continued negative surprises could also cause continued — or at least prolonged — change.

[4] Fisher does recognize (pp. 88-89) that changes in expectations can be destabilizing. However, he considers only the possibility of exogenous events that cause expectations to change, but does not consider the possibility that expectations may change endogenously in a destabilizing fashion in the course of an adjustment process following a displacement from a prior equilibrium. See, however, his discussion (p. 91) of the distinction between exogenous and endogenous shocks.

How is . . . an [“exogenous”] shock to be distinguished from the “endogenous” shock brought about by adjustment to the original shock? No Favorable Surprise may not be precisely what is wanted as an assumption in this area, but it is quite difficult to see exactly how to refine it.

A proof of stability under No Favorable Surprise, then, seems quite desirable for a number of related reasons. First, it is the strongest version of an assumption of No Favorable Exogenous Surprise (whatever that may mean precisely); hence, if stability does not hold under No Favorable Surprise it cannot be expected to hold under the more interesting weaker assumption.  

[5] Presumably because the income and output are maximized at the equilibrium path, it is unlikely that an economy will overshoot the path unless entrepreneurial or policy error cause such overshooting which is presumably an unlikely occurrence, although Austrian business cycle theory and perhaps certain other monetary business cycle theories suggest that such overshooting is not or has not always been an uncommon event.

Dangerous Metaphors

A couple of days ago, I wrote post gently (I hope) chiding Olivier Blanchard for what seemed to me to be a muddled attempt to attribute inflation to conflicts between various interest groups (labor, capital, creditors, debtors) that the political system is unable, or unwilling, to resolve,leavin, those conflicts to be addressed, albeit implicitly, by the monetary authority. In those circumstances, groups seek to protect, or even advance their interests, by seeking prices increases for their goods or services, triggering a continuing cycle of price and wage increases, aka a wage-price spiral.

My criticism of Blanchard wasn’t that the distributional conflicts that worry him don’t exist — they obviously do — or are irrelevant — they clearly aren’t, but that focusing attention on those conflicts tells us very little about the mechanisms that generate inflation: the macroeconomic policies (monetary or fiscal) under the control of governments and central banks. We live in complex societies consisting of many diverse and independent, yett deeply interrelated and interdependent, agents. Macroeconomic polilcies are adopted and implemented in an economic and social environment shaped by the various, and possibly conflicting, interests of these agents, so it would be absurd to argue that the conflicts and tensions that inevitably arise between those agents do not influence, or even dictate, the policy choices of governments and monetary authorities responsible for adopting and implementing macroeconomic policies.

Because distributional conflicts are inherent in any economy composed of a diverse set of agents pursuing their own inconsistent self-interests, so it seems quixotic to suppose or even imagine that distributional conflicts can be resolved by a formal negotiating process in the way that Blanchard seems to be suggesting. There are too many interests at play, too many conflicts to reconcile, too many terms to negotiate, too many uncertain conditions and too many unforeseen events requiring previously reached agreements to be renegotiated for these deep-seated conflicts to be resolved by any conceivable negotiation process.

The point that I tried to make is that, because it is unrealistic to think that the fundamental conflicts of interest characteristic of any modern economy can be reconciled by negotiation, the monetary authority should aim to adopt a policy on which economic agents can rely on in forming their expectations about the future. The best policy that the monetary authority can hope to achieve is one that aims for total nominal spending and total nominal income to increase at a predictable rate consistent with an inflation rate low enough to be politically uncontroversial. If such a policy is implemented, with nominal spending and income increasing at roughly the target rate, private expectations would likely converge toward that targeted rate, thereby contributing to the mutual consistency of private expectaions that would allow inflation to remain at an acceptably low rate.

Brad Delong kindly noticed my comment about Blanchard on his substack blog and on Twitter, opining that Blanchard and I were not really disagreeing but were talking past each other.

I don’t necessarily disagree with Brad’s take, but I’m not sure that I agree either, because I’m not sure that I understand what Blanchard is actually saying. I actually tried to hint at my uncertainty about what Blanchard’s argument actually is (and whether I disagree with it) by borrowing (with slight modification) the lyric of George and Ira Gershwin’s standard “Let’s Call the Whole Thing Off.” (Or, try out this version.)

Paul Krugman also weighed in, defending Blanchard’s analysis against the argument which he attributes to John Cochrane and to me that inflation is always the result of excessive demand.

Although Blanchard is nobody’s idea of a leftist (OK, Republicans seem to consider anyone more liberal than Attila the Hun a Marxist, but still), he nonetheless got immediate pushback from economists who insisted that inflation is always the result of excessive demand, of too much money chasing too few goods or, what is roughly the same thing, the consequence of an excessively hot economy.

https://www.nytimes.com/2023/01/03/opinion/inflation-economy.html?searchResultPosition=1

I’m always grateful to be noticed by Krugman, but I’ll just note in passing that he’s not quite correct in attributing to me the view that inflation is always the consequence of an excessively hot economy; I was simply working with Blanchard’s own framing in his original Twitter thread.

But the point in Krugman’s post that I want to comment on is his football metaphor.

At one level, of course Blanchard is right. Companies that charge higher prices and workers who demand higher wages aren’t doing so because the money supply has increased; they’re trying to increase their incomes (or offset declines in their incomes caused by, say, rising energy prices). And inflation happens when the attempts of firms and workers to claim a bigger share of the economic pie are inconsistent, when the additional purchasing power being demanded exceeds what the economy can deliver.

Reading the discussion, I found myself remembering a remark made way back in the 1970s by William Nordhaus, another eminent economist (and Nobel laureate) who happens to have been my first mentor in the field. Nordhaus compared inflation to what happens in a football stadium when the action on the field is especially exciting. (If you don’t find American football exciting, think of it as a soccer match.) Everyone stands up to get a better view, but this is collectively self-defeating — your view doesn’t improve because the people in front of you are also standing, and you’re less comfortable besides.

Nordhaus’s football metaphor is very apt as far as it goes. You can imagine that inflation starts as the result of an attempt by agents to increase their prices (wages) that turns out to be self-defeating because everyone’s attempt to increase his price or wage relative to everyone else’s turns out to be self-defeating when everyone else does the same thing, so that no one really improves his position compared to everyone else.

