Posts Tagged 'Jack Hirshleifer'

Roy Radner and the Equilibrium of Plans, Prices and Price Expectations

In this post I want to discuss Roy Radner’s treatment of an equilibrium of plans, prices, and price expectations (EPPPE) and its relationship to Hayek’s conception of intertemporal equilibrium, of which Radner’s treatment is a technically more sophisticated version. Although I seen no evidence that Radner was directly influenced by Hayek’s work, I consider Radner’s conception of EPPPE to be a version of Hayek’s conception of intertemporal equilibrium, because it captures essential properties of Hayek’s conception of intertemporal equilibrium as a situation in which agents independently formulate their own optimizing plans based on the prices that they actually observe – their common knowledge – and on the future prices that they expect to observe over the course of their planning horizons. While currently observed prices are common knowledge – not necessarily a factual description of economic reality but not an entirely unreasonable simplifying assumption – the prices that individual agents expect to observe in the future are subjective knowledge based on whatever common or private knowledge individuals may have and whatever methods they may be using to form their expectations of the prices that will be observed in the future. An intertemporal equilibrium refers to a set of decentralized plans that are both a) optimal from the standpoint of every agent’s own objectives given their common knowledge of current prices and their subjective expectations of future prices and b) mutually consistent.

If an agent has chosen an optimal plan given current and expected future prices, that plan will not be changed unless the agent acquires new information that renders the existing plan sub-optimal relative to the new information. Otherwise, there would be no reason for the agent to deviate from an optimal plan. The new information that could cause an agent to change a formerly optimal plan would either affect the preferences of the agent, the technology available to the agent, or would somehow be reflected in current prices or in expected future prices. But it seems improbable that there could be a change in preferences or technology would not also be reflected in current or expected future prices. So absent a change in current or expected future prices, there would seem to be almost no likelihood that an agent would deviate from a plan that was optimal given current prices and the future prices expected by the agent.

The mutual consistency of the optimizing plans of independent agents therefore turns out to be equivalent to the condition that all agents observe the same current prices – their common knowledge – and have exactly the same forecasts of the future prices upon which they have relied in choosing their optimal plans. Even should their forecasts of future prices turn out to be wrong, at the moment before their forecasts of future prices were changed or disproved by observation, their plans were still mutually consistent relative to the information on which their plans had been chosen. The failure of the equilibrium to be maintained could be attributed to a change in information that meant that the formerly optimal plans were no longer optimal given the newly acquired information. But until the new information became available, the mutual consistency of optimal plans at that (fleeting) moment signified an equilibrium state. Thus, the defining characteristic of an intertemporal equilibrium in which current prices are common knowledge is that all agents share the same expectations of the future prices on which their optimal plans have been based.

There are fundamental differences between the Arrow-Debreu-McKenzie (ADM) equilibrium and the EPPPE. One difference worth mentioning is that, under the standard assumptions of the ADM model, the equilibrium is Pareto-optimal, and any Pareto-optimum allocation, by a suitable redistribution of initial endowments, could be achieved as a general equilibrium (two welfare theorems). These results do not generally hold for EPPPE, because, in contrast to the ADM model, it is possible for agents in EPPPE to acquire additional information over time, not only passively, but by investing resources in the production of information. Investing resources in the production of information can cause inefficiency in two ways: first, by creating non-convexities (owing to start-up costs in information gathering activities) that are inconsistent with the uniform competitive prices characteristic of the ADM equilibrium, and second, by creating incentives to devote resources to produce information whose value is derived from profits in trading with less well-informed agents. The latter source of inefficiency was discovered by Jack Hirshleifer in his classic 1971 paper, which I have written about in several previous posts (here, here, here, and here).

But the important feature of Radner’s EPPPE that I want to emphasize here — and what radically distinguishes it from the ADM equilibrium — is its fragility. Unlike the ADM equilibrium which is established once and forever at time zero of a model in which all production and consumption starts in period one, the EPPPE, even if it ever exists, is momentary, and is subject to unraveling whenever there is a change in the underlying information upon which current prices and expected future prices depend, and upon which agents, in choosing their optimal plans, rely. Time is not just, as it is in the ADM model, an appendage to the EPPPE, and, as a result, EPPPE can account for many phenomena, practices, and institutions that are left out of the ADM model.

