Archive for the 'macroeconomics' Category

A Primer on Equilibrium

After my latest post about rational expectations, Henry from Australia, one of my most prolific commenters, has been engaging me in a conversation about what assumptions are made – or need to be made – for an economic model to have a solution and for that solution to be characterized as an equilibrium, and in particular, a general equilibrium. Equilibrium in economics is not always a clearly defined concept, and it can have a number of different meanings depending on the properties of a given model. But the usual understanding is that the agents in the model (as consumers or producers) are trying to do as well for themselves as they can, given the endowments of resources, skills and technology at their disposal and given their preferences. The conversation was triggered by my assertion that rational expectations must be “compatible with the equilibrium of the model in which those expectations are embedded.”

That was the key insight of John Muth in his paper introducing the rational-expectations assumption into economic modelling. So in any model in which the current and future actions of individuals depend on their expectations of the future, the model cannot arrive at an equilibrium unless those expectations are consistent with the equilibrium of the model. If the expectations of agents are incompatible or inconsistent with the equilibrium of the model, then, since the actions taken or plans made by agents are based on those expectations, the model cannot have an equilibrium solution.

Now Henry thinks that this reasoning is circular. My argument would be circular if I defined an equilibrium to be the same thing as correct expectations. But I am not so defining an equilibrium. I am saying that the correctness of expectations by all agents implies 1) that their expectations are mutually consistent, and 2) that, having made plans, based on their expectations, which, by assumption, agents felt were the best set of choices available to them given those expectations, if the expectations of the agents are realized, then they would not regret the decisions and the choices that they made. Each agent would be as well off as he could have made himself, given his perceived opportunities when the decision were made. That the correctness of expectations implies equilibrium is the consequence of assuming that agents are trying to optimize their decision-making process, given their available and expected opportunities. If all expected opportunities are correctly foreseen, then all decisions will have been the optimal decisions under the circumstances. But nothing has been said that requires all expectations to be correct, or even that it is possible for all expectations to be correct. If an equilibrium does not exist, and just because you can write down an economic model, it does not mean that a solution to the model exists, then the sweet spot where all expectations are consistent and compatible is just a blissful fantasy. So a logical precondition to showing that rational expectations are even possible is to prove that an equilibrium exists. There is nothing circular about the argument.

Now the key to proving the existence of a general equilibrium is to show that the general equilibrium model implies the existence of what mathematicians call a fixed point. A fixed point is said to exist when there is a mapping – a rule or a function – that takes every point in a convex compact set of points and assigns that point to another point in the same set. A convex, compact set has two important properties: 1) the line connecting any two points in the set is entirely contained within the boundaries of the set, and 2) there are no gaps between any two points in set. The set of points in a circle or a rectangle is a convex compact set; the set of points contained in the Star of David is not a convex set. Any two points in the circle will be connected by a line that lies completely within the circle; the points at adjacent edges of a Star of David will be connected by a line that lies entirely outside the Star of David.

If you think of the set of all possible price vectors for an economy, those vectors – each containing a price for each good or service in the economy – could be mapped onto itself in the following way. Given all the equations describing the behavior of each agent in the economy, the quantity demanded and supplied of each good could be calculated, giving us the excess demand (the difference between amount demand and supplied) for each good. Then the price of every good in excess demand would be raised, the price of every good in negative excess demand would be reduced, and the price of every good with zero excess demand would be held constant. To ensure that the mapping was taking a point from a given convex set onto itself, all prices could be normalized so that they would have the property that the sum of all the individual prices would always equal 1. The fixed point theorem ensures that for a mapping from one convex compact set onto itself there must be at least one fixed point, i.e., at least one point in the set that gets mapped onto itself. The price vector corresponding to that point is an equilibrium, because, given how our mapping rule was defined, a point would be mapped onto itself if and only if all excess demands are zero, so that no prices changed. Every fixed point – and there may be one or more fixed points – corresponds to an equilibrium price vector and every equilibrium price vector is associated with a fixed point.

Before going on, I ought to make an important observation that is often ignored. The mathematical proof of the existence of an equilibrium doesn’t prove that the economy operates at an equilibrium, or even that the equilibrium could be identified under the mapping rule described (which is a kind of formalization of the Walrasian tatonnement process). The mapping rule doesn’t guarantee that you would ever discover a fixed point in any finite amount of iterations. Walras thought the price adjustment rule of raising the prices of goods in excess demand and reducing prices of goods in excess supply would converge on the equilibrium price vector. But the conditions under which you can prove that the naïve price-adjustment rule converges to an equilibrium price vector turn out to be very restrictive, so even though we can prove that the competitive model has an equilibrium solution – in other words the behavioral, structural and technological assumptions of the model are coherent, meaning that the model has a solution, the model has no assumptions about how prices are actually determined that would prove that the equilibrium is ever reached. In fact, the problem is even more daunting than the previous sentence suggest, because even Walrasian tatonnement imposes an incredibly powerful restriction, namely that no trading is allowed at non-equilibrium prices. In practice there are almost never recontracting provisions allowing traders to revise the terms of their trades once it becomes clear that the prices at which trades were made were not equilibrium prices.

I now want to show how price expectations fit into all of this, because the original general equilibrium models were either one-period models or formal intertemporal models that were reduced to single-period models by assuming that all trading for future delivery was undertaken in the first period by long-lived agents who would eventually carry out the transactions that were contracted in period 1 for subsequent consumption and production. Time was preserved in a purely formal, technical way, but all economic decision-making was actually concluded in the first period. But even though the early general-equilibrium models did not encompass expectations, one of the extraordinary precursors of modern economics, Augustin Cournot, who was way too advanced for his contemporaries even to comprehend, much less make any use of, what he was saying, had incorporated the idea of expectations into the solution of his famous economic model of oligopolistic price setting.

The key to oligopolistic pricing is that each oligopolist must take into account not just consumer demand for his product, and his own production costs; he must consider as well what actions will be taken by his rivals. This is not a problem for a competitive producer (a price-taker) or a pure monopolist. The price-taker simply compares the price at which he can sell as much as he wants with his production costs and decides how much it is worthwhile to produce by comparing his marginal cost to price ,and increases output until the marginal cost rises to match the price at which he can sell. The pure monopolist, if he knows, as is assumed in such exercises, or thinks he knows the shape of the customer demand curve, selects the price and quantity combination on the demand curve that maximizes total profit (corresponding to the equality of marginal revenue and marginal cost). In oligopolistic situations, each producer must take into account how much his rivals will sell, or what prices they will set.

It was by positing such a situation and finding an analytic solution, that Cournot made a stunning intellectual breakthrough. In the simple duopoly case, Cournot posited that if the duopolists had identical costs, then each could find his optimal price conditional on the output chosen by the other. This is a simple profit-maximization problem for each duopolist, given a demand curve for the combined output of both (assumed to be identical, so that a single price must obtain for the output of both) a cost curve and the output of the other duopolist. Thus, for each duopolist there is a reaction curve showing his optimal output given the output of the other. See the accompanying figure.cournot

If one duopolist produces zero, the optimal output for the other is the monopoly output. Depending on what the level of marginal cost is, there is some output by either of the duopolists that is sufficient to make it unprofitable for the other duopolist to produce anything. That level of output corresponds to the competitive output where price just equals marginal cost. So the slope of the two reaction functions corresponds to the ratio of the monopoly output to the competitive output, which, with constant marginal cost is 2:1. Given identical costs, the two reaction curves are symmetric and the optimal output for each, given the expected output of the other, corresponds to the intersection of the two reaction curves, at which both duopolists produce the same quantity. The combined output of the two duopolists will be greater than the monopoly output, but less than the competitive output at which price equals marginal cost. With constant marginal cost, it turns out that each duopolist produces one-third of the competitive output. In the general case with n oligoplists, the ratio of the combined output of all n firms to the competitive output equals n/(n+1).

Cournot’s solution corresponds to a fixed point where the equilibrium of the model implies that both duopolists have correct expectations of the output of the other. Given the assumptions of the model, if the duopolists both expect the other to produce an output equal to one-third of the competitive output, their expectations will be consistent and will be realized. If either one expects the other to produce a different output, the outcome will not be an equilibrium, and each duopolist will regret his output decision, because the price at which he can sell his output will differ from the price that he had expected. In the Cournot case, you could define a mapping of a vector of the quantities that each duopolist had expected the other to produce and the corresponding planned output of each duopolist. An equilibrium corresponds to a case in which both duopolists expected the output planned by the other. If either duopolist expected a different output from what the other planned, the outcome would not be an equilibrium.

We can now recognize that Cournot’s solution anticipated John Nash’s concept of an equilibrium strategy in which player chooses a strategy that is optimal given his expectation of what the other player’s strategy will be. A Nash equilibrium corresponds to a fixed point in which each player chooses an optimal strategy based on the correct expectation of what the other player’s strategy will be. There may be more than one Nash equilibrium in many games. For example, rather than base their decisions on an expectation of the quantity choice of the other duopolist, the two duopolists could base their decisions on an expectation of what price the other duopolist would set. In the constant-cost case, this choice of strategies would lead to the competitive output because both duopolists would conclude that the optimal strategy of the other duopolist would be to charge a price just sufficient to cover his marginal cost. This was the alternative oligopoly model suggested by another French economist J. L. F. Bertrand. Of course there is a lot more to be said about how oligopolists strategize than just these two models, and the conditions under which one or the other model is the more appropriate. I just want to observe that assumptions about expectations are crucial to how we analyze market equilibrium, and that the importance of these assumptions for understanding market behavior has been recognized for a very long time.

But from a macroeconomic perspective, the important point is that expected prices become the critical equilibrating variable in the theory of general equilibrium and in macroeconomics in general. Single-period models of equilibrium, including general-equilibrium models that are formally intertemporal, but in which all trades are executed in the initial period at known prices in a complete array of markets determining all future economic activity, are completely sterile and useless for macroeconomics except as a stepping stone to analyzing the implications of imperfect forecasts of future prices. If we want to think about general equilibrium in a useful macroeconomic context, we have to think about a general-equilibrium system in which agents make plans about consumption and production over time based on only the vaguest conjectures about what future conditions will be like when the various interconnected stages of their plans will be executed.

Unlike the full Arrow-Debreu system of complete markets, a general-equilibrium system with incomplete markets cannot be equilibrated, even in principle, by price adjustments in the incomplete set of present markets. Equilibration depends on the consistency of expected prices with equilibrium. If equilibrium is characterized by a fixed point, the fixed point must be mapping of a set of vectors of current prices and expected prices on to itself. That means that expected future prices are as much equilibrating variables as current market prices. But expected future prices exist only in the minds of the agents, they are not directly subject to change by market forces in the way that prices in actual markets are. If the equilibrating tendencies of market prices in a system of complete markets are very far from completely effective, the equilibrating tendencies of expected future prices may not only be non-existent, but may even be potentially disequilibrating rather than equilibrating.

The problem of price expectations in an intertemporal general-equilibrium system is central to the understanding of macroeconomics. Hayek, who was the father of intertemporal equilibrium theory, which he was the first to outline in a 1928 paper in German, and who explained the problem with unsurpassed clarity in his 1937 paper “Economics and Knowledge,” unfortunately did not seem to acknowledge its radical consequences for macroeconomic theory, and the potential ineffectiveness of self-equilibrating market forces. My quarrel with rational expectations as a strategy of macroeconomic analysis is its implicit assumption, lacking any analytical support, that prices and price expectations somehow always adjust to equilibrium values. In certain contexts, when there is no apparent basis to question whether a particular market is functioning efficiently, rational expectations may be a reasonable working assumption for modelling observed behavior. However, when there is reason to question whether a given market is operating efficiently or whether an entire economy is operating close to its potential, to insist on principle that the rational-expectations assumption must be made, to assume, in other words, that actual and expected prices adjust rapidly to their equilibrium values allowing an economy to operate at or near its optimal growth path, is simply, as I have often said, an exercise in circular reasoning and question begging.

Paul Romer on Modern Macroeconomics, Or, the “All Models Are False” Dodge

Paul Romer has been engaged for some time in a worthy campaign against the travesty of modern macroeconomics. A little over a year ago I commented favorably about Romer’s takedown of Robert Lucas, but I also defended George Stigler against what I thought was an unfair attempt by Romer to identify George Stigler as an inspiration and role model for Lucas’s transgressions. Now just a week ago, a paper based on Romer’s Commons Memorial Lecture to the Omicron Delta Epsilon Society, has become just about the hottest item in the econ-blogosophere, even drawing the attention of Daniel Drezner in the Washington Post.