I will just observe parenthetically that it is not strictly true that no one improves his view of the field, because people who are taller than average likely will improve their view of the field, especially if they are sitting behind short people. But that is likely a second-order effect. Similarly, some people raising their prices may be well-positioned to increase their prices more than average, so that they may be net gainers from the process. But again those are likely second-order effects.

But here is where the football metaphor breaks down. Blanchard is not worried about a once and for all increase in the price level, which is what the football metaphor translates into. People standing up in a football game do not keep growing taller once they stand up. The process comes to an end, and is eventually reversed after people sit down again.

But inflation is unpopular because it supposedly is a continuing process of increasing prices. Larry Summers and Blanchard have been invoking the experience of the 1970s in which there was supposedly a self-generating or self-reinforcing wage-price spiral that could only be stopped by a brutal monetary tightening administered by Paul Volcker causing a severe recession with double-digit unemployment. To avoid another such catastrophic recession, Blanchard is urging everyone to be reasonable and not to try to increase prices or wages in a likely futile attempt to gain at the expense of others.

The problem with football metaphor is that it can’t explain how the inflation process can continue if it is not enabled by macroeconomic policies that cause the rate of nominal spending and income to keep increasing. Maybe Blanchard and Krugman believe that total nominal spending and total nominal income can keep increasing even if macroeconomic policies aren’t causing nominal spending and nominal income to increase.

I don’t think that’s what they believe, but if they do believe that, then they should explain how continuing increases in nominal spending and income can be generated without corresponding macroeconomic policies that promote those increases in nominal spending and income. As long as macroeconomic policy is focused on keeping the rate of increase in nominal spending at a rate consistent with the target rate of inflation, inflation will be just as transitory as episodes of standing by fans at football games.

My Paper “Robert Lucas and the Pretense of Science” Is now Available on SSRN

Peter Howitt, whom I got to know slightly when he spent a year at UCLA while we were both graduate students, received an honorary doctorate from Côte d’Azur University in September. Here is a link to the press release of the University marking the award.

Peter wrote his dissertation under Robert Clower, and when Clower moved from Northwestern to UCLA in the early 1970s, Peter followed Clower as he was finishing up his dissertation. Much of Peter’s early work was devoted to trying to develop the macroeconomic ideas of Clower and Leijonhufvud. His book The Keynesian Recovery collects those important early papers which, unfortunately, did not thwart the ascendance, as Peter was writing those papers, of the ideas of Robert Lucas and his many followers, or the eventual dominance of those ideas over modern macroeconomics.

In addition to the award, a workshop on Coordination Issues in Historical Perspective was organized in Peter’s honor, and my paper, “Robert Lucas and the Pretense of Science,” which shares many of Peter’s misgivings about the current state of macroeconomics, was one of the papers presented at the workshop. In writing the paper, I drew on several posts that I have written for this blog over the years. I have continued to revise the paper since then, and the current version is now available on SSRN.

Here’s the abstract:

Hayek and Lucas were both known for their critiques of Keynesian theory on both theoretical and methodological grounds. Hayek (1934) criticized the idea that continuous monetary expansion could permanently increase total investment, foreshadowing Friedman’s (1968) argument that monetary expansion could permanently increase employment. Friedman’s analysis set the stage for Lucas’s (1976) critique of macroeconomic policy analysis, a critique that Hayek (1975) had also anticipated. Hayek’s (1942-43) advocacy of methodological individualism might also be considered an anticipation of Lucas’s methodological insistence on the necessity of rejecting Keynesian and other macroeconomic theories not based on explicit microeconomic foundations. This paper compares Hayek’s methodological individualism with Lucasian microfoundations. While Lucasian microfoundations requires all agents to make optimal choices, Hayek recognized that optimization by interdependent agents is a contingent, not a necessary, state of reconciliation and that the standard equilibrium theory on which Lucas relies does not prove that, or explain how, such a reconciliation is, or can be, achieved. The paper further argues that the Lucasian microfoundations is a form of what Popper called philosophical reductionism that is incompatible with Hayekian methodological individualism.

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4260708

You Say Potato, I Say Potahto; You Say Tomato, I Say Tomahto; You Say Distribution, I Say Expectation

Once again, the estimable Olivier Blanchard is weighing in on the question of inflation, expressing fears about an impending wage-price spiral that cannot be controlled by conventional monetary policy unless the monetary authority is prepared to impose sufficiently tight monetary conditions that would entail substantially higher unemployment than we have experienced since the aftermath of the 2008 financial crisis and Little Depression (aka Great Recession). Several months ago, Blanchard, supporting Larry Summers’s warnings that rising inflation was not likely to be transitory and instead would likely remain high and possibly increase over time, I tried to explain why his fears of high and rising inflation were likely exaggerated. Unpersuaded, he now returns to provide a deeper explanation of his belief that, unless the deep systemic forces that cause inflation are addressed politically rather than left, by default, to be handled by the monetary authority, inflation will remain a persistent and vexing problem.

I’m sorry to say that Professor Blanchard starts off with a massive overstatement. While I don’t discount the possibility — even the reality — that inflation may sometimes be triggered by the attempt of a particular sector of the economy to increase the relative price of the goods or services that it provides, thereby increasing its share of total income at the expense of other sectors, I seriously question whether this is a typical, or even frequent, source of inflation. For example, oil-price increases in the 1970s and wage increases in France after the May 1968 student uprisings did trigger substantial inflation. Inflation served as a method of (1) mitigating ing adverse macroeconomic effects on output and employment and (2) diluting the size of the resulting wealth transfer from other sectors.

Blanchard continues:

2/8. The source of the conflict may be too hot an economy: In the labor market, workers may be in a stronger position to bargain for higher wages given prices. But, in the goods market, firms may also be in a stronger position to increase prices given wages. And, on, it goes.