The two differences that are most relevant in this context are the existence of stock markets in which shares of firms are traded based on expectations of the future net income streams associated with those firms, and the existence of a medium of exchange supplied by private financial intermediaries known as banks. In the ADM model in which all transactions are executed in time zero, in advance of all the actual consumption and production activities determined by those transactions, there would be no reason to hold, or to supply, a medium of exchange. The ADM equilibrium allows for agents to borrow or lend at equilibrium interest rates to optimize the time profiles of their consumption relative to their endowments and the time profiles of their earnings. Since all such transactions are consummated in time zero, and since, through some undefined process, the complete solvency and the integrity of all parties to all transactions is ascertained in time zero, the probability of a default on any loan contracted at time zero is zero. As a result, each agent faces a single intertemporal budget constraint at time zero over all periods from 1 to n. Walras’s Law therefore holds across all time periods for this intertemporal budget constraint, each agent transacting at the same prices in each period as every other agent does.

Once an equilibrium price vector is established in time zero, each agent knows that his optimal plan based on that price vector (which is the common knowledge of all agents) will be executed over time exactly as determined in time zero. There is no reason for any exchange of ownership shares in firms, the future income streams from each firm being known in advance.

The ADM equilibrium is a model of an economic process very different from Radner’s EPPPE, because in EPPPE, agents have no reason to assume that their current plans, even if they are momentarily both optimal and mutually consistent with the plans of all other agents, will remain optimal and consistent with the plans of all other agents. New information can arrive or be produced that will necessitate a revision in plans. Because even equilibrium plans are subject to revision, agents must take into account the solvency and credit worthiness of counterparties with whom they enter into transactions. The potentially imperfect credit-worthiness of at least some agents enables certain financial intermediaries (aka banks) to provide a service by offering to exchange their debt, which is widely considered to be more credit-worthy than the debt of ordinary agents, to agents seeking to borrow to finance purchases of either consumption or investment goods. Many agents seeking to borrow therefore prefer exchanging their debt for bank debt, bank debt being acceptable by other agents at face value. In addition, because the acquisition of new information is possible, there is a reason for agents to engage in speculative trades of commodities or assets. Such assets include ownership shares of firms, and agents may revise their valuations of those firms as they revise their expectations about future prices and their expectations about the revised plans of those firms in response to newly acquired information.

I will discuss the special role of banks at greater length in my next post on temporary equilibrium. But for now, I just want to underscore a key point: in the EPPE, unless all agents have the same expectations of future prices, Walras’s Law need not hold. The proof that Walras’s holds depends on the assumption that individual plans to buy and sell are based on the assumption that every agent buys or sells each commodity at the same price that every other transactor buys  or sells that commodity. But in the intertemporal context, in which only current, not future prices, are observed, plans for current and future prices are made based on expectations about future prices. If agents don’t share the same expectations about future prices, agents making plans for future purchases based on overly optimistic expectations about the prices at which they will be able to sell, may make commitments to buy in the future (or commitment to repay loans to finance purchases in the present) that they will be unable to discharge. Reneging on commitments to buy in the future or to repay obligations incurred in the present may rule out the existence of even a temporary equilibrium in the future.

Finally, let me add a word about Radner’s terminology. In his 1987 entry on “Uncertainty and General Equilibrium” for the New Palgrave Dictionary of Economics, (Here is a link to the revised version on line), Radner writes:

A trader’s expectations concern both future environmental events and future prices. Regarding expectations about future environmental events, there is no conceptual problem. According to the Expected Utility Hypothesis, each trader is characterized by a subjective probability measure on the set of complete histories of the environment. Since, by definition, the evolution of the environment is exogenous, a trader’s conditional probability of a future event, given the information to date, is well defined.

It is not so obvious how to proceed with regard to trader’s expectations about future prices. I shall contrast two possible approaches. In the first, which I shall call the perfect foresight approach, let us assume that the behaviour of traders is such as to determine, for each complete history of the environment, a unique corresponding sequence of price system[s]. . .

Thus, the perfect foresight approach implies that, in equilibrium, traders have common price expectation functions. These price expectation functions indicate, for each date-event pair, what the equilibrium price system would be in the corresponding market at that date event pair. . . . [I]t follows that, in equilibrium the traders would have strategies (plans) such that if these strategies were carried out, the markets would be cleared at each date-event pair. Call such plans consistent. A set of common price expectations and corresponding consistent plans is called an equilibrium of plans, prices, and price expectations.