I have already written critically about modern macroeconomics in my five years of blogging, and here are some links to previous posts (link, link, link, link). It’s good to see that Romer is continuing to voice his criticisms, and that they are gaining a lot of attention. But the macroeconomic hierarchy is used to criticism, and has its standard responses to criticism, which are being dutifully deployed by defenders of the powers that be.

Romer’s most effective rhetorical strategy is to point out that the RBC core of modern DSGE models posit unobservable taste and technology shocks to account for fluctuations in the economic time series, but that these taste and technology shocks are themselves simply inferred from the fluctuations in the times-series data, so that the entire structure of modern macroeconometrics is little more than an elaborate and sophisticated exercise in question-begging.

In this post, I just want to highlight one of the favorite catch-phrases of modern macroeconomics which serves as a kind of default excuse and self-justification for the rampant empirical failures of modern macroeconomics (documented by Lipsey and Carlaw as I showed in this post). When confronted by evidence that the predictions of their models are wrong, the standard and almost comically self-confident response of the modern macroeconomists is: All models are false. By which the modern macroeconomists apparently mean something like: “And if they are all false anyway, you can’t hold us accountable, because any model can be proven wrong. What really matters is that our models, being microfounded, are not subject to the Lucas Critique, and since all other models than ours are not micro-founded, and, therefore, being subject to the Lucas Critique, they are simply unworthy of consideration. This is what I have called methodological arrogance. That response is simply not true, because the Lucas Critique applies even to micro-founded models, those models being strictly valid only in equilibrium settings and being unable to predict the adjustment of economies in the transition between equilibrium states. All models are subject to the Lucas Critique.

Here is Romer’s take:

In response to the observation that the shocks are imaginary, a standard defense invokes Milton Friedman’s (1953) methodological assertion from unnamed authority that “the more significant the theory, the more unrealistic the assumptions (p.14).” More recently, “all models are false” seems to have become the universal hand-wave for dismissing any fact that does not conform to the model that is the current favorite.

Friedman’s methodological assertion would have been correct had Friedman substituted “simple” for “unrealistic.” Sometimes simplifications are unrealistic, but they don’t have to be. A simplification is a generalization of something complicated. By simplifying, we can transform a problem that had been too complex to handle into a problem more easily analyzed. But such simplifications aren’t necessarily unrealistic. To say that all models are false is simply a dodge to avoid having to account for failure. The excuse of course is that all those other models are subject to the Lucas Critique, so my model wins. But your model is subject to the Lucas Critique even though you claim it’s not, so even according to the rules you have arbitrarily laid down, you don’t win.

So I was just curious about where the little phrase “all models are false” came from. I was expecting that Karl Popper might have said it, in which case to use the phrase as a defense mechanism against empirical refutation would have been a particularly fraudulent tactic, because it would have been a perversion of Popper’s methodological stance, which was to force our theoretical constructs to face up to, not to insulate it from, empirical testing. But when I googled “all theories are false” what I found was not Popper, but the British statistician, G. E. P. Box who wrote in his paper “Science and Statistics” based on his R. A. Fisher Memorial Lecture to the American Statistical Association: “All models are wrong.” Here’s the exact quote:

Since all models are wrong the scientist cannot obtain a “correct” one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity.

Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad. Pure mathematics is concerned with propositions like “given that A is true, does B necessarily follow?” Since the statement is a conditional one, it has nothing whatsoever to do with the truth of A nor of the consequences B in relation to real life. The pure mathematician, acting in that capacity, need not, and perhaps should not, have any contact with practical matters at all.

In applying mathematics to subjects such as physics or statistics we make tentative assumptions about the real world which we know are false but which we believe may be useful nonetheless. The physicist knows that particles have mass and yet certain results, approximating what really happens, may be derived from the assumption that they do not. Equally, the statistician knows, for example, that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world. It follows that, although rigorous derivation of logical consequences is of great importance to statistics, such derivations are necessarily encapsulated in the knowledge that premise, and hence consequence, do not describe natural truth.

It follows that we cannot know that any statistical technique we develop is useful unless we use it. Major advances in science and in the science of statistics in particular, usually occur, therefore, as the result of the theory-practice iteration.

One of the most annoying conceits of modern macroeconomists is the constant self-congratulatory references to themselves as scientists because of their ostentatious use of axiomatic reasoning, formal proofs, and higher mathematical techniques. The tiresome self-congratulation might get toned down ever so slightly if they bothered to read and take to heart Box’s lecture.

There Is No Intertemporal Budget Constraint

Last week Nick Rowe posted a link to a just published article in a special issue of the Review of Keynesian Economics commemorating the 80th anniversary of the General Theory. Nick’s article discusses the confusion in the General Theory between saving and hoarding, and Nick invited readers to weigh in with comments about his article. The ROKE issue also features an article by Simon Wren-Lewis explaining the eclipse of Keynesian theory as a result of the New Classical Counter-Revolution, correctly identified by Wren-Lewis as a revolution inspired not by empirical success but by a methodological obsession with reductive micro-foundationalism. While deploring the New Classical methodological authoritarianism, Wren-Lewis takes solace from the ability of New Keynesians to survive under the New Classical methodological regime, salvaging a role for activist counter-cyclical policy by, in effect, negotiating a safe haven for the sticky-price assumption despite its shaky methodological credentials. The methodological fiction that sticky prices qualify as micro-founded allowed New Keynesianism to survive despite the ascendancy of micro-foundationalist methodology, thereby enabling the core Keynesian policy message to survive.

I mention the Wren-Lewis article in this context because of an exchange between two of the commenters on Nick’s article: the presumably pseudonymous Avon Barksdale and blogger Jason Smith about microfoundations and Keynesian economics. Avon began by chastising Nick for wasting time discussing Keynes’s 80-year old ideas, something Avon thinks would never happen in a discussion about a true science like physics, the 100-year-old ideas of Einstein being of no interest except insofar as they have been incorporated into the theoretical corpus of modern physics. Of course, this is simply vulgar scientism, as if the only legitimate way to do economics is to mimic how physicists do physics. This methodological scolding is typically charming New Classical arrogance. Sort of reminds one of how Friedrich Engels described Marxian theory as scientific socialism. I mean who, other than a religious fanatic, would be stupid enough to argue with the assertions of science?

Avon continues with a quotation from David Levine, a fine economist who has done a lot of good work, but who is also enthralled by the New Classical methodology. Avon’s scientism provoked the following comment from Jason Smith, a Ph. D. in physics with a deep interest in and understanding of economics.

You quote from Levine: “Keynesianism as argued by people such as Paul Krugman and Brad DeLong is a theory without people either rational or irrational”

This is false. The L in ISLM means liquidity preference and e.g. here …

… Krugman mentions an Euler equation. The Euler equation essentially says that an agent must be indifferent between consuming one more unit today on the one hand and saving that unit and consuming in the future on the other if utility is maximized.

So there are agents in both formulations preferring one state of the world relative to others.

Avon replied:


“This is false. The L in ISLM means liquidity preference and e.g. here”

I know what ISLM is. It’s not recursive so it really doesn’t have people in it. The dynamics are not set by any micro-foundation. If you’d like to see models with people in them, try Ljungqvist and Sargent, Recursive Macroeconomic Theory.

To which Jason retorted:


So the definition of “people” is restricted to agents making multi-period optimizations over time, solving a dynamic programming problem?

Well then any such theory is obviously wrong because people don’t behave that way. For example, humans don’t optimize the dictator game. How can you add up optimizing agents and get a result that is true for non-optimizing agents … coincident with the details of the optimizing agents mattering.

Your microfoundation requirement is like saying the ideal gas law doesn’t have any atoms in it. And it doesn’t! It is an aggregate property of individual “agents” that don’t have properties like temperature or pressure (or even volume in a meaningful sense). Atoms optimize entropy, but not out of any preferences.

So how do you know for a fact that macro properties like inflation or interest rates are directly related to agent optimizations? Maybe inflation is like temperature — it doesn’t exist for individuals and is only a property of economics in aggregate.

These questions are not answered definitively, and they’d have to be to enforce a requirement for microfoundations … or a particular way of solving the problem.

Are quarks important to nuclear physics? Not really — it’s all pions and nucleons. Emergent degrees of freedom. Sure, you can calculate pion scattering from QCD lattice calculations (quark and gluon DoF), but it doesn’t give an empirically better result than chiral perturbation theory (pion DoF) that ignores the microfoundations (QCD).

Assuming quarks are required to solve nuclear physics problems would have been a giant step backwards.

To which Avon rejoined:


The microfoundation of nuclear physics and quarks is quantum mechanics and quantum field theory. How the degrees of freedom reorganize under the renormalization group flow, what effective field theory results is an empirical question. Keynesian economics is worse tha[n] useless. It’s wrong empirically, it has no theoretical foundation, it has no laws. It has no microfoundation. No serious grad school has taught Keynesian economics in nearly 40 years.

To which Jason answered:


RG flow is irrelevant to chiral perturbation theory which is based on the approximate chiral symmetry of QCD. And chiral perturbation theory could exist without QCD as the “microfoundation”.

Quantum field theory is not a ‘microfoundation’, but rather a framework for building theories that may or may not have microfoundations. As Weinberg (1979) said:

” … quantum field theory itself has no content beyond analyticity, unitarity,
cluster decomposition, and symmetry.”

If I put together an NJL model, there is no requirement that the scalar field condensate be composed of quark-antiquark pairs. In fact, the basic idea was used for Cooper pairs as a model of superconductivity. Same macro theory; different microfoundations. And that is a general problem with microfoundations — different microfoundations can lead to the same macro theory, so which one is right?

And the IS-LM model is actually pretty empirically accurate (for economics):

To which Avon responded:

First, ISLM analysis does not hold empirically. It just doesn’t work. That’s why we ended up with the macro revolution of the 70s and 80s. Keynesian economics ignores intertemporal budget constraints, it violates Ricardian equivalence. It’s just not the way the world works. People might not solve dynamic programs to set their consumption path, but at least these models include a future which people plan over. These models work far better than Keynesian ISLM reasoning.

As for chiral perturbation theory and the approximate chiral symmetries of QCD, I am not making the case that NJL models requires QCD. NJL is an effective field theory so it comes from something else. That something else happens to be QCD. It could have been something else, that’s an empirical question. The microfoundation I’m talking about with theories like NJL is QFT and the symmetries of the vacuum, not the short distance physics that might be responsible for it. The microfoundation here is about the basic laws, the principles.

ISLM and Keynesian economics has none of this. There is no principle. The microfoundation of modern macro is not about increasing the degrees of freedom to model every person in the economy on some short distance scale, it is about building the basic principles from consistent economic laws that we find in microeconomics.

Well, I totally agree that IS-LM is a flawed macroeconomic model, and, in its original form, it was borderline-incoherent, being a single-period model with an interest rate, a concept without meaning except as an intertemporal price relationship. These deficiencies of IS-LM became obvious in the 1970s, so the model was extended to include a future period, with an expected future price level, making it possible to speak meaningfully about real and nominal interest rates, inflation and an equilibrium rate of spending. So the failure of IS-LM to explain stagflation, cited by Avon as the justification for rejecting IS-LM in favor of New Classical macro, was not that hard to fix, at least enough to make it serviceable. And comparisons of the empirical success of augmented IS-LM and the New Classical models have shown that IS-LM models consistently outperform New Classical models.

What Avon fails to see is that the microfoundations that he considers essential for macroeconomics are themselves derived from the assumption that the economy is operating in macroeconomic equilibrium. Thus, insisting on microfoundations – at least in the formalist sense that Avon and New Classical macroeconomists understand the term – does not provide a foundation for macroeconomics; it is just question begging aka circular reasoning or petitio principia.

The circularity is obvious from even a cursory reading of Samuelson’s Foundations of Economic Analysis, Robert Lucas’s model for doing economics. What Samuelson called meaningful theorems – thereby betraying his misguided acceptance of the now discredited logical positivist dogma that only potentially empirically verifiable statements have meaning – are derived using the comparative-statics method, which involves finding the sign of the derivative of an endogenous economic variable with respect to a change in some parameter. But the comparative-statics method is premised on the assumption that before and after the parameter change the system is in full equilibrium or at an optimum, and that the equilibrium, if not unique, is at least locally stable and the parameter change is sufficiently small not to displace the system so far that it does not revert back to a new equilibrium close to the original one. So the microeconomic laws invoked by Avon are valid only in the neighborhood of a stable equilibrium, and the macroeconomics that Avon’s New Classical mentors have imposed on the economics profession is a macroeconomics that, by methodological fiat, is operative only in the neighborhood of a locally stable equilibrium.