Again, I’m sorry to say that I find this remark incomprehensible. Blanchard says “the source of the conflict may be too hot an economy,” and in the very next breath says that in the labor market (as if it made sense to view the labor market, accounting for more than half the nominal income of the economy, as a single homogeneous market with stable supply and demand curves), “workers may be in a strong position to bargain for higher wages given prices,” while in the goods market firms may be in a strong position to bargain for higher prices relative to wages. What kind of bargaining position is Blanchard talking about? Is it real, reflecting underlying economic conditions, or is it nominal, reflecting macroeconomic conditions. He doesn’t seem to know. And if he does know, he’s not saying. But he began by saying that the source of the conflict “may be too hot an economy,” suggesting that the source of the conflict is macroeconomic, not a conflict over shares. So I’m confused. We can only follow him a bit further to see what he may be thinking.

3/8. The source of the conflict may be in too high prices of commodities, such as energy. Firms want to increase prices given wages, to reflect the higher cost of intermediate inputs. Workers want to resist the decrease in the real wage, and ask for higher wages. And on it goes.

Now Blanchard seems to be attributing the conflict to an exogenous — and unexmplained — increase in commodity prices. One sector presumably enjoys an improvement in its bargaining position relative to the rest of the economy, thereby being enabled to increase its share of total income. Rather than consider the appropriate response to such an exercise of raw market power, Blanchard simply assumes that, but doesn’t explain how, this increase in share triggers a vicious cycle of compensating increases in the prices and wages of other sectors, rather than a one-off distributional change to reflect a new balance of economic power. This is a complicated story with interesting macroeconomic implications, but Blanchard doesn’t bother to do more than assert that the disturbance sets in motion an ongoing, possibly unlimited, cycle of price and wage increases.

4/8. The state can play various roles. Through fiscal policy, it can slow down the economy and eliminate the overheating. It can subsidize the cost of energy, limiting the decrease in the real wage and the pressure on nominal wages.

5/8. It can finance the subsidies by increasing taxes on some current taxpayers, say exceptional profit taxes, or through deficits and eventual taxes on future taxpayers (who have little say in the process…)

These two statements from the thread are largely innocuous and contribute little or nothing to an understanding of the cause or causes of inflation or of the policies that might mitigate inflation or its effect,

6/8. But, in the end, forcing the players to accept the outcome, and thus stabilizing inflation, is typically left to the central bank. By slowing down the economy, it can force firms to accept lower prices given wages, and workers to accept lower wages given prices.

It’s not clear to me what constitutes “acceptance” of the outcome. Under any circumstance, the players will presumably still seek to choose and execute what, given the situation in which they find themselves, they regard as an optimal plan. Whether the players can execute the plan that they choose will depend on the plans chosen by other players and on the policies adopted by the central bank and other policy makers. If policy makers adopt a consistent set of policies that are feasible and are aligned with the outcomes expected by the players, then the players will likely succeed in implementing what they regard as optimal plans. If the policies that are followed are not consistent and not feasible, then those policies will not be aligned with the outcomes expected by the players. In the latter case, matters will likely get worse not better.

7/8. It is a highly inefficient way to deal with distributional conflicts. One can/should dream of a negotiation between workers, firms, and the state, in which the outcome is achieved without triggering inflation and requiring a painful slowdown.

I can’t help but observe the vagueness associated with the pronoun “it” and its unidentified antecedent. The outcome of a complex economic process cannot be achieved by a negotiation between workers,firms and the state. Things don’t work that way. Whatever negotiation Professor Blanchard is dreaming about, no negotiation can possibly determine the details of an outcome. What is possible is some agreement on policy goals or targets for inflation and some feasible set of policies aimed at achieving, or coming close to, a target rate of inflation. The key variable over which policy makers have some control is total aggregate demand for the economy measured either as a rate of nominal spending and nominal income over a year or as a rate of growth in spending and income compared to the previous year. Since inflation is itself a rate of change, presumaby the relevant target should be a rate of change in total nominal spending and nominal income. Thus, the appropriate target for policy makers to aim for is the yearly rate of growth in total nominal spending and total nominal income.

Given some reasonable expectation about the rate of technical progress (labor productivity) and the rate of increase in the labor force, a target rate of inflation implies a target rate of increase in total nominal spending and total nominal income. Given expectations about the increase in labor productivity, there is an implied rate of increase in nominal wages that is broadly consistent with the inflation target. But that average rate of increase in nominal wages can hardly be expected to be uniform for all industries and all firms and all workers, and it would be folly, on purely technical reasons, to attempt to enforce such a target in average nominal wage growth. And for legal and political reasons, it would be an even greater folly to try to do so.

Besides announcing the underlying basis for the targeted rate of nominal income growth, and encouraging workers and firms to take those targets seriously when negotiating wage contracts and setting prices, while recognizing that deviations from those targets are often reasonable and appropriate in the light of the specific circumstances in which particular firms and industries and labor unions are operating, policy makers have no constructive role to play in the setting of prices or wages for individual firms industries or labor contracts. But providing useful benchmarks for private agents to use as a basis for forming their own expectations about the future to guide their planning for the future is entirely appropriate and useful.

I should acknowledge that, as I have done previously, that the approach to policy making summarized here is based on the analysis developed by Ralph Hawtrey over the course of more than a half century as both a monetary theorist and a policy advisor, and, especially, as Hawtrey explained over a half-century ago in his final book, Incomes and Money.

8/8. But, unfortunately, this requires more trust than can be hoped for and just does not happen. Still, this way of thinking inflation shows what the problem is, and how to think of the least painful solution.

Insofar as policymakers can show that they are coming reasonably close to meeting their announced targets, they will encourage private actors to take those announced targets seriously when forming their own expectations and when negotiating with counterparties on the terms of their economic relationships. The least painful solutions are those in which economic agents align their expectations with the policy targets announced — and achieved — by policy makers.

Originally tweeted by Olivier Blanchard (@ojblanchard1) on December 30, 2022.