My only problem with Radner’s formulation here is that he is defining his equilibrium concept in terms of the intrinsic capacity of the traders to predict prices rather the simple fact that traders form correct expectations. For purposes of the formal definition of EPPE, it is irrelevant whether traders predictions of future prices are correct because they are endowed with the correct model of the economy or because they are all lucky and randomly have happened simultaneously to form the same expectations of future prices. Radner also formulates an alternative version of his perfect-foresight approach in which agents don’t all share the same information. In such cases, it becomes possible for traders to make inferences about the environment by observing prices differ from what they had expected.

The situation in which traders enter the market with different non-price information presents an opportunity for agents to learn about the environment from prices, since current prices reflect, in a possibly complicated manner, the non-price information signals received by the various agents. To take an extreme example, the “inside information” of a trader in a securities market may lead him to bid up the price to a level higher than it otherwise would have been. . . . [A]n astute market observer might be able to infer that an insider has obtained some favourable information, just by careful observation of the price movement.

The ability to infer non-price information from otherwise inexplicable movements in prices leads Radner to define a concept of rational expectations equilibrium.

[E]conomic agents have the opportunity to revise their individual models in the light of observations and published data. Hence, there is a feedback from the true relationship to the individual models. An equilibrium of this system, in which the individual models are identical with the true model, is called a rational expectations equilibrium. This concept of equilibrium is more subtle, of course, that the ordinary concept of equilibrium of supply and demand. In a rational expectations equilibrium, not only are prices determined so as to equate supply and demand, but individual economic agents correctly perceive the true relationship between the non-price information received by the market participants and the resulting equilibrium market prices.

Though this discussion is very interesting from several theoretical angles, as an explanation of what is entailed by an economic equilibrium, it misses the key point, which is the one that Hayek identified in his 1928 and (especially) 1937 articles mentioned in my previous posts. An equilibrium corresponds to a situation in which all agents have identical expectations of the future prices upon which they are making optimal plans given the commonly observed current prices and the expected future prices. If all agents are indeed formulating optimal plans based on the information that they have at that moment, their plans will be mutually consistent and will be executable simultaneously without revision as long as the state of their knowledge at that instant does not change. How it happened that they arrived at identical expectations — by luck chance or supernatural powers of foresight — is irrelevant to that definition of equilibrium. Radner does acknowledge that, under the perfect-foresight approach, he is endowing economic agents with a wildly unrealistic powers of imagination and computational capacity, but from his exposition, I am unable to decide whether he grasped the subtle but crucial point about the irrelevance of an assumption about the capacities of agents to the definition of EPPPE.

Although it is capable of describing a richer set of institutions and behavior than is the Arrow-Debreu model, the perfect-foresight approach is contrary to the spirit of much of competitive market theory in that it postulates that individual traders must be able to forecast, in some sense, the equilibrium prices that will prevail in the future under all alternative states of the environment. . . .[T]his approach . . . seems to require of the traders a capacity for imagination and computation far beyond what is realistic. . . .

These last considerations lead us in a different direction, which I shall call the bounded rationality approach. . . . An example of the bounded-rationality approach is the theory of temporary equilibrium.

By eschewing any claims about the rationality of the agents or their computational powers, one can simply talk about whether agents do or do not have identical expectations of future prices and what the implications of those assumptions are. When expectations do agree, there is at least a momentary equilibrium of plans, prices and price expectations. When they don’t agree, the question becomes whether even a temporary equilibrium exists and what kind of dynamic process is implied by the divergence of expectations. That it seems to me would be a fruitful way forward for macroeconomics to follow. In my next post, I will discuss some of the characteristics and implications of a temporary-equilibrium approach to macroeconomics.


Armen Alchian, The Economists’ Economist

The first time that I ever heard of Armen Alchian was when I took introductory economics at UCLA as a freshman, and his book (co-authored with his colleague William R. Allen who was probably responsible for the macro and international chapters) University Economics (the greatest economics textbook ever written) was the required text. I had only just started to get interested in economics, and was still more interested in political philosophy than in economics, but I found myself captivated by what I was reading in Alchian’s textbook, even though I didn’t find the professor teaching the course very exciting. And after 10 weeks (the University of California had switched to a quarter system) of introductory micro, I changed my major to economics. So there is no doubt that I became an economist because the textbook that I was taught from was written by Alchian.