Avon dismisses Keynesian economics because it ignores intertemporal budget constraints. But the intertemporal budget constraint doesn’t exist in any objective sense. Certainly macroeconomics has to take into account intertemporal choice, but the idea of an intertemporal budget constraint analogous to the microeconomic budget constraint underlying the basic theory of consumer choice is totally misguided. In the static theory of consumer choice, the consumer has a given resource endowment and known prices at which consumers can transact at will, so the utility-maximizing vector of purchases and sales can be determined as the solution of a constrained-maximization problem.

In the intertemporal context, consumers have a given resource endowment, but prices are not known. So consumers have to make current transactions based on their expectations about future prices and a variety of other circumstances about which consumers can only guess. Their budget constraints are thus not real but totally conjectural based on their expectations of future prices. The optimizing Euler equations are therefore entirely conjectural as well, and subject to continual revision in response to changing expectations. The idea that the microeconomic theory of consumer choice is straightforwardly applicable to the intertemporal choice problem in a setting in which consumers don’t know what future prices will be and agents’ expectations of future prices are a) likely to be very different from each other and thus b) likely to be different from their ultimate realizations is a huge stretch. The intertemporal budget constraint has a completely different role in macroeconomics from the role it has in microeconomics.

If I expect that the demand for my services will be such that my disposable income next year would be $500k, my consumption choices would be very different from what they would have been if I were expecting a disposable income of $100k next year. If I expect a disposable income of $500k next year, and it turns out that next year’s income is only $100k, I may find myself in considerable difficulty, because my planned expenditure and the future payments I have obligated myself to make may exceed my disposable income or my capacity to borrow. So if there are a lot of people who overestimate their future incomes, the repercussions of their over-optimism may reverberate throughout the economy, leading to bankruptcies and unemployment and other bad stuff.

A large enough initial shock of mistaken expectations can become self-amplifying, at least for a time, possibly resembling the way a large initial displacement of water can generate a tsunami. A financial crisis, which is hard to model as an equilibrium phenomenon, may rather be an emergent phenomenon with microeconomic sources, but whose propagation can’t be described in microeconomic terms. New Classical macroeconomics simply excludes such possibilities on methodological grounds by imposing a rational-expectations general-equilibrium structure on all macroeconomic models.

This is not to say that the rational expectations assumption does not have a useful analytical role in macroeconomics. But the most interesting and most important problems in macroeconomics arise when the rational expectations assumption does not hold, because it is when individual expectations are very different and very unstable – say, like now, for instance — that macroeconomies become vulnerable to really scary instability.

Simon Wren-Lewis makes a similar point in his paper in the Review of Keynesian Economics.

Much discussion of current divisions within macroeconomics focuses on the ‘saltwater/freshwater’ divide. This understates the importance of the New Classical Counter Revolution (hereafter NCCR). It may be more helpful to think about the NCCR as involving two strands. The one most commonly talked about involves Keynesian monetary and fiscal policy. That is of course very important, and plays a role in the policy reaction to the recent Great Recession. However I want to suggest that in some ways the second strand, which was methodological, is more important. The NCCR helped completely change the way academic macroeconomics is done.

Before the NCCR, macroeconomics was an intensely empirical discipline: something made possible by the developments in statistics and econometrics inspired by The General Theory. After the NCCR and its emphasis on microfoundations, it became much more deductive. As Hoover (2001, p. 72) writes, ‘[t]he conviction that macroeconomics must possess microfoundations has changed the face of the discipline in the last quarter century’. In terms of this second strand, the NCCR was triumphant and remains largely unchallenged within mainstream academic macroeconomics.

Perhaps I will have some more to say about Wren-Lewis’s article in a future post. And perhaps also about Nick Rowe’s article.

HT: Tom Brown

Update (02/11/16):

On his blog Jason Smith provides some further commentary on his exchange with Avon on Nick Rowe’s blog, explaining at greater length how irrelevant microfoundations are to doing real empirically relevant physics. He also expands on and puts into a broader meta-theoretical context my point about the extremely narrow range of applicability of the rational-expectations equilibrium assumptions of New Classical macroeconomics.

David Glasner found a back-and-forth between me and a commenter (with the pseudonym “Avon Barksdale” after [a] character on The Wire who [didn’t end] up taking an economics class [per Tom below]) on Nick Rowe’s blog who expressed the (widely held) view that the only scientific way to proceed in economics is with rigorous microfoundations. “Avon” held physics up as a purported shining example of this approach.
I couldn’t let it go: even physics isn’t that reductionist. I gave several examples of cases where the microfoundations were actually known, but not used to figure things out: thermodynamics, nuclear physics. Even modern physics is supposedly built on string theory. However physicists do not require every pion scattering amplitude be calculated from QCD. Some people do do so-called lattice calculations. But many resort to the “effective” chiral perturbation theory. In a sense, that was what my thesis was about — an effective theory that bridges the gap between lattice QCD and chiral perturbation theory. That effective theory even gave up on one of the basic principles of QCD — confinement. It would be like an economist giving up opportunity cost (a basic principle of the micro theory). But no physicist ever said to me “your model is flawed because it doesn’t have true microfoundations”. That’s because the kind of hard core reductionism that surrounds the microfoundations paradigm doesn’t exist in physics — the most hard core reductionist natural science!
In his post, Glasner repeated something that he had before and — probably because it was in the context of a bunch of quotes about physics — I thought of another analogy.

Glasner says:

But the comparative-statics method is premised on the assumption that before and after the parameter change the system is in full equilibrium or at an optimum, and that the equilibrium, if not unique, is at least locally stable and the parameter change is sufficiently small not to displace the system so far that it does not revert back to a new equilibrium close to the original one. So the microeconomic laws invoked by Avon are valid only in the neighborhood of a stable equilibrium, and the macroeconomics that Avon’s New Classical mentors have imposed on the economics profession is a macroeconomics that, by methodological fiat, is operative only in the neighborhood of a locally stable equilibrium.


This hits on a basic principle of physics: any theory radically simplifies near an equilibrium.

Go to Jason’s blog to read the rest of his important and insightful post.

Representative Agents, Homunculi and Faith-Based Macroeconomics

After my previous post comparing the neoclassical synthesis in its various versions to the mind-body problem, there was an interesting Twitter exchange between Steve Randy Waldman and David Andolfatto in which Andolfatto queried whether Waldman and I are aware that there are representative-agent models in which the equilibrium is not Pareto-optimal. Andalfatto raised an interesting point, but what I found interesting about it might be different from what Andalfatto was trying to show, which, I am guessing, was that a representative-agent modeling strategy doesn’t necessarily commit the theorist to the conclusion that the world is optimal and that the solutions of the model can never be improved upon by a monetary/fiscal-policy intervention. I concede the point. It is well-known I think that, given the appropriate assumptions, a general-equilibrium model can have a sub-optimal solution. Given those assumptions, the corresponding representative-agent will also choose a sub-optimal solution. So I think I get that, but perhaps there’s a more subtle point  that I’m missing. If so, please set me straight.

But what I was trying to argue was not that representative-agent models are necessarily optimal, but that representative-agent models suffer from an inherent, and, in my view, fatal, flaw: they can’t explain any real macroeconomic phenomenon, because a macroeconomic phenomenon has to encompass something more than the decision of a single agent, even an omniscient central planner. At best, the representative agent is just a device for solving an otherwise intractable general-equilibrium model, which is how I think Lucas originally justified the assumption.

Yet just because a general-equilibrium model can be formulated so that it can be solved as the solution of an optimizing agent does not explain the economic mechanism or process that generates the solution. The mathematical solution of a model does not necessarily provide any insight into the adjustment process or mechanism by which the solution actually is, or could be, achieved in the real world. Your ability to find a solution for a mathematical problem does not mean that you understand the real-world mechanism to which the solution of your model corresponds. The correspondence between your model may be a strictly mathematical correspondence which may not really be in any way descriptive of how any real-world mechanism or process actually operates.

Here’s an example of what I am talking about. Consider a traffic-flow model explaining how congestion affects vehicle speed and the flow of traffic. It seems obvious that traffic congestion is caused by interactions between the different vehicles traversing a thoroughfare, just as it seems obvious that market exchange arises as the result of interactions between the different agents seeking to advance their own interests. OK, can you imagine building a useful traffic-flow model based on solving for the optimal plan of a representative vehicle?

I don’t think so. Once you frame the model in terms of a representative vehicle, you have abstracted from the phenomenon to be explained. The entire exercise would be pointless – unless, that is, you assumed that interactions between vehicles are so minimal that they can be ignored. But then why would you be interested in congestion effects? If you want to claim that your model has any relevance to the effect of congestion on traffic flow, you can’t base the claim on an assumption that there is no congestion.

Or to take another example, suppose you want to explain the phenomenon that, at sporting events, all, or almost all, the spectators sit in their seats but occasionally get up simultaneously from their seats to watch the play on the field or court. Would anyone ever think that an explanation in terms of a representative spectator could explain that phenomenon?

In just the same way, a representative-agent macroeconomic model necessarily abstracts from the interactions between actual agents. Obviously, by abstracting from the interactions, the model can’t demonstrate that there are no interactions between agents in the real world or that their interactions are too insignificant to matter. I would be shocked if anyone really believed that the interactions between agents are unimportant, much less, negligible; nor have I seen an argument that interactions between agents are unimportant, the concept of network effects, to give just one example, being an important topic in microeconomics.

It’s no answer to say that all the interactions are accounted for within the general-equilibrium model. That is just a form of question-begging. The representative agent is being assumed because without him the problem of finding a general-equilibrium solution of the model is very difficult or intractable. Taking into account interactions makes the model too complicated to work with analytically, so it is much easier — but still hard enough to allow the theorist to perform some fancy mathematical techniques — to ignore those pesky interactions. On top of that, the process by which the real world arrives at outcomes to which a general-equilibrium model supposedly bears at least some vague resemblance can’t even be described by conventional modeling techniques.

The modeling approach seems like that of a neuroscientist saying that, because he could simulate the functions, electrical impulses, chemical reactions, and neural connections in the brain – which he can’t do and isn’t even close to doing, even though a neuroscientist’s understanding of the brain far surpasses any economist’s understanding of the economy – he can explain consciousness. Simulating the operation of a brain would not explain consciousness, because the computer on which the neuroscientist performed the simulation would not become conscious in the course of the simulation.

Many neuroscientists and other materialists like to claim that consciousness is not real, that it’s just an epiphenomenon. But we all have the subjective experience of consciousness, so whatever it is that someone wants to call it, consciousness — indeed the entire world of mental phenomena denoted by that term — remains an unexplained phenomenon, a phenomenon that can only be dismissed as unreal on the basis of a metaphysical dogma that denies the existence of anything that can’t be explained as the result of material and physical causes.

I call that metaphysical belief a dogma not because it’s false — I have no way of proving that it’s false — but because materialism is just as much a metaphysical belief as deism or monotheism. It graduates from belief to dogma when people assert not only that the belief is true but that there’s something wrong with you if you are unwilling to believe it as well. The most that I would say against the belief in materialism is that I can’t understand how it could possibly be true. But I admit that there are a lot of things that I just don’t understand, and I will even admit to believing in some of those things.

New Classical macroeconomists, like, say, Robert Lucas and, perhaps, Thomas Sargent, like to claim that unless a macroeconomic model is microfounded — by which they mean derived from an explicit intertemporal optimization exercise typically involving a representative agent or possibly a small number of different representative agents — it’s not an economic model, because the model, being vulnerable to the Lucas critique, is theoretically superficial and vacuous. But only models of intertemporal equilibrium — a set of one or more mutually consistent optimal plans — are immune to the Lucas critique, so insisting on immunity to the Lucas critique as a prerequisite for a macroeconomic model is a guarantee of failure if your aim to explain anything other than an intertemporal equilibrium.

Unless, that is, you believe that real world is in fact the realization of a general equilibrium model, which is what real-business-cycle theorists, like Edward Prescott, at least claim to believe. Like materialist believers that all mental states are epiphenomenous, and that consciousness is an (unexplained) illusion, real-business-cycle theorists purport to deny that there is such a thing as a disequilibrium phenomenon, the so-called business cycle, in their view, being nothing but a manifestation of the intertemporal-equilibrium adjustment of an economy to random (unexplained) productivity shocks. According to real-business-cycle theorists, such characteristic phenomena of business cycles as surprise, regret, disappointed expectations, abandoned and failed plans, the inability to find work at wages comparable to wages that other similar workers are being paid are not real phenomena; they are (unexplained) illusions and misnomers. The real-business-cycle theorists don’t just fail to construct macroeconomic models; they deny the very existence of macroeconomics, just as strict materialists deny the existence of consciousness.