Franklin Fisher on the Disequilibrium Foundations of Economics and the Stability of General Equilibium

As I’ve pointed out many times on this blog, equilibrium is an extremely important, but very problematic, concept in economic theory. What economists even mean when they talk about equilibrium is often unclear and how the concept relates to the real world as opposed to an imagined abstract world is even less clear. Nevertheless, almost all the propositions of economic theory that are used by economists in analyzing the world and in making either conditional or unconditional predictions about the world or in analyzing current or historical events are based on propositions of economic theory deduced from the theoretical analysis of equilibrium states,

Last year I wrote a paper for a conference marking the hundredth anniversary of Carl Menger’s death in 1921 and 150 years after his seminal work launching, along with Jevons and Walras, what eventually became neoclassical economic theory. Here is a link to that paper. Of late I have been revising the paper and I have now substantially rewritten (and I hope improved) one of the sections of the paper discussing Franklin Fisher’s important work on the stability of general equilibrium, which I have been puzzling over and writing about for several years, e.g., here and here, as well as chapter 17 of my book, Studies in the History of Monetary Theory: Controversies and Clarifications.

I’ve recently been revising that paper — one of a number of distractions that have prevented me from posting recently — and have substantially rewritten a couple sections of the paper, especially section 7 about Fisher’s treatment of the stability of general equilibrium. Because I’m not totally sure that I’ve properly characterized Fisher’s own proof of stability under a different set of assumptions than the standard treatments of stability, I’m posting my new version of the section in hopes of eliciting feedback from readers. Here’s the new version of section 7 (not yet included in the SSRN version).

Unsuccessful attempts to prove, under standard neoclassical assumptions, the stability of general equilibrium led Franklin Fisher (1983) to suggest an alternative approach to proving stability. Fisher based his approach on three assumptions: (1) trading occurs at disequilibrium prices (in contrast to the standard assumption that no trading takes place until a new equilibrium is found with prices being adjusted under a tatonnement process); (2) all unsatisfied transactors — either unsatisfied demanders or unsatisfied suppliers — in any disequilibrated market are all either on the demand side or on the supply side of that market; (3) the “no favorable surprises” (NFS) assumption previously advanced by Hahn (1978).

At the starting point of a disequilibrium process, some commodities would be in excess demand, some in excess supply, and, perhaps, some in equilibrium. Let Zi denote the excess demand for any commodity, i ranging between 1 and n; let commodities in excess demand be numbered from 1 to k, commodities initially in equilibrium numbered from k+1 to m, and commodities in excess supply numbered from m+1 to n. Thus, by assumption, no agent had an excess supply of commodities numbered from 1 to k, no agent had an excess demand for commodities numbered from m+1 to n, and no agent had an excess demand or excess supply for commodities numbered between k+1 and m.

Fisher argued that, with prices rising in markets with excess demand and falling in markets with excess supply, and not changing in markets with zero excess demand, the sequence of adjustments would converge on an equilibrium price vector. Prices would rise in markets with excess demand and fall in markets with excess supply, because unsatisfied demanders and suppliers would seek to execute their unsuccessful attempts by offering to pay more for commodities in excess demand, or accept less for commodities in excess supply, than currently posted prices. And insofar as those attempts were successful, arbitrage would cause all prices for commodities in excess demand to increase and all prices for commodities in excess supply to decrease.

Fisher then defined a function in which the actual utility of agents after trading would be subtracted from their expected utility before trading. For agents who succeed in executing planned purchases at the expected prices, the value of the function would be zero, but for agents unable to execute planned purchases at the expected prices, the value of the function would be positive, their realized utility being less than their expected utility, as agents with excess demands had to pay higher prices than they had expected and agents with excess supplies had to accept lower prices than expected. As prices of goods in excess demand rise while prices of goods in excess supply fall, the value of the function would fall until equilibrium was reached, thereby satisfying the stability condition for a Lyapunov function, thereby confirming the stability of the disequilibrium arbitrage proces.

It may well be true that an economy of rational agents who understand that there is disequilibrium and act arbitrage opportunities is driven toward equilibrium, but not if these agents continually perceive new previously unanticipated opportunities for further arbitrage. The appearance of such new and unexpected opportunities will generally disturb the system until they are absorbed.

Such opportunities can be of different kinds. The most obvious sort is the appearance of unforeseen technological developments – the unanticipated development of new products or processes. There are other sorts of new opportunities as well. An unanticipated change in tastes or the development of new uses for old products is one; the discovery of new sources of raw materials another. Further, efficiency improvements in firms are not restricted to technological developments. The discovery of a more efficidnt mode of internal organization or of a better way of marketing can also present a new opportunity.

Because a favorable surprise during the adjustment process following the displacement of a prior equilibrium would potentially violate the stability condition that a Lyapunov function be non-increasing, the NFS assumption is needed for a proof that arbitrage of price differences leads to convergence on a new equilibrium. It is not, of course, only favorable surprises that can cause instability, inasmuch as the Lyapunov function must be positive as well as being non-increasing, and a sufficiently large unfavorable surprise would violate the non-negativity condition.[1] While listing several possible causes of favorable surprises that might prevent convergence, Fisher considered the assumption plausible enough to justify accepting stability as a working hypothesis for applied microeconomics and macroeconomics.

However, the NFS assumption suffers from two problems deeper than Fisher acknowledged. First, it reckons only with equilibrating adjustments in current prices without considering that equilibrating adjustments are required in agents’ expectations of future prices on which their plans for current and future transactions depend. Unlike the market feedback on current prices in current markets conveyed by unsatisfied demanders and suppliers, inconsistencies in agents’ notional plans for future transactions convey no discernible feedback, in an economic setting of incomplete markets, on their expectations of future prices. Without such feedback on expectations, a plausible account of how expectations of future prices are equilibrated cannot — except under implausibly extreme assumptions — easily be articulated.[2] Nor can the existence of a temporary equilibrium of current prices in current markets, beset by agents’ inconsistent and conflicting expectations, be taken for granted under standard assumptions. And even if a temporary equilibrium exists, it cannot, under standard assumptions, be shown to be optimal. (Arrow and Hahn, 1971, 136-51).