In my four years as an undergraduate at UCLA, I took three classes from Axel Leijonhufvud, two from Ben Klein, two from Bill Allen, and one each from Robert Rooney, Nicos Devletoglou, James Buchanan, Jack Hirshleifer, George Murphy, and Jean Balbach. But Alchian, who in those days was not teaching undergrads, was a looming presence. It became obvious that Alchian was the central figure in the department, the leader and the role model that everyone else looked up to. I would see him occasionally on campus, but was too shy or too much in awe of him to introduce myself to him. One incident that I particularly recall is when, in my junior year, F. A. Hayek visited UCLA in the fall and winter quarters (in the department of philosophy!) teaching an undergraduate course in the philosophy of the social sciences and a graduate seminar on the first draft of Law, Legislation and Liberty. I took Hayek’s course on the philosophy of the social sciences, and audited his graduate seminar, and I occasionally used to visit his office to ask him some questions. I once asked his advice about which graduate programs he would suggest that I apply to. He mentioned two schools, Chicago, of course, and Princeton where his friends Fritz Machlup and Jacob Viner were still teaching, before asking, “but why would you think of going to graduate school anywhere else than UCLA? You will get the best training in economics in the world from Alchian, Hirshleifer and Leijonhufvud.” And so it was, I applied to, and was accepted at, Chicago, but stayed at UCLA.

As a first year graduate student, I took the (three-quarter) microeconomics sequence from Jack Hirshleifer (who in the scholarly hierarachy at UCLA ranked only slightly below Alchian) and the two-quarter macroeconomics sequence from Leijonhufvud. Hirshleifer taught a great course. He was totally prepared, very organized and his lectures were always clear and easy to follow. To do well, you had to sit back listen, review the lecture notes, read through the reading assignments, and do the homework problems. For me at least, with the benefit of four years of UCLA undergraduate training, it was a breeze.

Great as Hirshleifer was as a teacher, I still felt that I was missing out by not having been taught by Alchian. Perhaps Alchian felt that the students who took the microeconomics sequence from Hirshleifer should get some training from him as well, so the next year he taught a graduate seminar in topics in price theory, to give us an opportunity to learn from him how to do economics. You could also see how Alchian operated if you went to a workshop or lecture by a visiting scholar, when Alchian would start to ask questions. He would smile, put his head on his forehead, and say something like, “I just don’t understand that,” and force whoever it was to try to explain the logic by which he had arrived at some conclusion. And Alchian would just keep smiling, explain what the problem was with the answer he got, and ask more questions. Alchian didn’t shout or rant or rave, but if Alchian was questioning you, you were not in a very comfortable position.

So I was more than a bit apprehensive going into Alchian’s seminar. There were all kinds of stories told by graduate students about how tough Alchian could be on his students if they weren’t able to respond adequately when subjected to his questioning in the Socratic style. But the seminar could not have been more enjoyable. There was give and take, but I don’t remember seeing any blood spilled. Perhaps by the time I got to his seminar, Alchian, then about 57, had mellowed a bit, or, maybe, because we had all gone through the graduate microeconomics sequence, he felt that we didn’t require such an intense learning environment. At any rate, the seminar, which met twice a week for an hour and a quarter for 10 weeks, usually involved Alchian picking a story from the newspaper and asking us how to analyze the economics underlying the story. Armed with nothing but a chalkboard and piece of chalk, Alchian would lead us relatively painlessly from confusion to clarity, from obscurity to enlightenment. The key concepts with which to approach any problem were to understand the choices available to those involved, to define the relevant costs, and to understand the constraints under which choices are made, the constraints being determined largely by the delimitation of the property rights under which the resources can be used or exchanged, or, to be more precise, the property rights to use those resources can be exchanged.

