Archive for the 'general equilibrium' Category

Next Entries »

Price Stickiness and Macroeconomics

Published April 17, 2015 expectations , Franklin Fisher , general equilibrium , Hayek , J. R. Hicks , macroeconomics , microfoundations , Noah Smith , rational expectations , Stephen Williamson 29 Comments
Tags: , , ,

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

Published December 12, 2014 Brian Arthur , complexity economics , coordination failure , general equilibrium , macroeconomics , microfoundations , multiplier 15 Comments
Tags: , , ,

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.

Hicks on IS-LM and Temporary Equilibrium

Published October 14, 2014 expectations , general equilibrium , intertemporal equilibrium , IS-LM , J. R. Hicks , Keynes , temporary equilibrium , wage stickiness , Walrasian equilibrium 9 Comments
Tags: , , ,

Jan, commenting on my recent post about Krugman, Minsky and IS-LM, quoted the penultimate paragraph of J. R. Hicks’s 1980 paper on IS-LM in the Journal of Post-Keynesian Economics, a brand of economics not particularly sympathetic to Hicks’s invention. Hicks explained that in the mid-1930s he had been thinking along lines similar to Keynes’s even before the General Theory was published, and had the basic idea of IS-LM in his mind even before he had read the General Theory, while also acknowledging that his enthusiasm for the IS-LM construct had waned considerably over the years.

Hicks discussed both the similarities and the differences between his model and IS-LM. But as the discussion proceeds, it becomes clear that what he is thinking of as his model is what became his model of temporary equilibrium in Value and Capital. So it really is important to understand what Hicks felt were the similarities as well as the key differences between the temporary- equilibrium model, and the IS-LM model. Here is how Hicks put it:

I recognized immediately, as soon as I read The General Theory, that my model and Keynes’ had some things in common. Both of us fixed our attention on the behavior of an economy during a period—a period that had a past, which nothing that was done during the period could alter, and a future, which during the period was unknown. Expectations of the future would nevertheless affect what happened during the period. Neither of us made any assumption about “rational expectations” ; expectations, in our models, were strictly exogenous.3 (Keynes made much more fuss over that than I did, but there is the same implication in my model also.) Subject to these data— the given equipment carried over from the past, the production possibilities within the period, the preference schedules, and the given expectations— the actual performance of the economy within the period was supposed to be determined, or determinable. It would be determined as an equilibrium performance, with respect to these data.

There was all this in common between my model and Keynes’; it was enough to make me recognize, as soon as I saw The General Theory, that his model was a relation of mine and, as such, one which I could warmly welcome. There were, however, two differences, on which (as we shall see) much depends. The more obvious difference was that mine was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model. I shall have much to say about this difference, but I may as well note, at the start, that I do not think it matters much. I did not think, even in 1936, that it mattered much. IS-LM was in fact a translation of Keynes’ nonflexprice model into my terms. It seemed to me already that that could be done; but how it is done requires explanation.

The other difference is more fundamental; it concerns the length of the period. Keynes’ (he said) was a “short-period,” a term with connotations derived from Marshall; we shall not go far wrong if we think of it as a year. Mine was an “ultra-short-period” ; I called it a week. Much more can happen in a year than in a week; Keynes has to allow for quite a lot of things to happen. I wanted to avoid so much happening, so that my (flexprice) markets could reflect propensities (and expectations) as they are at a moment. So it was that I made my markets open only on a Monday; what actually happened during the ensuing week was not to affect them. This was a very artificial device, not (I would think now) much to be recommended. But the point of it was to exclude the things which might happen, and must disturb the markets, during a period of finite length; and this, as we shall see, is a very real trouble in Keynes. (pp. 139-40)

Hicks then explained how the specific idea of the IS-LM model came to him as a result of working on a three-good Walrasian system in which the solution could be described in terms of equilibrium in two markets, the third market necessarily being in equilibrium if the other two were in equilibrium. That’s an interesting historical tidbit, but the point that I want to discuss is what I think is Hicks’s failure to fully understand the significance of his own model, whose importance, regrettably, he consistently underestimated in later work (e.g., in Capital and Growth and in this paper).