Second, in Fisher’s account, price changes occur when transactors cannot execute their desired transactions at current prices, those price changes then creating arbitrage opportunities that induce further price changes. Fisher’s stability argument hinges on defining a Lyapunov function in which actual prices of goods in excess demand gradually rise to eliminate excess demands and actual prices of goods in excess supply gradually fall to eliminate those excess demands and supplies. But the argument works only if a price adjustment in one market caused by a previous excess demand or excess supply does not simultaneously create excess demands or supplies in markets not previously in disequilibrium, cause markets previously in excess demand to become markets in excess supply, or cause excess demands or excess supplies to increase rather than decrease.

To understand why, Fisher’s ad hoc assumptions do not guarantee that the Lyapunov function he defined will be continuously non-increasing, it will be helpful to refer to the famous Lipsey and Lancaster (1956) second-best theorem. According to their theorem, if one optimality condition in an economic model is unsatisfied because a relevant variable is constrained, the second-best solution, rather than satisfy the other unconstrained optimum conditions, involves revision of at least some of the unconstrained optimum conditions to take account of the constraint.

Contrast Fisher’s statement of the No Favorable Surprise assumption with how Lipsey and Lancaster (1956, 11) described the import of their theorem.

From this theorem there follows the important negative corollary that there is no a priori way to judge as between various situations in which some of the Paretian optimum conditions are fulfilled while others are not. Specifically, it is not true that a situation in which more, but not all, of the optimum conditions are fulfilled is necessarily, or is even likely to be, superior to a situation in which fewer are fulfilled. It follows, therefore, that in a situation in which there exist many constraints which prevent the fulfilment of the Paretian optimum conditions the removal of any one constraint may affect welfare or efficiency either by raising it, by lowering it, or by leaving it unchanged.

The general theorem of the second best states that if one of the Paretian optimum conditions cannot be fulfilled a second-best optimum situation is achieved only by departing from all other optimum conditions. It is important to note that in general, nothing can be said about the direction or the magnitude of the secondary departures from optimum conditions made necessary by the original non-fulfillment of one condition.

Although Lipsey and Lancaster were not referring to the adjustment process triggered by an adjustment process that follows a displacement from a prior equilibrium, nevertheless, their discussion implies that the stability of an adjustment process depends on the specific sequence of adjustments in that process, inasmuch as each successive price adjustment, aside from its immediate effect on the particular market in which the price adjusts, transmits feedback effects to related markets. A price adjustment in one market may increase, decrease, or leave unchanged, the efficiency of other markets, and the equilibrating tendency of a price adjustment in one market may be offset by indirect disequilibrating tendencies in other markets. When a price adjustment in one market indirectly reduces efficiency in other markets, the resulting price adjustments that follow may well trigger yet further indirect efficiency reductions.

Thus, in adjustment processes involving interrelated markets, price changes in one market can cause favorable surprises in other markets in which prices are not already at their general-equilibrium levels, by indirectly causing net increases in utility through feedback effects on related markets.

Consider a macroeconomic equilibrium satisfying all optimality conditions between marginal rates of substitution in production and consumption and relative prices. If that equilibrium is subjected to a macoreconomic disturbance affecting all, or most, individual markets, thereby changing all optimality conditions corresponding to the prior equilibrium, the new equilibrium will likely entail a different set of optimality conditions. While systemic optimality requires price adjustments to satisfy all the optimality conditions, actual price adjustments occur sequentially, in piecemeal fashion, with prices changing market by market or firm by firm, price changes occurring as agents perceive demand or cost changes. Those changes need not always induce equilibrating adjustments, nor is the arbitraging of price differences necessarily equilibrating when, under suboptimal conditions, prices have generally deviated from their equilibrium values. 

Smithian invisible-hand theorems are of little relevance in explaining the transition to a new equilibrium following a macroeconomic disturbance, because, in this context, the invisible-hand theorem begs the relevant question by assuming that the equilibrium price vector has been found. When all markets are in disequilibrium, moving toward equilibrium in one market will have repercussions on other markets, and the simple story of how price adjustment in response to a disequilibrium restores equilibrium breaks down, because market conditions in every market depend on market conditions in every other market. So, unless all optimality conditions are satisfied simultaneously, there is no assurance that piecemeal adjustments will bring the system closer to an optimal, or even a second-best, state.

If my interpretation of the NFS assumption is correct, Fisher’s stability results may provide support for Leijonhufvud’s (1973) suggestion that there is a corridor of stability around an equilibrium time path within which, under normal circumstances, an economy will not be displaced too far from path, so that an economy, unless displaced outside that corridor, will revert, more or less on its own, to its equilibrium path.[3]

Leijonhufvud attributed such resilience to the holding of buffer stocks of inventories of goods, holdings of cash and the availability of credit lines enabling agents to operate normally despite disappointed expectations. If negative surprises persist, agents will be unable to add to, or draw from, inventories indefinitely, or to finance normal expenditures by borrowing or drawing down liquid assets. Once buffer stocks are exhausted, the stabilizing properties of the economy have been overwhelmed by the destabilizing tendencies, income-constrained agents cut expenditures, as implied by the Keynesian multiplier analysis, triggering a cumulative contraction, and rendering a spontaneous recovery without compensatory fiscal or monetary measures, impossible.


[1] It was therefore incorrect for Fisher (1983, 88) to assert: “we can hope to show that  that the continued presence new opportunities is a necessary condition for instability — for continued change,” inasmuch as continued negative surprises can also cause continued — or at least prolonged — change.

[2] Fisher does recognize (pp. 88-89) that changes in expectations can be destabilizing. However, he considers only the possibility of exogenous events that cause expectations to change, but does not consider the possibility that expectations may change endogenously in a destabilizing fashion in the course of an adjustment process following a displacement from a prior equilibrium. See, however, his discussion (p. 91)

How is . . . an [“exogenous”] shock to be distinguished from the “endogenous” shock brought about by adjustment to the original shock? No Favorable Surprise may not be precisely what is wanted as an assumption in this area, but it is quite difficult to see exactly how to refine it.

A proof of stability under No Favorable Surprise, then, seems quite desirable for a number of related reasons. First, it is the strongest version of an assumption of No Favorable Exogenous Surprise (whatever that may mean precisely); hence, if stability does not hold under No Favorable Surprise it cannot be expected to hold under the more interesting weaker assumption.  