Ultimately, the lesson that I learned from Alchian is that, at its best, economic theory is a tool for solving actual real problems, and the nature of the problem ought to dictate the way in which the theory (verbal, numerical, graphical, higher mathematical) is deployed, not the other way around. The goal is not to reach any particular conclusion, but to apply the tools in the best and most authentic way that they can be applied. Alchian did not wear his politics on his sleeve, though it wasn’t too hard to figure out that he was politically conservative with libertarian tendencies. But you never got the feeling that his politics dictated his economic analysis. In many respects, Alchian’s closest disciple was Earl Thompson, who studied under Alchian as an undergraduate, and then, after playing minor-league baseball for a couple of years, going to Harvard for graduate school, eventually coming back to UCLA as an assistant professor where he remained for his entire career. Earl, discarding his youthful libertarianism early on, developed many completely original, often eccentric, theories about the optimality of all kinds of government interventions – even protectionism – opposed by most economists, but Alchian took them all in stride. Mere policy disagreements never affected their close personal bond, and Alchian wrote the forward to Earl’s book with Charles Hickson, Ideology and the Evolution of Vital Economics Institutions. If Alchian was friendly with and an admirer of Milton Friedman, he just as friendly with, and just as admiring of, Paul Samuelson and Kenneth Arrow, with whom he collaborated on several projects in the 1950s when they consulted for the Rand Corporation. Alchian cared less about the policy conclusion than he did about the quality of the underlying economic analysis.

As I have pointed out on several prior occasions, it is simply scandalous that Alchian was not awarded the Noble Prize. His published output was not as voluminous as that of some other luminaries, but there is a remarkably high proportion of classics among his publications. So many important ideas came from him, especially thinking about economic competition as an evolutionary process, the distinction between the functional relationship between cost and volume of output and cost and rate of output, the effect of incomplete information on economic action, the economics of property rights, the effects of inflation on economic activity. (Two volumes of his Collected Works, a must for anyone really serious about economics, contain a number of previously unpublished or hard to find papers, and are available here.) Perhaps in the future I will discuss some of my favorites among his articles.

Although Alchian did not win the Nobel Prize, in 1990 the Nobel Prize was awarded to Harry Markowitz, Merton Miller, and William F. Sharpe for their work on financial economics. Sharp, went to UCLA, writing his Ph.D. dissertation on securities prices under Alchian, and worked at the Rand Corporation in the 1950s and 1960s with Markowitz.  Here’s what Sharpe wrote about Alchian:

Armen Alchian, a professor of economics, was my role model at UCLA. He taught his students to question everything; to always begin an analysis with first principles; to concentrate on essential elements and abstract from secondary ones; and to play devil’s advocate with one’s own ideas. In his classes we were able to watch a first-rate mind work on a host of fascinating problems. I have attempted to emulate his approach to research ever since.

And if you go to the Amazon page for University Economics and look at the comments you will see a comment from none other than Harry Markowitz:

I am about to order this book. I have just read its quite favorable reviews, and I am not a bit surprised at their being impressed by Armen Alchian’s writings. I was a colleague of Armen’s, at the Rand Corporation “think tank,” during the 1950s, and hold no economist in higher regard. When I sat down at my keyboard just now it was to find out what happened to Armen’s works. One Google response was someone saying that Armen should get a Nobel Prize. I concur. My own Nobel Prize in Economics was awarded in 1990 along with the prize for Wm. Sharpe. I see in Wikipedia that Armen “influenced” Bill, and that Armen is still alive and is 96 years old. I’ll see if I can contact him, but first I’ll buy this book.

I will always remember Alchian’s air of amused, philosophical detachment, occasionally bemused (though, perhaps only apparently so, as he tried to guide his students and colleagues with question to figure out a point that he already grasped), always curious, always eager for the intellectual challenge of discovery and problem solving. Has there ever been a greater teacher of economics than Alchian? Perhaps, but I don’t know who. I close with one more quotation, this one from Axel Leijonhufvud written about Alchian 25 years ago.  It still rings true.

[Alchian’s] unique brand of price theory is what gave UCLA Economics its own intellectual profile and achieved for us international recognition as an independent school of some importance—as a group of scholars who did not always take their leads from MIT, Chicago or wherever. When I came here (in 1964) the Department had Armen’s intellectual stamp on it (and he remained the obvious leader until just a couple of years ago ….). Even people outside Armen’s fields, like myself, learned to do Armen’s brand of economic analysis and a strong esprit de corps among both faculty and graduate students sprang from the consciousness that this ‘New Institutional Economics’ was one of the waves of the future and that we, at UCLA, were surfing it way ahead of the rest. But Armen’s true importance to the UCLA school did not stem just from the new ideas he taught or the outwardly recognized “brandname” that he created for us. For many of his young colleagues he embodied qualities of mind and character that seemed the more important to seek to emulate the more closely you got to know him.

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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