The point that I want to focus on is in the second paragraph quoted above where Hicks says “mine [i.e. temporary equilibrium] was a flexprice model, a perfect competition model, in which all prices were flexible, while in Keynes’ the level of money wages (at least) was exogenously determined. So Keynes’ was a model that was consistent with unemployment, while mine, in his terms, was a full employment model.” This, it seems to me, is all wrong, because Hicks, is taking a very naïve and misguided view of what perfect competition and flexible prices mean. Those terms are often mistakenly assumed to meant that if prices are simply allowed to adjust freely, all  markets will clear and all resources will be utilized.

I think that is a total misconception, and the significance of the temporary-equilibrium construct is in helping us understand why an economy can operate sub-optimally with idle resources even when there is perfect competition and markets “clear.” What prevents optimality and allows resources to remain idle despite freely adjustming prices and perfect competition is that the expectations held by agents are not consistent. If expectations are not consistent, the plans based on those expectations are not consistent. If plans are not consistent, then how can one expect resources to be used optimally or even at all? Thus, for Hicks to assert, casually without explicit qualification, that his temporary-equilibrium model was a full-employment model, indicates to me that Hicks was unaware of the deeper significance of his own model.

If we take a full equilibrium as our benchmark, and look at how one of the markets in that full equilibrium clears, we can imagine the equilibrium as the intersection of a supply curve and a demand curve, whose positions in the standard price/quantity space depend on the price expectations of suppliers and of demanders. Different, i.e, inconsistent, price expectations would imply shifts in both the demand and supply curves from those corresponding to full intertemporal equilibrium. Overall, the price expectations consistent with a full intertemporal equilibrium will in some sense maximize total output and employment, so when price expectations are inconsistent with full intertemporal equilibrium, the shifts of the demand and supply curves will be such that they will intersect at points corresponding to less output and less employment than would have been the case in full intertemporal equilibrium. In fact, it is possible to imagine that expectations on the supply side and the demand side are so inconsistent that the point of intersection between the demand and supply curves corresponds to an output (and hence employment) that is way less than it would have been in full intertemporal equilibrium. The problem is not that the price in the market doesn’t allow the market to clear. Rather, given the positions of the demand and supply curves, their point of intersection implies a low output, because inconsistent price expectations are such that potentially advantageous trading opportunities are not being recognized.

So for Hicks to assert that his flexprice temporary-equilibrium model was (in Keynes’s terms) a full-employment model without noting the possibility of a significant contraction of output (and employment) in a perfectly competitive flexprice temporary-equilibrium model when there are significant inconsistencies in expectations suggests strongly that Hicks somehow did not fully comprehend what his own creation was all about. His failure to comprehend his own model also explains why he felt the need to abandon the flexprice temporary-equilibrium model in his later work for a fixprice model.

There is, of course, a lot more to be said about all this, and Hicks’s comments concerning the choice of a length of the period are also of interest, but the clear (or so it seems to me) misunderstanding by Hicks of what is entailed by a flexprice temporary equilibrium is an important point to recognize in evaluating both Hicks’s work and his commentary on that work and its relation to Keynes.

Franklin Fisher on the Stability(?) of General Equilibrium

Published October 2, 2014 Franklin Fisher , general equilibrium , microfoundations , Walras's Law 11 Comments
Tags: , , , , , ,

The eminent Franklin Fisher, winner of the J. B. Clark Medal in 1973, a famed econometrician and antitrust economist, who was the expert economics witness for IBM in its long battle with the U. S. Department of Justice, and was later the expert witness for the Justice Department in the antitrust case against Microsoft, currently emeritus professor professor of microeconomics at MIT, visited the FTC today to give a talk about proposals the efficient sharing of water between Israel, Palestine, and Jordan. The talk was interesting and informative, but I must admit that I was more interested in Fisher’s views on the stability of general equilibrium, the subject of a monograph he wrote for the econometric society Disequilibrium Foundations of Equilibrium Economics, a book which I have not yet read, but hope to read before very long.