[3] Presumably because the income and output are maximized at the equilibrium path, it is unlikely that an economy will overshoot the path unless entrepreneurial or policy error cause such overshooting which is presumably an unlikely occurrence, although Austrian business cycle theory and perhaps certain other monetary business cycle theories suggest that such overshooting is not or has not always been an uncommon event.

Robert Lucas and Real Business-Cycle Theory

In 1978 Robert Lucas and Thomas Sargent launched a famous attack on Keynes and Keynesian economics, which they viewed as having been discredited by the confluence of high inflation and high unemployment in the 1970s. They also expressed optimistism that an equilibrium approach to business-cycle modeling would succeed in replicating reasonably well the observed time-series variables relating to output and employment. In particular they posited that a model subjected to an unexpected monetary shock causing an immediate downturn from an equilibrium time path would be followed by a gradual reversion to that time path, thereby capturing the main stylized facts of historical business cycles. Their optimism was disappointed, because the model that Lucas had developed, based on an informational imperfection preventing agents from distinguishing immediately between real and nominal price changes, could not account for downturns because the informational imperfection assumed by Lucas could not account for the typical multi-period duration of business-cycle downturns.

It was this empirical anomaly in Lucas’s monetary business-cycle model that prompted Kydland and Prescott to construct their real-business cycle model. Lucas warmly welcomed their contribution, the abandonment of the monetary-theoretical motivation that Lucas had inherited from his academic training at Chicago being a small price to pay for the advancement of the larger research agenda derived from his methodological imperatives.

The real-business cycle variant of the Lucasian research program rested on two empirical pillars: (1) the identification of technology shocks with deviations, as measured by the Solow residual, from the trend rate of increase in total factor productivity, positive residuals corresponding to positive shocks and negative residuals corresponding to negative shocks; and (2) estimates of elasticities of intertemporal rates of labor substitution.

Positive productivity shocks induce wage increases, and negative shocks induce wage decreases. Responding to the shifts in wages, presumed to be temporary, workers increase the amount of labor supplied in response to above-trend increases in wages and decrease the amount of labor supplied in response to below-trend increases in wages. The higher the elasticity of intertemporal labor substitution, the greater the supply response to a given deviation of actual wages from the expected trend rate of increase in wages. Real-business-cycle theorists used calibration techniques to obtain estimates labor-supply elasticities from microeconomic studies.

The real-business-cycle variant of the Lucasian research program embraced all the dubious methodological precepts of its parent while adding further dubious practices of its own. Most problematic, of course, is the methodological insistence that equilibrium is necessarily and continuously maintained, which is possible only if all agents correctly anticipate future prices and wages. If equilibrium is not continuously maintained, then Solow residuals may capture not productivity shocks, but, depending on their sign, either movements away from, or toward, equilibrium. In disequilibrium, labor and capital may be held idle by firms in anticipation of subsequent increases in output, so that measured productivity does not reflect the state of technology, but the inherent inefficiency of unemployment resulting from coordination failure, a contingency explicitly deemed by Lucasian methodology to be off limits.

Such ad hocery is generally frowned upon by scientists. Ad hoc assumptions are not always unscientific or unproductive, as famously exemplified by the discovery of Neptune. But in the latter case, the ad hoc assumption was subject to empirical testing; Neptune might not have been there waiting to be discovered. But no independent test of the presence or absence of a technology shock, aside from the Solow residual itself, is available. Even this situation might be tolerable, if Lucasian methodology permitted one to inquire whether the world or an economy might not be in an equilibrium state. But Lucasian methodology forbids such an inquiry.

The use of calibration to estimate intertemporal labor-supply elasticities from microeconomic studies are also extremely dubious, because microeconomic estimates of labor-supply elasticities are typically made under conditions approximating equilibrium, when workers have some flexibility in choosing whether to work more or less in the present or in the future. Those are not the conditions in which workers find themselves in periods of high aggregate unemployment, and are, therefore, not confident that they will retain their jobs in the present and near future, or, if they lose their jobs, that they will succeed in finding another job at an acceptable wage. The calibrated estimates of labor-supply elasticity are, for exactly the reasons identified in the Lucas Critique, unreliable for use in replicating time series.

An early real-business-cycle theorist Charles Plosser (“Understanding Real Business Cycles”) responded to criticisms of the RBC techniques as follows:

If the measured technological shocks are poor estimates (that is, they are confounded by other factors such as “demand” shocks, preference shocks or change in government policies, and so on) then feeding these values into our real business cycle model should result in poor predictions for the behavior of consumption, investment, hours worked, wages and output.

Plosser’s response ignores the question-begging nature of the RBC model; the supposed productivity shocks that cause cyclical fluctuations in the model are identified by the very time series that the model purports to explain. Nor does calibration provide clear and unambiguous estimates that the modeler can transfer without exercising discretion about which studies and which values to insert into an RBC model. Plosser’s defense of RBC is not so very different from the sort of defense made on behalf of the highly accurate epicyclical replications of observed planetary movements, replications that were based largely on the ingenuity and diligence of the epicyclist.

Eventually, the methodological prohibitions against heliocentrism were overcome. Perhaps, one day, the methodological prohibitions against non-reductionist macroeconomic theories will also be overcome.

Lucasian macroeconomics gained not only ascendance, but dominance, on the basis of  conceptual and methodological misunderstandings. The continued dominance of the offspring of the early Lucasian theories has been portrayed as a scientific advance by Lucas and his followers. In fact, the theories and the supposed methodological imperatives by which they have been justified are scientifically suspect because they rely on circular, question-begging arguments and reject alternative theories based on specious reductionist arguments.

Lucas and Sargent on Optimization and Equilibrium in Macroeconomics

In a famous contribution to a conference sponsored by the Federal Reserve Bank of Boston, Robert Lucas and Thomas Sargent (1978) harshly attacked Keynes and Keynesian macroeconomics for shortcomings both theoretical and econometric. The econometric criticisms, drawing on the famous Lucas Critique (Lucas 1976), were focused on technical identification issues and on the dependence of estimated regression coefficients of econometric models on agents’ expectations conditional on the macroeconomic policies actually in effect, rendering those econometric models an unreliable basis for policymaking. But Lucas and Sargent reserved their harshest criticism for abandoning what they called the classical postulates.