What is so preposterous about the New-Classical/real-business-cycle methodological position is not the belief that the business cycle can somehow be modeled as a purely equilibrium phenomenon, implausible as that idea seems, but the insistence that only micro-founded business-cycle models are methodologically acceptable. It is one thing to believe that ultimately macroeconomics and business-cycle theory will be reduced to the analysis of individual agents and their interactions. But current micro-founded models can’t provide explanations for what many of us think are basic features of macroeconomic and business-cycle phenomena. If non-micro-founded models can provide explanations for those phenomena, even if those explanations are not fully satisfactory, what basis is there for rejecting them just because of a methodological precept that disqualifies all non-micro-founded models?

According to Kevin Hoover, the basis for insisting that only micro-founded macroeconomic models are acceptable, even if the microfoundation consists in a single representative agent optimizing for an entire economy, is eschatological. In other words, because of a belief that economics will eventually develop analytical or computational techniques sufficiently advanced to model an entire economy in terms of individual interacting agents, an analysis based on a single representative agent, as the first step on this theoretical odyssey, is somehow methodologically privileged over alternative models that do not share that destiny. Hoover properly rejects the presumptuous notion that an avowed, but unrealized, theoretical destiny, can provide a privileged methodological status to an explanatory strategy. The reductionist microfoundationalism of New-Classical macroeconomics and real-business-cycle theory, with which New Keynesian economists have formed an alliance of convenience, is truly a faith-based macroeconomics.

The remarkable similarity between the reductionist microfoundational methodology of New-Classical macroeconomics and the reductionist materialist approach to the concept of mind suggests to me that there is also a close analogy between the representative agent and what philosophers of mind call a homunculus. The Cartesian materialist theory of mind maintains that, at some place or places inside the brain, there resides information corresponding to our conscious experience. The question then arises: how does our conscious experience access the latent information inside the brain? And the answer is that there is a homunculus (or little man) that processes the information for us so that we can perceive it through him. For example, the homunculus (see the attached picture of the little guy) views the image cast by light on the retina as if he were watching a movie projected onto a screen.


But there is an obvious fallacy, because the follow-up question is: how does our little friend see anything? Well, the answer must be that there’s another, smaller, homunculus inside his brain. You can probably already tell that this argument is going to take us on an infinite regress. So what purports to be an explanation turns out to be just a form of question-begging. Sound familiar? The only difference between the representative agent and the homunculus is that the representative agent begs the question immediately without having to go on an infinite regress.

PS I have been sidetracked by other responsibilities, so I have not been blogging much, if at all, for the last few weeks. I hope to post more frequently, but I am afraid that my posting and replies to comments are likely to remain infrequent for the next couple of months.

Romer v. Lucas

A couple of months ago, Paul Romer created a stir by publishing a paper in the American Economic Review “Mathiness in the Theory of Economic Growth,” an attack on two papers, one by McGrattan and Prescott and the other by Lucas and Moll on aspects of growth theory. He accused the authors of those papers of using mathematical modeling as a cover behind which to hide assumptions guaranteeing results by which the authors could promote their research agendas. In subsequent blog posts, Romer has sharpened his attack, focusing it more directly on Lucas, whom he accuses of a non-scientific attachment to ideological predispositions that have led him to violate what he calls Feynman integrity, a concept eloquently described by Feynman himself in a 1974 commencement address at Caltech.

It’s a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty–a kind of leaning over backwards. For example, if you’re doing an experiment, you should report everything that you think might make it invalid–not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you’ve eliminated by some other experiment, and how they worked–to make sure the other fellow can tell they have been eliminated.

Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can–if you know anything at all wrong, or possibly wrong–to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it. There is also a more subtle problem. When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition.

Romer contrasts this admirable statement of what scientific integrity means with another by George Stigler, seemingly justifying, or at least excusing, a kind of special pleading on behalf of one’s own theory. And the institutional and perhaps ideological association between Stigler and Lucas seems to suggest that Lucas is inclined to follow the permissive and flexible Stiglerian ethic rather than rigorous Feynman standard of scientific integrity. Romer regards this as a breach of the scientific method and a step backward for economics as a science.

I am not going to comment on the specific infraction that Romer accuses Lucas of having committed; I am not familiar with the mathematical question in dispute. Certainly if Lucas was aware that his argument in the paper Romer criticizes depended on the particular mathematical assumption in question, Lucas should have acknowledged that to be the case. And even if, as Lucas asserted in responding to a direct question by Romer, he could have derived the result in a more roundabout way, then he should have pointed that out, too. However, I don’t regard the infraction alleged by Romer to be more than a misdemeanor, hardly a scandalous breach of the scientific method.

Why did Lucas, who as far as I can tell was originally guided by Feynman integrity, switch to the mode of Stigler conviction? Market clearing did not have to evolve from auxiliary hypothesis to dogma that could not be questioned.

My conjecture is economists let small accidents of intellectual history matter too much. If we had behaved like scientists, things could have turned out very differently. It is worth paying attention to these accidents because doing so might let us take more control over the process of scientific inquiry that we are engaged in. At the very least, we should try to reduce the odds that that personal frictions and simple misunderstandings could once again cause us to veer off on some damaging trajectory.

I suspect that it was personal friction and a misunderstanding that encouraged a turn toward isolation (or if you prefer, epistemic closure) by Lucas and colleagues. They circled the wagons because they thought that this was the only way to keep the rational expectations revolution alive. The misunderstanding is that Lucas and his colleagues interpreted the hostile reaction they received from such economists as Robert Solow to mean that they were facing implacable, unreasoning resistance from such departments as MIT. In fact, in a remarkably short period of time, rational expectations completely conquered the PhD program at MIT.

More recently Romer, having done graduate work both at MIT and Chicago in the late 1970s, has elaborated on the personal friction between Solow and Lucas and how that friction may have affected Lucas, causing him to disengage from the professional mainstream. Paul Krugman, who was at MIT when this nastiness was happening, is skeptical of Romer’s interpretation.

My own view is that being personally and emotionally attached to one’s own theories, whether for religious or ideological or other non-scientific reasons, is not necessarily a bad thing as long as there are social mechanisms allowing scientists with different scientific viewpoints an opportunity to make themselves heard. If there are such mechanisms, the need for Feynman integrity is minimized, because individual lapses of integrity will be exposed and remedied by criticism from other scientists; scientific progress is possible even if scientists don’t live up to the Feynman standards, and maintain their faith in their theories despite contradictory evidence. But, as I am going to suggest below, there are reasons to doubt that social mechanisms have been operating to discipline – not suppress, just discipline – dubious economic theorizing.

My favorite example of the importance of personal belief in, and commitment to the truth of, one’s own theories is Galileo. As discussed by T. S. Kuhn in The Structure of Scientific Revolutions. Galileo was arguing for a paradigm change in how to think about the universe, despite being confronted by empirical evidence that appeared to refute the Copernican worldview he believed in: the observations that the sun revolves around the earth, and that the earth, as we directly perceive it, is, apart from the occasional earthquake, totally stationary — good old terra firma. Despite that apparently contradictory evidence, Galileo had an alternative vision of the universe in which the obvious movement of the sun in the heavens was explained by the spinning of the earth on its axis, and the stationarity of the earth by the assumption that all our surroundings move along with the earth, rendering its motion imperceptible, our perception of motion being relative to a specific frame of reference.

At bottom, this was an almost metaphysical world view not directly refutable by any simple empirical test. But Galileo adopted this worldview or paradigm, because he deeply believed it to be true, and was therefore willing to defend it at great personal cost, refusing to recant his Copernican view when he could have easily appeased the Church by describing the Copernican theory as just a tool for predicting planetary motion rather than an actual representation of reality. Early empirical tests did not support heliocentrism over geocentrism, but Galileo had faith that theoretical advancements and improved measurements would eventually vindicate the Copernican theory. He was right of course, but strict empiricism would have led to a premature rejection of heliocentrism. Without a deep personal commitment to the Copernican worldview, Galileo might not have articulated the case for heliocentrism as persuasively as he did, and acceptance of heliocentrism might have been delayed for a long time.

Imre Lakatos called such deeply-held views underlying a scientific theory the hard core of the theory (aka scientific research program), a set of beliefs that are maintained despite apparent empirical refutation. The response to any empirical refutation is not to abandon or change the hard core but to adjust what Lakatos called the protective belt of the theory. Eventually, as refutations or empirical anomalies accumulate, the research program may undergo a crisis, leading to its abandonment, or it may simply degenerate if it fails to solve new problems or discover any new empirical facts or regularities. So Romer’s criticism of Lucas’s dogmatic attachment to market clearing – Lucas frequently makes use of ad hoc price stickiness assumptions; I don’t know why Romer identifies market-clearing as a Lucasian dogma — may be no more justified from a history of science perspective than would criticism of Galileo’s dogmatic attachment to heliocentrism.

So while I have many problems with Lucas, lack of Feynman integrity is not really one of them, certainly not in the top ten. What I find more disturbing is his narrow conception of what economics is. As he himself wrote in an autobiographical sketch for Lives of the Laureates, he was bewitched by the beauty and power of Samuelson’s Foundations of Economic Analysis when he read it the summer before starting his training as a graduate student at Chicago in 1960. Although it did not have the transformative effect on me that it had on Lucas, I greatly admire the Foundations, but regardless of whether Samuelson himself meant to suggest such an idea (which I doubt), it is absurd to draw this conclusion from it:

I loved the Foundations. Like so many others in my cohort, I internalized its view that if I couldn’t formulate a problem in economic theory mathematically, I didn’t know what I was doing. I came to the position that mathematical analysis is not one of many ways of doing economic theory: It is the only way. Economic theory is mathematical analysis. Everything else is just pictures and talk.

Oh, come on. Would anyone ever think that unless you can formulate the problem of whether the earth revolves around the sun or the sun around the earth mathematically, you don’t know what you are doing? And, yet, remarkably, on the page following that silly assertion, one finds a totally brilliant description of what it was like to take graduate price theory from Milton Friedman.

Friedman rarely lectured. His class discussions were often structured as debates, with student opinions or newspaper quotes serving to introduce a problem and some loosely stated opinions about it. Then Friedman would lead us into a clear statement of the problem, considering alternative formulations as thoroughly as anyone in the class wanted to. Once formulated, the problem was quickly analyzed—usually diagrammatically—on the board. So we learned how to formulate a model, to think about and decide which features of a problem we could safely abstract from and which he needed to put at the center of the analysis. Here “model” is my term: It was not a term that Friedman liked or used. I think that for him talking about modeling would have detracted from the substantive seriousness of the inquiry we were engaged in, would divert us away from the attempt to discover “what can be done” into a merely mathematical exercise. [my emphasis].

Despite his respect for Friedman, it’s clear that Lucas did not adopt and internalize Friedman’s approach to economic problem solving, but instead internalized the caricature he extracted from Samuelson’s Foundations: that mathematical analysis is the only legitimate way of doing economic theory, and that, in particular, the essence of macroeconomics consists in a combination of axiomatic formalism and philosophical reductionism (microfoundationalism). For Lucas, the only scientifically legitimate macroeconomic models are those that can be deduced from the axiomatized Arrow-Debreu-McKenzie general equilibrium model, with solutions that can be computed and simulated in such a way that the simulations can be matched up against the available macroeconomics time series on output, investment and consumption.

This was both bad methodology and bad science, restricting the formulation of economic problems to those for which mathematical techniques are available to be deployed in finding solutions. On the one hand, the rational-expectations assumption made finding solutions to certain intertemporal models tractable; on the other, the assumption was justified as being required by the rationality assumptions of neoclassical price theory.

In a recent review of Lucas’s Collected Papers on Monetary Theory, Thomas Sargent makes a fascinating reference to Kenneth Arrow’s 1967 review of the first two volumes of Paul Samuelson’s Collected Works in which Arrow referred to the problematic nature of the neoclassical synthesis of which Samuelson was a chief exponent.

Samuelson has not addressed himself to one of the major scandals of current price theory, the relation between microeconomics and macroeconomics. Neoclassical microeconomic equilibrium with fully flexible prices presents a beautiful picture of the mutual articulations of a complex structure, full employment being one of its major elements. What is the relation between this world and either the real world with its recurrent tendencies to unemployment of labor, and indeed of capital goods, or the Keynesian world of underemployment equilibrium? The most explicit statement of Samuelson’s position that I can find is the following: “Neoclassical analysis permits of fully stable underemployment equilibrium only on the assumption of either friction or a peculiar concatenation of wealth-liquidity-interest elasticities. . . . [The neoclassical analysis] goes far beyond the primitive notion that, by definition of a Walrasian system, equilibrium must be at full employment.” . . .