However, I did find a short paper by Fisher, “The Stability of General Equilibrium – What Do We Know and Why Is It Important?” (available here) which was included in a volume General Equilibrium Analysis: A Century after Walras edited by Pacal Bridel.

Fisher’s contribution was to show that the early stability analyses of general equilibrium, despite the efforts of some of the most best economists of the mid-twentieth century, e.g, Hicks, Samuelson, Arrow and Hurwicz (all Nobel Prize winners) failed to provide a useful analysis of the question whether the general equilibrium described by Walras, whose existence was first demonstrated under very restrictive assumptions by Abraham Wald, and later under more general conditions by Arrow and Debreu, is stable or not.

Although we routinely apply comparative-statics exercises to derive what Samuelson mislabeled “meaningful theorems,” meaning refutable propositions about the directional effects of a parameter change on some observable economic variable(s), such as the effect of an excise tax on the price and quantity sold of the taxed commodity, those comparative-statics exercises are predicated on the assumption that the exercise starts from an initial position of equilibrium and that the parameter change leads, in a short period of time, to a new equilibrium. But there is no theory describing the laws of motion leading from one equilibrium to another, so the whole exercise is built on the mere assumption that a general equilibrium is sufficiently stable so that the old and the new equilibria can be usefully compared. In other words, microeconomics is predicated on macroeconomic foundations, i.e., the stability of a general equilibrium. The methodological demand for microfoundations for macroeconomics is thus a massive and transparent exercise in question begging.

In his paper on the stability of general equilibrium, Fisher observes that there are four important issues to be explored by general-equilibrium theory: existence, uniqueness, optimality, and stability. Of these he considers optimality to be the most important, as it provides a justification for a capitalistic market economy. Fisher continues:

So elegant and powerful are these results, that most economists base their conclusions upon them and work in an equilibrium framework – as they do in partial equilibrium analysis. But the justification for so doing depends on the answer to the fourth question listed above, that of stability, and a favorable answer to that is by no means assured.

It is important to understand this point which is generally ignored by economists. No matter how desirable points of competitive general equilibrium may be, that is of no consequence if they cannot be reached fairly quickly or maintained thereafter, or, as might happen when a country decides to adopt free markets, there are bad consequences on the way to equilibrium.

Milton Friedman remarked to me long ago that the study of the stability of general equilibrium is unimportant, first, because it is obvious that the economy is stable, and, second, because if it isn’t stable we are wasting our time. He should have known better. In the first place, it is not at all obvious that the actual economy is stable. Apart from the lessons of the past few years, there is the fact that prices do change all the time. Beyond this, however, is a subtler and possibly more important point. Whether or not the actual economy is stable, we largely lack a convincing theory of why that should be so. Lacking such a theory, we do not have an adequate theory of value, and there is an important lacuna in the center of microeconomic theory.

Yet economists generally behave as though this problem did not exist. Perhaps the most extreme example of this is the view of the theory of Rational Expectations that any disequilibrium disappears so fast that it can be ignored. (If the 50-dollar bill were really on the sidewalk, it would be gone already.) But this simply assumes the problem away. The pursuit of profits is a major dynamic force in the competitive economy. To only look at situations where the Invisible Hand has finished its work cannot lead to a real understanding of how that work is accomplished. (p. 35)

I would also note that Fisher confirms a proposition that I have advanced a couple of times previously, namely that Walras’s Law is not generally valid except in a full general equilibrium with either a complete set of markets or correct price expectations. Outside of general equilibrium, Walras’s Law is valid only if trading is not permitted at disequilibrium prices, i.e., Walrasian tatonnement. Here’s how Fisher puts it.

In this context, it is appropriate to remark that Walras’s Law no longer holds in its original form. Instead of the sum of the money value of all excess demands over all agents being zero, it now turned out that, at any moment of time, the same sum (including the demands for shares of firms and for money) equals the difference between the total amount of dividends that households expect to receive at that time and the amount that firms expect to pay. This difference disappears in equilibrium where expectations are correct, and the classic version of Walras’s Law then holds.

About Me

David Glasner
Washington, DC

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

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

Follow me on Twitter @david_glasner

Archives

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

Join 665 other subscribers
Follow Uneasy Money on WordPress.com