Economists prior to the 1930s did not recognize a need for a special branch of economics, with its own special postulates, designed to explain the business cycle. Keynes founded that subdiscipline, called macroeconomics, because he thought that it was impossible to explain the characteristics of business cycles within the discipline imposed by classical economic theory, a discipline imposed by its insistence on . . . two postulates (a) that markets . . . clear, and (b) that agents . . . act in their own self-interest [optimize]. The outstanding fact that seemed impossible to reconcile with these two postulates was the length and severity of business depressions and the large scale unemployment which they entailed. . . . After freeing himself of the straight-jacket (or discipline) imposed by the classical postulates, Keynes described a model in which rules of thumb, such as the consumption function and liquidity preference schedule, took the place of decision functions that a classical economist would insist be derived from the theory of choice. And rather than require that wages and prices be determined by the postulate that markets clear — which for the labor market seemed patently contradicted by the severity of business depressions — Keynes took as an unexamined postulate that money wages are “sticky,” meaning that they are set at a level or by a process that could be taken as uninfluenced by the macroeconomic forces he proposed to analyze[1]. . . .

In recent years, the meaning of the term “equilibrium” has undergone such dramatic development that a theorist of the 1930s would not recognize it. It is now routine to describe an economy following a multivariate stochastic process as being “in equilibrium,” by which is meant nothing more than that at each point in time, postulates (a) and (b) above are satisfied. This development, which stemmed mainly from work by K. J. Arrow and G. Debreu, implies that simply to look at any economic time series and conclude that it is a “disequilibrium phenomenon” is a meaningless observation. Indeed, a more likely conjecture, on the basis of recent work by Hugo Sonnenschein, is that the general hypothesis that a collection of time series describes an economy in competitive equilibrium is without content. (pp. 58-59)

Lucas and Sargent maintain that ‘classical” (by which they obviously mean “neoclassical”) economics is based on the twin postulates of (a) market clearing and (b) optimization. But optimization is a postulate about individual conduct or decision making under ideal conditions in which individuals can choose costlessly among alternatives that they can rank. Market clearing is not a postulate about individuals, it is the outcome of a process that neoclassical theory did not, and has not, described in any detail.

Instead of describing the process by which markets clear, neoclassical economic theory provides a set of not too realistic stories about how markets might clear, of which the two best-known stories are the Walrasian auctioneer/tâtonnement story, widely regarded as merely heuristic, if not fantastical, and the clearly heuristic and not-well-developed Marshallian partial-equilibrium story of a “long-run” equilibrium price for each good correctly anticipated by market participants corresponding to the long-run cost of production. However, the cost of production on which the Marhsallian long-run equilibrium price depends itself presumes that a general equilibrium of all other input and output prices has been reached, so it is not an alternative to, but must be subsumed under, the Walrasian general equilibrium paradigm.

Thus, in invoking the neoclassical postulates of market-clearing and optimization, Lucas and Sargent unwittingly, or perhaps wittingly, begged the question how market clearing, which requires that the plans of individual optimizing agents to buy and sell reconciled in such a way that each agent can carry out his/her/their plan as intended, comes about. Rather than explain how market clearing is achieved, they simply assert – and rather loudly – that we must postulate that market clearing is achieved, and thereby submit to the virtuous discipline of equilibrium.

Because they could provide neither empirical evidence that equilibrium is continuously achieved nor a plausible explanation of the process whereby it might, or could be, achieved, Lucas and Sargent try to normalize their insistence that equilibrium is an obligatory postulate that must be accepted by economists by calling it “routine to describe an economy following a multivariate stochastic process as being ‘in equilibrium,’ by which is meant nothing more than that at each point in time, postulates (a) and (b) above are satisfied,” as if the routine adoption of any theoretical or methodological assumption becomes ipso facto justified once adopted routinely. That justification was unacceptable to Lucas and Sargent when made on behalf of “sticky wages” or Keynesian “rules of thumb, but somehow became compelling when invoked on behalf of perpetual “equilibrium” and neoclassical discipline.

Using the authority of Arrow and Debreu to support the normalcy of the assumption that equilibrium is a necessary and continuous property of reality, Lucas and Sargent maintained that it is “meaningless” to conclude that any economic time series is a disequilibrium phenomenon. A proposition ismeaningless if and only if neither the proposition nor its negation is true. So, in effect, Lucas and Sargent are asserting that it is nonsensical to say that an economic time either reflects or does not reflect an equilibrium, but that it is, nevertheless, methodologically obligatory to for any economic model to make that nonsensical assumption.

It is curious that, in making such an outlandish claim, Lucas and Sargent would seek to invoke the authority of Arrow and Debreu. Leave aside the fact that Arrow (1959) himself identified the lack of a theory of disequilibrium pricing as an explanatory gap in neoclassical general-equilibrium theory. But if equilibrium is a necessary and continuous property of reality, why did Arrow and Debreu, not to mention Wald and McKenzie, devoted so much time and prodigious intellectual effort to proving that an equilibrium solution to a system of equations exists. If, as Lucas and Sargent assert (nonsensically), it makes no sense to entertain the possibility that an economy is, or could be, in a disequilibrium state, why did Wald, Arrow, Debreu and McKenzie bother to prove that the only possible state of the world actually exists?

Having invoked the authority of Arrow and Debreu, Lucas and Sargent next invoke the seminal contribution of Sonnenschein (1973), though without mentioning the similar and almost simultaneous contributions of Mantel (1974) and Debreu (1974), to argue that it is empirically empty to argue that any collection of economic time series is either in equilibrium or out of equilibrium. This property has subsequently been described as an “Anything Goes Theorem” (Mas-Colell, Whinston, and Green, 1995).