In view of the Phillips curve concept in which Samuelson has elsewhere shown such interest, I take the second sentence in the above quotation to mean that wages are stationary whenever unemployment is X percent, with X positive; thus stationary unemployment is possible. In general, one can have a neoclassical model modified by some elements of price rigidity which will yield Keynesian-type implications. But such a model has yet to be constructed in full detail, and the question of why certain prices remain rigid becomes of first importance. . . . Certainly, as Keynes emphasized the rigidity of prices has something to do with the properties of money; and the integration of the demand and supply of money with general competitive equilibrium theory remains incomplete despite attempts beginning with Walras himself.

If the neoclassical model with full price flexibility were sufficiently unrealistic that stable unemployment equilibrium be possible, then in all likelihood the bulk of the theorems derived by Samuelson, myself, and everyone else from the neoclassical assumptions are also contrafactual. The problem is not resolved by what Samuelson has called “the neoclassical synthesis,” in which it is held that the achievement of full employment requires Keynesian intervention but that neoclassical theory is valid when full employment is reached. . . .

Obviously, I believe firmly that the mutual adjustment of prices and quantities represented by the neoclassical model is an important aspect of economic reality worthy of the serious analysis that has been bestowed on it; and certain dramatic historical episodes – most recently the reconversion of the United States from World War II and the postwar European recovery – suggest that an economic mechanism exists which is capable of adaptation to radical shifts in demand and supply conditions. On the other hand, the Great Depression and the problems of developing countries remind us dramatically that something beyond, but including, neoclassical theory is needed.

Perhaps in a future post, I may discuss this passage, including a few sentences that I have omitted here, in greater detail. For now I will just say that Arrow’s reference to a “neoclassical microeconomic equilibrium with fully flexible prices” seems very strange inasmuch as price flexibility has absolutely no role in the proofs of the existence of a competitive general equilibrium for which Arrow and Debreu and McKenzie are justly famous. All the theorems Arrow et al. proved about the neoclassical equilibrium were related to existence, uniqueness and optimaiity of an equilibrium supported by an equilibrium set of prices. Price flexibility was not involved in those theorems, because the theorems had nothing to do with how prices adjust in response to a disequilibrium situation. What makes this juxtaposition of neoclassical microeconomic equilibrium with fully flexible prices even more remarkable is that about eight years earlier Arrow wrote a paper (“Toward a Theory of Price Adjustment”) whose main concern was the lack of any theory of price adjustment in competitive equilibrium, about which I will have more to say below.

Sargent also quotes from two lectures in which Lucas referred to Don Patinkin’s treatise Money, Interest and Prices which provided perhaps the definitive statement of the neoclassical synthesis Samuelson espoused. In one lecture (“My Keynesian Education” presented to the History of Economics Society in 2003) Lucas explains why he thinks Patinkin’s book did not succeed in its goal of integrating value theory and monetary theory:

I think Patinkin was absolutely right to try and use general equilibrium theory to think about macroeconomic problems. Patinkin and I are both Walrasians, whatever that means. I don’t see how anybody can not be. It’s pure hindsight, but now I think that Patinkin’s problem was that he was a student of Lange’s, and Lange’s version of the Walrasian model was already archaic by the end of the 1950s. Arrow and Debreu and McKenzie had redone the whole theory in a clearer, more rigorous, and more flexible way. Patinkin’s book was a reworking of his Chicago thesis from the middle 1940s and had not benefited from this more recent work.

In the other lecture, his 2003 Presidential address to the American Economic Association, Lucas commented further on why Patinkin fell short in his quest to unify monetary and value theory:

When Don Patinkin gave his Money, Interest, and Prices the subtitle “An Integration of Monetary and Value Theory,” value theory meant, to him, a purely static theory of general equilibrium. Fluctuations in production and employment, due to monetary disturbances or to shocks of any other kind, were viewed as inducing disequilibrium adjustments, unrelated to anyone’s purposeful behavior, modeled with vast numbers of free parameters. For us, today, value theory refers to models of dynamic economies subject to unpredictable shocks, populated by agents who are good at processing information and making choices over time. The macroeconomic research I have discussed today makes essential use of value theory in this modern sense: formulating explicit models, computing solutions, comparing their behavior quantitatively to observed time series and other data sets. As a result, we are able to form a much sharper quantitative view of the potential of changes in policy to improve peoples’ lives than was possible a generation ago.

So, as Sargent observes, Lucas recreated an updated neoclassical synthesis of his own based on the intertemporal Arrow-Debreu-McKenzie version of the Walrasian model, augmented by a rationale for the holding of money and perhaps some form of monetary policy, via the assumption of credit-market frictions and sticky prices. Despite the repudiation of the updated neoclassical synthesis by his friend Edward Prescott, for whom monetary policy is irrelevant, Lucas clings to neoclassical synthesis 2.0. Sargent quotes this passage from Lucas’s 1994 retrospective review of A Monetary History of the US by Friedman and Schwartz to show how tightly Lucas clings to neoclassical synthesis 2.0 :

In Kydland and Prescott’s original model, and in many (though not all) of its descendants, the equilibrium allocation coincides with the optimal allocation: Fluctuations generated by the model represent an efficient response to unavoidable shocks to productivity. One may thus think of the model not as a positive theory suited to all historical time periods but as a normative benchmark providing a good approximation to events when monetary policy is conducted well and a bad approximation when it is not. Viewed in this way, the theory’s relative success in accounting for postwar experience can be interpreted as evidence that postwar monetary policy has resulted in near-efficient behavior, not as evidence that money doesn’t matter.

Indeed, the discipline of real business cycle theory has made it more difficult to defend real alternaltives to a monetary account of the 1930s than it was 30 years ago. It would be a term-paper-size exercise, for example, to work out the possible effects of the 1930 Smoot-Hawley Tariff in a suitably adapted real business cycle model. By now, we have accumulated enough quantitative experience with such models to be sure that the aggregate effects of such a policy (in an economy with a 5% foreign trade sector before the Act and perhaps a percentage point less after) would be trivial.

Nevertheless, in the absence of some catastrophic error in monetary policy, Lucas evidently believes that the key features of the Arrow-Debreu-McKenzie model are closely approximated in the real world. That may well be true. But if it is, Lucas has no real theory to explain why.

In his 1959 paper (“Towards a Theory of Price Adjustment”) I just mentioned, Arrow noted that the theory of competitive equilibrium has no explanation of how equilibrium prices are actually set. Indeed, the idea of competitive price adjustment is beset by a paradox: all agents in a general equilibrium being assumed to be price takers, how is it that a new equilibrium price is ever arrived at following any disturbance to an initial equilibrium? Arrow had no answer to the question, but offered the suggestion that, out of equilibrium, agents are not price takers, but price searchers, possessing some measure of market power to set price in the transition between the old and new equilibrium. But the upshot of Arrow’s discussion was that the problem and the paradox awaited solution. Almost sixty years on, some of us are still waiting, but for Lucas and the Lucasians, there is neither problem nor paradox, because the actual price is the equilibrium price, and the equilibrium price is always the (rationally) expected price.

If the social functions of science were being efficiently discharged, this rather obvious replacement of problem solving by question begging would not have escaped effective challenge and opposition. But Lucas was able to provide cover for this substitution by persuading the profession to embrace his microfoundational methodology, while offering irresistible opportunities for professional advancement to younger economists who could master the new analytical techniques that Lucas and others were rapidly introducing, thereby neutralizing or coopting many of the natural opponents to what became modern macroeconomics. So while Romer considers the conquest of MIT by the rational-expectations revolution, despite the opposition of Robert Solow, to be evidence for the advance of economic science, I regard it as a sign of the social failure of science to discipline a regressive development driven by the elevation of technique over substance.

Krugman’s Second Best

A couple of days ago Paul Krugman discussed “Second-best Macroeconomics” on his blog. I have no real quarrel with anything he said, but I would like to amplify his discussion of what is sometimes called the problem of second-best, because I think the problem of second best has some really important implications for macroeconomics beyond the limited application of the problem that Krugman addressed. The basic idea underlying the problem of second best is not that complicated, but it has many applications, and what made the 1956 paper (“The General Theory of Second Best”) by R. G. Lipsey and Kelvin Lancaster a classic was that it showed how a number of seemingly disparate problems were really all applications of a single unifying principle. Here’s how Krugman frames his application of the second-best problem.

[T]he whole western world has spent years suffering from a severe shortfall of aggregate demand; in Europe a severe misalignment of national costs and prices has been overlaid on this aggregate problem. These aren’t hard problems to diagnose, and simple macroeconomic models — which have worked very well, although nobody believes it — tell us how to solve them. Conventional monetary policy is unavailable thanks to the zero lower bound, but fiscal policy is still on tap, as is the possibility of raising the inflation target. As for misaligned costs, that’s where exchange rate adjustments come in. So no worries: just hit the big macroeconomic That Was Easy button, and soon the troubles will be over.

Except that all the natural answers to our problems have been ruled out politically. Austerians not only block the use of fiscal policy, they drive it in the wrong direction; a rise in the inflation target is impossible given both central-banker prejudices and the power of the goldbug right. Exchange rate adjustment is blocked by the disappearance of European national currencies, plus extreme fear over technical difficulties in reintroducing them.

As a result, we’re stuck with highly problematic second-best policies like quantitative easing and internal devaluation.

I might quibble with Krugman about the quality of the available macroeconomic models, by which I am less impressed than he, but that’s really beside the point of this post, so I won’t even go there. But I can’t let the comment about the inflation target pass without observing that it’s not just “central-banker prejudices” and the “goldbug right” that are to blame for the failure to raise the inflation target; for reasons that I don’t claim to understand myself, the political consensus in both Europe and the US in favor of perpetually low or zero inflation has been supported with scarcely any less fervor by the left than the right. It’s only some eccentric economists – from diverse positions on the political spectrum – that have been making the case for inflation as a recovery strategy. So the political failure has been uniform across the political spectrum.

OK, having registered my factual disagreement with Krugman about the source of our anti-inflationary intransigence, I can now get to the main point. Here’s Krugman:

“[S]econd best” is an economic term of art. It comes from a classic 1956 paper by Lipsey and Lancaster, which showed that policies which might seem to distort markets may nonetheless help the economy if markets are already distorted by other factors. For example, suppose that a developing country’s poorly functioning capital markets are failing to channel savings into manufacturing, even though it’s a highly profitable sector. Then tariffs that protect manufacturing from foreign competition, raise profits, and therefore make more investment possible can improve economic welfare.

The problems with second best as a policy rationale are familiar. For one thing, it’s always better to address existing distortions directly, if you can — second best policies generally have undesirable side effects (e.g., protecting manufacturing from foreign competition discourages consumption of industrial goods, may reduce effective domestic competition, and so on). . . .

But here we are, with anything resembling first-best macroeconomic policy ruled out by political prejudice, and the distortions we’re trying to correct are huge — one global depression can ruin your whole day. So we have quantitative easing, which is of uncertain effectiveness, probably distorts financial markets at least a bit, and gets trashed all the time by people stressing its real or presumed faults; someone like me is then put in the position of having to defend a policy I would never have chosen if there seemed to be a viable alternative.

In a deep sense, I think the same thing is involved in trying to come up with less terrible policies in the euro area. The deal that Greece and its creditors should have reached — large-scale debt relief, primary surpluses kept small and not ramped up over time — is a far cry from what Greece should and probably would have done if it still had the drachma: big devaluation now. The only way to defend the kind of thing that was actually on the table was as the least-worst option given that the right response was ruled out.

That’s one example of a second-best problem, but it’s only one of a variety of problems, and not, it seems to me, the most macroeconomically interesting. So here’s the second-best problem that I want to discuss: given one distortion (i.e., a departure from one of the conditions for Pareto-optimality), reaching a second-best sub-optimum requires violating other – likely all the other – conditions for reaching the first-best (Pareto) optimum. The strategy for getting to the second-best suboptimum cannot be to achieve as many of the conditions for reaching the first-best optimum as possible; the conditions for reaching the second-best optimum are in general totally different from the conditions for reaching the first-best optimum.

So what’s the deeper macroeconomic significance of the second-best principle?

I would put it this way. Suppose there’s a pre-existing macroeconomic equilibrium, all necessary optimality conditions between marginal rates of substitution in production and consumption and relative prices being satisfied. Let the initial equilibrium be subjected to a macoreconomic disturbance. The disturbance will immediately affect a range — possibly all — of the individual markets, and all optimality conditions will change, so that no market will be unaffected when a new optimum is realized. But while optimality for the system as a whole requires that prices adjust in such a way that the optimality conditions are satisfied in all markets simultaneously, each price adjustment that actually occurs is a response to the conditions in a single market – the relationship between amounts demanded and supplied at the existing price. Each price adjustment being a response to a supply-demand imbalance in an individual market, there is no theory to explain how a process of price adjustment in real time will ever restore an equilibrium in which all optimality conditions are simultaneously satisfied.