Presumably, Lucas and Sargent believe the empirically empty hypothesis that a collection of economic time series is, or, alternatively is not, in equilibrium is an argument supporting the methodological imperative of maintaining the assumption that the economy absolutely and necessarily is in a continuous state of equilibrium. But what Sonnenschein (and Mantel and Debreu) showed was that even if the excess demands of all individual agents are continuous, are homogeneous of degree zero, and even if Walras’s Law is satisfied, aggregating the excess demands of all agents would not necessarily cause the aggregate excess demand functions to behave in such a way that a unique or a stable equilibrium. But if we have no good argument to explain why a unique or at least a stable neoclassical general-economic equilibrium exists, on what methodological ground is it possible to insist that no deviation from the admittedly empirically empty and meaningless postulate of necessary and continuous equilibrium may be tolerated by conscientious economic theorists? Or that the gatekeepers of reputable neoclassical economics must enforce appropriate standards of professional practice?

As Franklin Fisher (1989) showed, inability to prove that there is a stable equilibrium leaves neoclassical economics unmoored, because the bread and butter of neoclassical price theory (microeconomics), comparative statics exercises, is conditional on the assumption that there is at least one stable general equilibrium solution for a competitive economy.

But it’s not correct to say that general equilibrium theory in its Arrow-Debreu-McKenzie version is empirically empty. Indeed, it has some very strong implications. There is no money, no banks, no stock market, and no missing markets; there is no advertising, no unsold inventories, no search, no private information, and no price discrimination. There are no surprises and there are no regrets, no mistakes and no learning. I could go on, but you get the idea. As a theory of reality, the ADM general-equilibrium model is simply preposterous. And, yet, this is the model of economic reality on the basis of which Lucas and Sargent proposed to build a useful and relevant theory of macroeconomic fluctuations. OMG!

Lucas, in various writings, has actually disclaimed any interest in providing an explanation of reality, insisting that his only aim is to devise mathematical models capable of accounting for the observed values of the relevant time series of macroeconomic variables. In Lucas’s conception of science, the only criterion for scientific knowledge is the capacity of a theory – an algorithm for generating numerical values to be measured against observed time series – to generate predicted values approximating the observed values of the time series. The only constraint on the algorithm is Lucas’s methodological preference that the algorithm be derived from what he conceives to be an acceptable microfounded version of neoclassical theory: a set of predictions corresponding to the solution of a dynamic optimization problem for a “representative agent.”

In advancing his conception of the role of science, Lucas has reverted to the approach of ancient astronomers who, for methodological reasons of their own, believed that the celestial bodies revolved around the earth in circular orbits. To ensure that their predictions matched the time series of the observed celestial positions of the planets, ancient astronomers, following Ptolemy, relied on epicycles or second-order circular movements of planets while traversing their circular orbits around the earth to account for their observed motions.

Kepler and later Galileo conceived of the solar system in a radically different way from the ancients, placing the sun, not the earth, at the fixed center of the solar system and proposing that the orbits of the planets were elliptical, not circular. For a long time, however, the actual time series of geocentric predictions outperformed the new heliocentric predictions. But even before the heliocentric predictions started to outperform the geocentric predictions, the greater simplicity and greater realism of the heliocentric theory attracted an increasing number of followers, forcing methodological supporters of the geocentric theory to take active measures to suppress the heliocentric theory.

I hold no particular attachment to the pre-Lucasian versions of macroeconomic theory, whether Keynesian, Monetarist, or heterodox. Macroeconomic theory required a grounding in an explicit intertemporal setting that had been lacking in most earlier theories. But the ruthless enforcement, based on a preposterous methodological imperative, lacking scientific or philosophical justification, of formal intertemporal optimization models as the only acceptable form of macroeconomic theorizing has sidetracked macroeconomics from a more relevant inquiry into the nature and causes of intertemporal coordination failures that Keynes, along with many some of his predecessors and contemporaries, had initiated.

Just as the dispute about whether planetary motion is geocentric or heliocentric was a dispute about what the world is like, not just about the capacity of models to generate accurate predictions of time series variables, current macroeconomic disputes are real disputes about what the world is like and whether aggregate economic fluctuations are the result of optimizing equilibrium choices by economic agents or about coordination failures that cause economic agents to be surprised and disappointed and rendered unable to carry out their plans in the manner in which they had hoped and expected to be able to do. It’s long past time for this dispute about reality to be joined openly with the seriousness that it deserves, instead of being suppressed by a spurious pseudo-scientific methodology.

HT: Arash Molavi Vasséi, Brian Albrecht, and Chris Edmonds


[1] Lucas and Sargent are guilty of at least two misrepresentations in this paragraph. First, Keynes did not “found” macroeconomics, though he certainly influenced its development decisively. Keynes used the term “macroeconomics,” and his work, though crucial, explicitly drew upon earlier work by Marshall, Wicksell, Fisher, Pigou, Hawtrey, and Robertson, among others. See Laidler (1999). Second, having explicitly denied and argued at length that his results did not depend on the assumption of sticky wages, Keynes certainly never introduced the assumption of sticky wages himself. See Leijonhufvud (1968)

Although RATEX Must Be a Contingent Property of any Economic Model, RATEX Is an Unlikely Property of Reality

Without searching through my old posts, I’m confident that I’ve already made this point many times in passing, but I just want to restate this point up front — highlighted and underscored. Any economic model must satisfy the following rational-expectations condition:

If the agents in the model expect the equilibrium outcome of the model (or, if there are multiple equilibrium outcomes, they all expect the same one of those equilibrium outcomes), that expected equilibrium outcome will be realized.

When the agents in an economic model all expect the equilibrium outcome of the model, the agents may be said to have rational expectations, and those rational expectations are self-fulfilling. Any economic model that lacks this contingent RATEX property is incoherent. But unless an economic model provides a theory of expectation formation whereby the agents all form correct expectations of the equilibrium outcome of the model, RATEX is a merely contingent, not an essential, property of the model.

Although an actual expectation-formation theory of rational expectations has never, to my knowledge, been derived from plausible assumptions, the RATEX assumption is disingenuously insisted upon as a property of rational decision-making implied by neoclassical theory. Such tyrannizing methodological intimidation is groundless and entails the reductio ad absurdum of the Milgrom and Stokey No-Trade Theorem.


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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