Invoking a general Smithian invisible-hand theorem won’t work, because, in this context, the invisible-hand theorem tells us only that if an equilibrium price vector were reached, the system would be in an optimal state of rest with no tendency to change. The invisible-hand theorem provides no account of how the equilibrium price vector is discovered by any price-adjustment process in real time. (And even tatonnement, a non-real-time process, is not guaranteed to work as shown by the Sonnenschein-Mantel-Debreu Theorem). With price adjustment in each market entirely governed by the demand-supply imbalance in that market, market prices determined in individual markets need not ensure that all markets clear simultaneously or satisfy the optimality conditions.

Now it’s true that we have a simple theory of price adjustment for single markets: prices rise if there’s an excess demand and fall if there’s an excess supply. If demand and supply curves have normal slopes, the simple price adjustment rule moves the price toward equilibrium. But that partial-equilibriuim story is contingent on the implicit assumption that all other markets are in equilibrium. 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 markets arrive at equilibrium simultaneously, there’s no guarantee that equilibrium will obtain in any of the markets. Disequilibrium in any market can mean disequilibrium in every market. And if a single market is out of kilter, the second-best, suboptimal solution for the system is totally different from the first-best solution for all markets.

In the standard microeconomics we are taught in econ 1 and econ 101, all these complications are assumed away by restricting the analysis of price adjustment to a single market. In other words, as I have pointed out in a number of previous posts (here and here), standard microeconomics is built on macroeconomic foundations, and the currently fashionable demand for macroeconomics to be microfounded turns out to be based on question-begging circular reasoning. Partial equilibrium is a wonderful pedagogical device, and it is an essential tool in applied microeconomics, but its limitations are often misunderstood or ignored.

An early macroeconomic application of the theory of second is the statement by the quintessentially orthodox pre-Keynesian Cambridge economist Frederick Lavington who wrote in his book The Trade Cycle “the inactivity of all is the cause of the inactivity of each.” Each successive departure from the conditions for second-, third-, fourth-, and eventually nth-best sub-optima has additional negative feedback effects on the rest of the economy, moving it further and further away from a Pareto-optimal equilibrium with maximum output and full employment. The fewer people that are employed, the more difficult it becomes for anyone to find employment.

This insight was actually admirably, if inexactly, expressed by Say’s Law: supply creates its own demand. The cause of the cumulative contraction of output in a depression is not, as was often suggested, that too much output had been produced, but a breakdown of coordination in which disequilibrium spreads in epidemic fashion from market to market, leaving individual transactors unable to compensate by altering the terms on which they are prepared to supply goods and services. The idea that a partial-equilibrium response, a fall in money wages, can by itself remedy a general-disequilibrium disorder is untenable. Keynes and the Keynesians were therefore completely wrong to accuse Say of committing a fallacy in diagnosing the cause of depressions. The only fallacy lay in the assumption that market adjustments would automatically ensure the restoration of something resembling full-employment equilibrium.

Price Stickiness and Macroeconomics

Noah Smith has a classically snide rejoinder to Stephen Williamson’s outrage at Noah’s Bloomberg paean to price stickiness and to the classic Ball and Maniw article on the subject, an article that provoked an embarrassingly outraged response from Robert Lucas when published over 20 years ago. I don’t know if Lucas ever got over it, but evidently Williamson hasn’t.

Now to be fair, Lucas’s outrage, though misplaced, was understandable, at least if one understands that Lucas was so offended by the ironic tone in which Ball and Mankiw cast themselves as defenders of traditional macroeconomics – including both Keynesians and Monetarists – against the onslaught of “heretics” like Lucas, Sargent, Kydland and Prescott that he just stopped reading after the first few pages and then, in a fit of righteous indignation, wrote a diatribe attacking Ball and Mankiw as religious fanatics trying to halt the progress of science as if that was the real message of the paper – not, to say the least, a very sophisticated reading of what Ball and Mankiw wrote.

While I am not hostile to the idea of price stickiness — one of the most popular posts I have written being an attempt to provide a rationale for the stylized (though controversial) fact that wages are stickier than other input, and most output, prices — it does seem to me that there is something ad hoc and superficial about the idea of price stickiness and about many explanations, including those offered by Ball and Mankiw, for price stickiness. I think that the negative reactions that price stickiness elicits from a lot of economists — and not only from Lucas and Williamson — reflect a feeling that price stickiness is not well grounded in any economic theory.

Let me offer a slightly different criticism of price stickiness as a feature of macroeconomic models, which is simply that although 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.

The usual argument is that if prices are free to adjust in response to market forces, they will adjust to balance supply and demand, and an equilibrium will be restored by the automatic adjustment of prices. That is what students are taught in Econ 1. And it is an important lesson, but it is also a “partial” lesson. It is partial, because it applies to a single market that is out of equilibrium. The implicit assumption in that exercise is that nothing else is changing, which means that all other markets — well, not quite all other markets, but I will ignore that nuance – are in equilibrium. That’s what I mean when I say (as I have done before) that just as macroeconomics needs microfoundations, microeconomics needs macrofoundations.

Now it’s pretty easy to show that in a single market with an upward-sloping supply curve and a downward-sloping demand curve, that a price-adjustment rule that raises price when there’s an excess demand and reduces price when there’s an excess supply will lead to an equilibrium market price. But that simple price-adjustment rule is hard to generalize when many markets — not just one — are in disequilibrium, because reducing disequilibrium in one market may actually exacerbate disequilibrium, or create a disequilibrium that wasn’t there before, in another market. Thus, even if there is an equilibrium price vector out there, which, if it were announced to all economic agents, would sustain a general equilibrium in all markets, there is no guarantee that following the standard price-adjustment rule of raising price in markets with an excess demand and reducing price in markets with an excess supply will ultimately lead to the equilibrium price vector. Even more disturbing, the standard price-adjustment rule may not, even under a tatonnement process in which no trading is allowed at disequilibrium prices, lead to the discovery of the equilibrium price vector. Of course, in the real world trading occurs routinely at disequilibrium prices, so that the “mechanical” forces tending an economy toward equilibrium are even weaker than the standard analysis of price-adjustment would suggest.

This doesn’t mean that an economy out of equilibrium has no stabilizing tendencies; it does mean that those stabilizing tendencies are not very well understood, and we have almost no formal theory with which to describe how such an adjustment process leading from disequilibrium to equilibrium actually works. We just assume that such a process exists. Franklin Fisher made this point 30 years ago in an important, but insufficiently appreciated, volume Disequilibrium Foundations of Equilibrium Economics. But the idea goes back even further: to Hayek’s important work on intertemporal equilibrium, especially his classic paper “Economics and Knowledge,” formalized by Hicks in the temporary-equilibrium model described in Value and Capital.

The key point made by Hayek in this context is that there can be an intertemporal equilibrium if and only if all agents formulate their individual plans on the basis of the same expectations of future prices. If their expectations for future prices are not the same, then any plans based on incorrect price expectations will have to be revised, or abandoned altogether, as price expectations are disappointed over time. For price adjustment to lead an economy back to equilibrium, the price adjustment must converge on an equilibrium price vector and on correct price expectations. But, as Hayek understood in 1937, and as Fisher explained in a dense treatise 30 years ago, we have no economic theory that explains how such a price vector, even if it exists, is arrived at, and even under a tannonement process, much less under decentralized price setting. Pinning the blame on this vague thing called price stickiness doesn’t address the deeper underlying theoretical issue.

Of course for Lucas et al. to scoff at price stickiness on these grounds is a bit rich, because Lucas and his followers seem entirely comfortable with assuming that the equilibrium price vector is rationally expected. Indeed, rational expectation of the equilibrium price vector is held up by Lucas as precisely the microfoundation that transformed the unruly field of macroeconomics into a real science.

Traffic Jams and Multipliers

Since my previous post which I closed by quoting the abstract of Brian Arthur’s paper “Complexity Economics: A Different Framework for Economic Thought,” I have been reading his paper and some of the papers he cites, especially Magda Fontana’s paper “The Santa Fe Perspective on Economics: Emerging Patterns in the Science of Complexity,” and Mark Blaug’s paper “The Formalist Revolution of the 1950s.” The papers bring together a number of themes that I have been emphasizing in previous posts on what I consider the misguided focus of modern macroeconomics on rational-expectations equilibrium as the organizing principle of macroeconomic theory. Among these themes are the importance of coordination failures in explaining macroeconomic fluctuations, the inappropriateness of the full general-equilibrium paradigm in macroeconomics, the mistaken transformation of microfoundations from a theoretical problem to be solved into an absolute methodological requirement to be insisted upon (almost exactly analogous to the absurd transformation of the mind-body problem into a dogmatic insistence that the mind is merely a figment of our own imagination), or, stated another way, a recognition that macrofoundations are just as necessary for economics as microfoundations.

Let me quote again from Arthur’s essay; this time a beautiful passage which captures the interdependence between the micro and macro perspectives

To look at the economy, or areas within the economy, from a complexity viewpoint then would mean asking how it evolves, and this means examining in detail how individual agents’ behaviors together form some outcome and how this might in turn alter their behavior as a result. Complexity in other words asks how individual behaviors might react to the pattern they together create, and how that pattern would alter itself as a result. This is often a difficult question; we are asking how a process is created from the purposed actions of multiple agents. And so economics early in its history took a simpler approach, one more amenable to mathematical analysis. It asked not how agents’ behaviors would react to the aggregate patterns these created, but what behaviors (actions, strategies, expectations) would be upheld by — would be consistent with — the aggregate patterns these caused. It asked in other words what patterns would call for no changes in microbehavior, and would therefore be in stasis, or equilibrium. (General equilibrium theory thus asked what prices and quantities of goods produced and consumed would be consistent with — would pose no incentives for change to — the overall pattern of prices and quantities in the economy’s markets. Classical game theory asked what strategies, moves, or allocations would be consistent with — would be the best course of action for an agent (under some criterion) — given the strategies, moves, allocations his rivals might choose. And rational expectations economics asked what expectations would be consistent with — would on average be validated by — the outcomes these expectations together created.)

This equilibrium shortcut was a natural way to examine patterns in the economy and render them open to mathematical analysis. It was an understandable — even proper — way to push economics forward. And it achieved a great deal. Its central construct, general equilibrium theory, is not just mathematically elegant; in modeling the economy it re-composes it in our minds, gives us a way to picture it, a way to comprehend the economy in its wholeness. This is extremely valuable, and the same can be said for other equilibrium modelings: of the theory of the firm, of international trade, of financial markets.

But there has been a price for this equilibrium finesse. Economists have objected to it — to the neoclassical construction it has brought about — on the grounds that it posits an idealized, rationalized world that distorts reality, one whose underlying assumptions are often chosen for analytical convenience. I share these objections. Like many economists, I admire the beauty of the neoclassical economy; but for me the construct is too pure, too brittle — too bled of reality. It lives in a Platonic world of order, stasis, knowableness, and perfection. Absent from it is the ambiguous, the messy, the real. (pp. 2-3)

Later in the essay, Arthur provides a simple example of a non-equilibrium complex process: traffic flow.

A typical model would acknowledge that at close separation from cars in front, cars lower their speed, and at wide separation they raise it. A given high density of traffic of N cars per mile would imply a certain average separation, and cars would slow or accelerate to a speed that corresponds. Trivially, an equilibrium speed emerges, and if we were restricting solutions to equilibrium that is all we would see. But in practice at high density, a nonequilibrium phenomenon occurs. Some car may slow down — its driver may lose concentration or get distracted — and this might cause cars behind to slow down. This immediately compresses the flow, which causes further slowing of the cars behind. The compression propagates backwards, traffic backs up, and a jam emerges. In due course the jam clears. But notice three things. The phenomenon’s onset is spontaneous; each instance of it is unique in time of appearance, length of propagation, and time of clearing. It is therefore not easily captured by closed-form solutions, but best studied by probabilistic or statistical methods. Second, the phenomenon is temporal, it emerges or happens within time, and cannot appear if we insist on equilibrium. And third, the phenomenon occurs neither at the micro-level (individual car level) nor at the macro-level (overall flow on the road) but at a level in between — the meso-level. (p. 9)

This simple example provides an excellent insight into why macroeconomic reasoning can be led badly astray by focusing on the purely equilibrium relationships characterizing what we now think of as microfounded models. In arguing against the Keynesian multiplier analysis supposedly justifying increased government spending as a countercyclical tool, Robert Barro wrote the following in an unfortunate Wall Street Journal op-ed piece, which I have previously commented on here and here.

Keynesian economics argues that incentives and other forces in regular economics are overwhelmed, at least in recessions, by effects involving “aggregate demand.” Recipients of food stamps use their transfers to consume more. Compared to this urge, the negative effects on consumption and investment by taxpayers are viewed as weaker in magnitude, particularly when the transfers are deficit-financed.

Thus, the aggregate demand for goods rises, and businesses respond by selling more goods and then by raising production and employment. The additional wage and profit income leads to further expansions of demand and, hence, to more production and employment. As per Mr. Vilsack, the administration believes that the cumulative effect is a multiplier around two.

If valid, this result would be truly miraculous. The recipients of food stamps get, say, $1 billion but they are not the only ones who benefit. Another $1 billion appears that can make the rest of society better off. Unlike the trade-off in regular economics, that extra $1 billion is the ultimate free lunch.

How can it be right? Where was the market failure that allowed the government to improve things just by borrowing money and giving it to people? Keynes, in his “General Theory” (1936), was not so good at explaining why this worked, and subsequent generations of Keynesian economists (including my own youthful efforts) have not been more successful.

In the disequilibrium environment of a recession, it is at least possible that injecting additional spending into the economy could produce effects that a similar injection of spending, under “normal” macro conditions, would not produce, just as somehow withdrawing a few cars from a congested road could increase the average speed of all the remaining cars on the road, by a much greater amount than would withdrawing a few cars from an uncongested road. In other words, microresponses may be sensitive to macroconditions.

The Trouble with IS-LM (and its Successors)

Lately, I have been reading a paper by Roger Backhouse and David Laidler, “What Was Lost with IS-LM” (an earlier version is available here) which was part of a very interesting symposium of 11 papers on the IS-LM model published as a supplement to the 2004 volume of History of Political Economy. The main thesis of the paper is that the IS-LM model, like the General Theory of which it is a partial and imperfect distillation, aborted a number of promising developments in the rapidly developing, but still nascent, field of macroeconomics in the 1920 and 1930s, developments that just might, had they not been elbowed aside by the IS-LM model, have evolved into a more useful and relevant theory of macroeconomic fluctuations and policy than we now possess. Even though I have occasionally sparred with Scott Sumner about IS-LM – with me pushing back a bit at Scott’s attacks on IS-LM — I have a lot of sympathy for the Backhouse-Laidler thesis.

The Backhouse-Laidler paper is too long to summarize, but I will just note that there are four types of loss that they attribute to IS-LM, which are all, more or less, derivative of the static equilibrium character of Keynes’s analytic method in both the General Theory and the IS-LM construction.

1 The loss of dynamic analysis. IS-LM is a single-period model.

2 The loss of intertemporal choice and expectations. Intertemporal choice and expectations are excluded a priori in a single-period model.

3 The loss of policy regimes. In a single-period model, policy is a one-time affair. The problem of setting up a regime that leads to optimal results over time doesn’t arise.

4 The loss of intertemporal coordination failures. Another concept that is irrelevant in a one-period model.

There was one particular passage that I found especially impressive. Commenting on the lack of any systematic dynamic analysis in the GT, Backhouse and Laidler observe,

[A]lthough [Keynes] made many remarks that could be (and in some cases were later) turned into dynamic models, the emphasis of the General Theory was nevertheless on unemployment as an equilibrium phenomenon.

Dynamic accounts of how money wages might affect employment were only a little more integrated into Keynes’s formal analysis than they were later into IS-LM. Far more significant for the development in Keynes’s thought is how Keynes himself systematically neglected dynamic factors that had been discussed in previous explanations of unemployment. This was a feature of the General Theory remarked on by Bertil Ohlin (1937, 235-36):

Keynes’s theoretical system . . . is equally “old-fashioned” in the second respect which characterizes recent economic theory – namely, the attempt to break away from an explanation of economic events by means of orthodox equilibrium constructions. No other analysis of trade fluctuations in recent years – with the possible exception of the Mises-Hayek school – follows such conservative lines in this respect. In fact, Keynes is much more of an “equilibrium theorist” than such economists as Cassel and, I think, Marshall.

Backhouse and Laidler go on to cite the Stockholm School (of which Ohlin was a leading figure) as an example of explicitly dynamic analysis.

As Bjorn Hansson (1982) has shown, this group developed an explicit method, using the idea of a succession of “unit periods,” in which each period began with agents having plans based on newly formed expectations about the outcome of executing them, and ended with the economy in some new situation that was the outcome of executing them, and ended with the economy in some new situation that was the outcome of market processes set in motion by the incompatibility of those plans, and in which expectations had been reformulated, too, in the light of experience. They applied this method to the construction of a wide variety of what they called “model sequences,” many of which involved downward spirals in economic activity at whose very heart lay rising unemployment. This is not the place to discuss the vexed question of the extent to which some of this work anticipated the Keynesian multiplier process, but it should be noted that, in IS-LM, it is the limit to which such processes move, rather than the time path they follow to get there, that is emphasized.

The Stockholm method seems to me exactly the right way to explain business-cycle downturns. In normal times, there is a rough – certainly not perfect, but good enough — correspondence of expectations among agents. That correspondence of expectations implies that the individual plans contingent on those expectations will be more or less compatible with one another. Surprises happen; here and there people are disappointed and regret past decisions, but, on the whole, they are able to adjust as needed to muddle through. There is usually enough flexibility in a system to allow most people to adjust their plans in response to unforeseen circumstances, so that the disappointment of some expectations doesn’t become contagious, causing a systemic crisis.

But when there is some sort of major shock – and it can only be a shock if it is unforeseen – the system may not be able to adjust. Instead, the disappointment of expectations becomes contagious. If my customers aren’t able to sell their products, I may not be able to sell mine. Expectations are like networks. If there is a breakdown at some point in the network, the whole network may collapse or malfunction. Because expectations and plans fit together in interlocking networks, it is possible that even a disturbance at one point in the network can cascade over an increasingly wide group of agents, leading to something like a system-wide breakdown, a financial crisis or a depression.

But the “problem” with the Stockholm method was that it was open-ended. It could offer only “a wide variety” of “model sequences,” without specifying a determinate solution. It was just this gap in the Stockholm approach that Keynes was able to fill. He provided a determinate equilibrium, “the limit to which the Stockholm model sequences would move, rather than the time path they follow to get there.” A messy, but insightful, approach to explaining the phenomenon of downward spirals in economic activity coupled with rising unemployment was cast aside in favor of the neater, simpler approach of Keynes. No wonder Ohlin sounds annoyed in his comment, quoted by Backhouse and Laidler, about Keynes. Tractability trumped insight.

Unfortunately, that is still the case today. Open-ended models of the sort that the Stockholm School tried to develop still cannot compete with the RBC and DSGE models that have displaced IS-LM and now dominate modern macroeconomics. The basic idea that modern economies form networks, and that networks have properties that are not reducible to just the nodes forming them has yet to penetrate the trained intuition of modern macroeconomists. Otherwise, how would it have been possible to imagine that a macroeconomic model could consist of a single representative agent? And just because modern macroeconomists have expanded their models to include more than a single representative agent doesn’t mean that the intellectual gap evidenced by the introduction of representative-agent models into macroeconomic discourse has been closed.

Another Complaint about Modern Macroeconomics

In discussing modern macroeconomics, I’ve have often mentioned my discomfort with a narrow view of microfoundations, but I haven’t commented very much on another disturbing feature of modern macro: the requirement that theoretical models be spelled out fully in axiomatic form. The rhetoric of axiomatization has had sweeping success in economics, making axiomatization a pre-requisite for almost any theoretical paper to be taken seriously, and even considered for publication in a reputable economics journal.

The idea that a good scientific theory must be derived from a formal axiomatic system has little if any foundation in the methodology or history of science. Nevertheless, it has become almost an article of faith in modern economics. I am not aware, but would be interested to know, whether, and if so how widely, this misunderstanding has been propagated in other (purportedly) empirical disciplines. The requirement of the axiomatic method in economics betrays a kind of snobbishness and (I use this word advisedly, see below) pedantry, resulting, it seems, from a misunderstanding of good scientific practice.

Before discussing the situation in economics, I would note that axiomatization did not become a major issue for mathematicians until late in the nineteenth century (though demands – luckily ignored for the most part — for logical precision followed immediately upon the invention of the calculus by Newton and Leibniz) and led ultimately to the publication of the great work of Russell and Whitehead, Principia Mathematica whose goal was to show that all of mathematics could be derived from the axioms of pure logic. This is yet another example of an unsuccessful reductionist attempt, though it seemed for a while that the Principia paved the way for the desired reduction. But 20 years after the Principia was published, Kurt Godel proved his famous incompleteness theorem, showing that, as a matter of pure logic, not even all the valid propositions of arithmetic, much less all of mathematics, could be derived from any system of axioms. This doesn’t mean that trying to achieve a reduction of a higher-level discipline to another, deeper discipline is not a worthy objective, but it certainly does mean that one cannot just dismiss, out of hand, a discipline simply because all of its propositions are not deducible from some set of fundamental propositions. Insisting on reduction as a prerequisite for scientific legitimacy is not a scientific attitude; it is merely a form of obscurantism.

As far as I know, which admittedly is not all that far, the only empirical science which has been axiomatized to any significant extent is theoretical physics. In his famous list of 23 unsolved mathematical problems, the great mathematician David Hilbert included the following (number 6).

Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part, in the first rank are the theory of probabilities and mechanics.

As to the axioms of the theory of probabilities, it seems to me desirable that their logical investigation should be accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gasses. . . . Boltzman’s work on the principles of mechanics suggests the problem of developing mathematically the limiting processes, there merely indicated, which lead from the atomistic view to the laws of motion of continua.

The point that I want to underscore here is that axiomatization was supposed to ensure that there was an adequate logical underpinning for theories (i.e., probability and the kinetic theory of gasses) that had already been largely worked out. Thus, Hilbert proposed axiomatization not as a method of scientific discovery, but as a method of checking for hidden errors and problems. Error checking is certainly important for science, but it is clearly subordinate to the creation and empirical testing of new and improved scientific theories.

The fetish for axiomitization in economics can largely be traced to Gerard Debreu’s great work, The Theory of Value: An Axiomatic Analysis of Economic Equilibrium, in which Debreu, building on his own work and that of Kenneth Arrow, presented a formal description of a decentralized competitive economy with both households and business firms, and proved that, under the standard assumptions of neoclassical theory (notably diminishing marginal rates of substitution in consumption and production and perfect competition) such an economy would have at least one, and possibly more than one, equilibrium.

A lot of effort subsequently went into gaining a better understanding of the necessary and sufficient conditions under which an equilibrium exists, and when that equilibrium would be unique and Pareto optimal. The subsequent work was then brilliantly summarized and extended in another great work, General Competitive Analysis by Arrow and Frank Hahn. Unfortunately, those two books, paragons of the axiomatic method, set a bad example for the future development of economic theory, which embarked on a needless and counterproductive quest for increasing logical rigor instead of empirical relevance.

A few months ago, I wrote a review of Kartik Athreya’s book Big Ideas in Macroeconomics. One of the arguments of Athreya’s book that I didn’t address was his defense of modern macroeconomics against the complaint that modern macroeconomics is too mathematical. Athreya is not responsible for the reductionist and axiomatic fetishes of modern macroeconomics, but he faithfully defends them against criticism. So I want to comment on a few paragraphs in which Athreya dismisses criticism of formalism and axiomatization.

Natural science has made significant progress by proceeding axiomatically and mathematically, and whether or not we [economists] will achieve this level of precision for any unit of observation in macroeconomics, it is likely to be the only rational alternative.

First, let me observe that axiomatization is not the same as using mathematics to solve problems. Many problems in economics cannot easily be solved without using mathematics, and sometimes it is useful to solve a problem in a few different ways, each way potentially providing some further insight into the problem not provided by the others. So I am not at all opposed to the use of mathematics in economics. However, the choice of tools to solve a problem should bear some reasonable relationship to the problem at hand. A good economist will understand what tools are appropriate to the solution of a particular problem. While mathematics has clearly been enormously useful to the natural sciences and to economics in solving problems, there are very few scientific advances that can be ascribed to axiomatization. Axiomatization was vital in proving the existence of equilibrium, but substantive refutable propositions about real economies, e.g., the Heckscher-Ohlin Theorem, or the Factor-Price Equalization Theorem, or the law of comparative advantage, were not discovered or empirically tested by way of axiomatization. Arthreya talks about economics achieving the “level of precision” achieved by natural science, but the concept of precision is itself hopelessly imprecise, and to set precision up as an independent goal makes no sense. Arthreya continues:

In addition to these benefits from the systematic [i.e. axiomatic] approach, there is the issue of clarity. Lowering mathematical content in economics represents a retreat from unambiguous language. Once mathematized, words in any given model cannot ever mean more than one thing. The unwillingness to couch things in such narrow terms (usually for fear of “losing something more intelligible”) has, in the past, led to a great deal of essentially useless discussion.

Arthreya writes as if the only source of ambiguity is imprecise language. That just isn’t so. Is unemployment voluntary or involuntary? Arthreya actually discusses the question intelligently on p. 283, in the context of search models of unemployment, but I don’t think that he could have provided any insight into that question with a purely formal, symbolic treatment. Again back to Arthreya:

The plaintive expressions of “fear of losing something intangible” are concessions to the forces of muddled thinking. The way modern economics gets done, you cannot possibly not know exactly what the author is assuming – and to boot, you’ll have a foolproof way of checking whether their claims of what follows from these premises is actually true or not.

So let me juxtapose this brief passage from Arthreya with a rather longer passage from Karl Popper in which he effectively punctures the fallacies underlying the specious claims made on behalf of formalism and against ordinary language. The extended quotations are from an addendum titled “Critical Remarks on Meaning Analysis” (pp. 261-77) to chapter IV of Realism and the Aim of Science (volume 1 of the Postscript to the Logic of Scientific Discovery). In this addendum, Popper begins by making the following three claims:

1 What-is? questions, such as What is Justice? . . . are always pointless – without philosophical or scientific interest; and so are all answers to what-is? questions, such as definitions. It must be admitted that some definitions may sometimes be of help in answering other questions: urgent questions which cannot be dismissed: genuine difficulties which may have arisen in science or in philosophy. But what-is? questions as such do not raise this kind of difficulty.

2 It makes no difference whether a what-is question is raised in order to inquire into the essence or into the nature of a thing, or whether it is raised in order to inquire into the essential meaning or into the proper use of an expression. These kinds of what-is questions are fundamentally the same. Again, it must be admitted that an answer to a what-is question – for example, an answer pointing out distinctions between two meanings of a word which have often been confused – may not be without point, provided the confusion led to serious difficulties. But in this case, it is not the what-is question which we are trying to solve; we hope rather to resolve certain contradictions that arise from our reliance upon somewhat naïve intuitive ideas. (The . . . example discussed below – that of the ideas of a derivative and of an integral – will furnish an illustration of this case.) The solution may well be the elimination (rather than the clarification) of the naïve idea. But an answer to . . . a what-is question is never fruitful. . . .

3 The problem, more especially, of replacing an “inexact” term by an “exact” one – for example, the problem of giving a definition in “exact” or “precise” terms – is a pseudo-problem. It depends essentially upon the inexact and imprecise terms “exact” and “precise.” These are most misleading, not only because they strongly suggest that there exists what does not exist – absolute exactness or precision – but also because they are emotionally highly charged: under the guise of scientific character and of scientific objectivity, they suggest that precision or exactness is something superior, a kind of ultimate value, and that it is wrong, or unscientific, or muddle-headed, to use inexact terms (as it is indeed wrong not to speak as lucidly and simply as possible). But there is no such thing as an “exact” term, or terms made “precise” by “precise definitions.” Also, a definition must always use undefined terms in its definiens (since otherwise we should get involved in an infinite regress or in a circle); and if we have to operate with a number of undefined terms, it hardly matters whether we use a few more. Of course, if a definition helps to solve a genuine problem, the situation is different; and some problems cannot be solved without an increase of precision. Indeed, this is the only way in which we can reasonably speak of precision: the demand for precision is empty, unless it is raised relative to some requirements that arise from our attempts to solve a definite problem. (pp. 261-63)

Later in his addendum Popper provides an enlightening discussion of the historical development of calculus despite its lack of solid logical axiomatic foundation. The meaning of an infinitesimal or a derivative was anything but precise. It was, to use Arthreya’s aptly chosen term, a muddle. Mathematicians even came up with a symbol for the derivative. But they literally had no precise idea of what they were talking about. When mathematicians eventually came up with a definition for the derivative, the definition did not clarify what they were talking about; it just provided a particular method of calculating what the derivative would be. However, the absence of a rigorous and precise definition of the derivative did not prevent mathematicians from solving some enormously important practical problems, thereby helping to change the world and our understanding of it.

The modern history of the problem of the foundations of mathematics is largely, it has been asserted, the history of the “clarification” of the fundamental ideas of the differential and integral calculus. The concept of a derivative (the slope of a curve of the rate of increase of a function) has been made “exact” or “precise” by defining it as the limit of the quotient of differences (given a differentiable function); and the concept of an integral (the area or “quadrature” of a region enclosed by a curve) has likewise been “exactly defined”. . . . Attempts to eliminate the contradictions in this field constitute not only one of the main motives of the development of mathematics during the last hundred or even two hundred years, but they have also motivated modern research into the “foundations” of the various sciences and, more particularly, the modern quest for precision or exactness. “Thus mathematicians,” Bertrand Russell says, writing about one of the most important phases of this development, “were only awakened from their “dogmatic slumbers” when Weierstrass and his followers showed that many of their most cherished propositions are in general false. Macaulay, contrasting the certainty of mathematics with the uncertainty of philosophy, asks who ever heard of a reaction against Taylor’s theorem. If he had lived now, he himself might have heard of such a reaction, for his is precisely one of the theorems which modern investigations have overthrown. Such rude shocks to mathematical faith have produced that love of formalism which appears, to those who are ignorant of its motive, to be mere outrageous pedantry.”

It would perhaps be too much to read into this passage of Russell’s his agreement with a view which I hold to be true: that without “such rude shocks” – that is to say, without the urgent need to remove contradictions – the love of formalism is indeed “mere outrageous pedantry.” But I think that Russell does convey his view that without an urgent need, an urgent problem to be solved, the mere demand for precision is indefensible.

But this is only a minor point. My main point is this. Most people, including mathematicians, look upon the definition of the derivative, in terms of limits of sequences, as if it were a definition in the sense that it analyses or makes precise, or “explicates,” the intuitive meaning of the definiendum – of the derivative. But this widespread belief is mistaken. . . .

Newton and Leibniz and their successors did not deny that a derivative, or an integral, could be calculated as a limit of certain sequences . . . . But they would not have regarded these limits as possible definitions, because they do not give the meaning, the idea, of a derivative or an integral.

For the derivative is a measure of a velocity, or a slope of a curve. Now the velocity of a body at a certain instant is something real – a concrete (relational) attribute of that body at that instant. By contrast the limit of a sequence of average velocities is something highly abstract – something that exists only in our thoughts. The average velocities themselves are unreal. Their unending sequence is even more so; and the limit of this unending sequence is a purely mathematical construction out of these unreal entities. Now it is intuitively quite obvious that this limit must numerically coincide with the velocity, and that, if the limit can be calculated, we can thereby calculate the velocity. But according to the views of Newton and his contemporaries, it would be putting the cart before the horse were we to define the velocity as being identical with this limit, rather than as a real state of the body at a certain instant, or at a certain point, of its track – to be calculated by any mathematical contrivance we may be able to think of.

The same holds of course for the slope of a curve in a given point. Its measure will be equal to the limit of a sequence of measures of certain other average slopes (rather than actual slopes) of this curve. But it is not, in its proper meaning or essence, a limit of a sequence: the slope is something we can sometimes actually draw on paper, and construct with a compasses and rulers, while a limit is in essence something abstract, rarely actually reached or realized, but only approached, nearer and nearer, by a sequence of numbers. . . .

Or as Berkeley put it “. . . however expedient such analogies or such expressions may be found for facilitating the modern quadratures, yet we shall not find any light given us thereby into the original real nature of fluxions considered in themselves.” Thus mere means for facilitating our calculations cannot be considered as explications or definitions.

This was the view of all mathematicians of the period, including Newton and Leibniz. If we now look at the modern point of view, then we see that we have completely given up the idea of definition in the sense in which it was understood by the founders of the calculus, as well as by Berkeley. We have given up the idea of a definition which explains the meaning (for example of the derivative). This fact is veiled by our retaining the old symbol of “definition” for some equivalences which we use, not to explain the idea or the essence of a derivative, but to eliminate it. And it is veiled by our retention of the name “differential quotient” or “derivative,” and the old symbol dy/dx which once denoted an idea which we have now discarded. For the name, and the symbol, now have no function other than to serve as labels for the defiens – the limit of a sequence.

Thus we have given up “explication” as a bad job. The intuitive idea, we found, led to contradictions. But we can solve our problems without it, retaining the bulk of the technique of calculation which originally was based upon the intuitive idea. Or more precisely we retain only this technique, as far as it was sound, and eliminate the idea its help. The derivative and the integral are both eliminated; they are replaced, in effect, by certain standard methods of calculating limits. (oo. 266-70)

Not only have the original ideas of the founders of calculus been eliminated, because they ultimately could not withstand logical scrutiny, but a premature insistence on logical precision would have had disastrous consequences for the ultimate development of calculus.

It is fascinating to consider that this whole admirable development might have been nipped in the bud (as in the days of Archimedes) had the mathematicians of the day been more sensitive to Berkeley’s demand – in itself quite reasonable – that we should strictly adhere to the rules of logic, and to the rule of always speaking sense.

We now know that Berkeley was right when, in The Analyst, he blamed Newton . . . for obtaining . . . mathematical results in the theory of fluxions or “in the calculus differentialis” by illegitimate reasoning. And he was completely right when he indicated that [his] symbols were without meaning. “Nothing is easier,” he wrote, “than to devise expressions and notations, for fluxions and infinitesimals of the first, second, third, fourth, and subsequent orders. . . . These expressions indeed are clear and distinct, and the mind finds no difficulty in conceiving them to be continued beyond any assignable bounds. But if . . . we look underneath, if, laying aside the expressions, we set ourselves attentively to consider the things themselves which are supposed to be expressed or marked thereby, we shall discover much emptiness, darkness, and confusion . . . , direct impossibilities, and contradictions.”

But the mathematicians of his day did not listen to Berkeley. They got their results, and they were not afraid of contradictions as long as they felt that they could dodge them with a little skill. For the attempt to “analyse the meaning” or to “explicate” their concepts would, as we know now, have led to nothing. Berkeley was right: all these concept were meaningless, in his sense and in the traditional sense of the word “meaning:” they were empty, for they denoted nothing, they stood for nothing. Had this fact been realized at the time, the development of the calculus might have been stopped again, as it had been stopped before. It was the neglect of precision, the almost instinctive neglect of all meaning analysis or explication, which made the wonderful development of the calculus possible.

The problem underlying the whole development was, of course, to retain the powerful instrument of the calculus without the contradictions which had been found in it. There is no doubt that our present methods are more exact than the earlier ones. But this is not due to the fact that they use “exactly defined” terms. Nor does it mean that they are exact: the main point of the definition by way of limits is always an existential assertion, and the meaning of the little phrase “there exists a number” has become the centre of disturbance in contemporary mathematics. . . . This illustrates my point that the attribute of exactness is not absolute, and that it is inexact and highly misleading to use the terms “exact” and “precise” as if they had any exact or precise meaning. (pp. 270-71)

Popper sums up his discussion as follows:

My examples [I quoted only the first of the four examples as it seemed most relevant to Arthreya’s discussion] may help to emphasize a lesson taught by the whole history of science: that absolute exactness does not exist, not even in logic and mathematics (as illustrated by the example of the still unfinished history of the calculus); that we should never try to be more exact than is necessary for the solution of the problem in hand; and that the demand for “something more exact” cannot in itself constitute a genuine problem (except, of course, when improved exactness may improve the testability of some theory). (p. 277)

I apologize for stringing together this long series of quotes from Popper, but I think that it is important to understand that there is simply no scientific justification for the highly formalistic manner in which much modern economics is now carried out. Of course, other far more authoritative critics than I, like Mark Blaug and Richard Lipsey (also here) have complained about the insistence of modern macroeconomics on microfounded, axiomatized models regardless of whether those models generate better predictions than competing models. Their complaints have regrettably been ignored for the most part. I simply want to point out that a recent, and in many ways admirable, introduction to modern macroeconomics failed to provide a coherent justification for insisting on axiomatized models. It really wasn’t the author’s fault; a coherent justification doesn’t exist.

About Me

David Glasner
Washington, DC

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

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