Saturday, November 29, 2008

Larry Summers As Dissenting Economist

"... formal econometric work, where elaborate technique is used to apply theory to data or isolate the direction of causal relationships when they are not obvious a priori, virtually always fails. The only empirical research that has contributed to thinking about substantive issues and the development of economics is pragmatic empirical work, based on methodological principles directly opposed to those that have become fashionable in recent years." - Lawrence H. Summers (1991) "The Scientific Illusion in Empirical Macroeconomics", Scandinavian Journal of Economics, V. 93, N. 2: 129-148

Friday, November 28, 2008

Everything Old Is New Again

An orthodox response to the Cambridge Capital Controversy (CCC) is to assert that mainstream price theory is centered around General Equilibrium theory. Very short run models of intertemporal and temporary equilibrium are, it is claimed, unaffected by the CCC. I think that capital reversing is manifested in such models by dynamic equilibrium paths with counter-intuitive behavior.

For example, suppose the labor supply increases along such a path in that later generations increasingly prefer to consume commodities, not leisure. A dynamic equilibrium path can be constructed in which this increasing labor supply is associated with an increasing wage. Likewise, suppose instead that the supply of capital increases in that later consumers increasingly prefer to defer present consumption in favor of future consumption. Here, too, such increased savings can be associated with an increasing interest rate.

I have expressed this view before. I have decided that I am not going to develop concrete numerical examples any time soon. So I have put up what I have so far as a paper over on the Social Sciences Research Network (SSRN).

If I were to continue, the next step in the analysis is conceptually straightforward, although tedious. One would linearize the stationary state solutions around limit points for the dynamic equilibrium points. An examination of eigenvalues of the resulting matrix reveals local stability properties. I expect at least some equilibria will have, at best, the stability of saddle points. But multiple equilibria arise, and perhaps the desired dynamic equilibrium paths can be constructed. One might consider other forms of the utility maximization problem, if different stability properties are desired.

Sunday, November 23, 2008

Let The Sunshine In

I was on travel last week. I find intriguing the application of solar, wind, geothermal, hydroelectric, and tide power generation on an industrial scale. In the meridian of a highway near the Denver airport they have an array, which I took a photo of.
Solar Power Generation

It seems solar and wind are becoming quite practical as a matter of dollars and cents, even without having internalized the externalities of various power generation sources. From Richard Stevenson ("First Solar: Quest for the $1 Watt", IEEE Spectrum, V. 45, N. 8 (August 2008): 26-31), I learn to be competitive for off-peak power generation, solar cells need to be priced to generate electricity at $1 per watt. Apparently, a number of companies are developing competing technologies that may attain this goal in a couple of years.

Disclaimer: In mentioning First Solar and their Cadmium Telluride (CdTe) technology, I am "talking my book" - a phrase I learned from D-Squared - in a small way.

Saturday, November 22, 2008

Ricardo On Profits

Sraffa started a controversy on the interpretation of Ricardo's theory of value and distribution. Or perhaps Hollander did in his reaction against Sraffa.

In Sraffa's view, important developments in Ricardo's understanding happened the year before Ricardo's 1815 publication of "An Essay on the Influence of a low Price of Corn on the Profits of Stock". A fortiori, these developments precede the 1817 first edition of On the Principles of Political Economy and Taxation.

Hutches Trower, in his 2 March 1814 letter to Ricardo, states he is returning Ricardo's now lost "papers on the profits of Capital". Ricardo's response is important evidence for Sraffa's interpretation. Here is Ricardo's letter in full:
Upper Brook Street
8th March 1814

Dear Trower

I called at your house yesterday; I wished to tell you that though well disposed to enter into the defence of my opinions, I was now so much occupied by business, that I could not devote the necessary time to it. Not having found you at home I must tell you so by “these present”. At the same time I must observe that what I feared, I believe, has happened. To one not aware of the whole difference between Mr. Malthus and me, the papers you read were not clear, and I think you have not entirely made out the subject in dispute.

Without entering further into the question I will endeavor to state the question itself. When Capital increases in a country, and the means of employing Capital already exists, or increases, in the same proportion, the rate of interest and of profits will not fall.

Interest rises only when the means of employment for Capital bears a greater proportion than before to the Capital itself, and falls when the Capital bears a greater proportion to the arena, as Mr. Malthus has called it, for its employment. On these points I believe we are all agreed, but I contend that the arena for the employment of new Capital cannot increase in any country in the same or greater proportion than the Capital itself, [footnote:] the following to be inserted: unless Capital be withdrawn from the land [end footnote] unless there be improvements in husbandry, - or new facilities be offered for the introduction of food from foreign countries; - that in short it is the profits of the farmer which regulate the profits of all other trades, - and as the profits of the farmer must necessarily decrease with every augmentation of Capital employed on the land, provided no improvements be at the same time made in husbandry, all other profits must diminish and therefore the rate of interest must fall. To this proposition Mr. Malthus does not agree. He thinks that the arena for the employment of Capital may increase, and consequently profits and interest may rise, altho' there should be no new facilities, either by importation, or improved tillage, for the production of food; - that the profits of the farmer no more regulate the profits of other trades, than the profits of other trades regulate the profits of the farmer, and consequently if new markets are discovered, in which we can obtain a greater quantity of foreign commodities in exchange for our commodities, than before the discovery of such markets, profits will increase and interest will rise.

In such a state of things the rate of interest would rise as well as the profits of the farmer, he thinks even if more Capital were employed on the land. Do you understand?

Nothing, I say, can increase the profits permanently on trade, with the same or an increased Capital, but a really cheaper mode of obtaining food. A cheaper mode of obtaining food will undoubtedly increase profits says Mr. Malthus but there are many other circumstances which may also increase profits with an increase of Capital. The discovery of a new market where there will be a great demand for our manufactures is one.

Believe me
Yrs very faithfully
David Ricardo

I have written this in great haste after devoting the necessary time to my accounts. You must excuse the scrawl, and corrections.

For Sraffa, Ricardo can be understood as claiming that wages are spent entirely on corn and that corn is the only basic commodity in the system. Sraffa defines "basic commodities" in his book. According to this interpretation, the rate of profits is a physical ratio in agriculture. The prices of manufactured commodities adjust, under the Classical understanding of supply and demand, until this same rate of profit prevails, both in agriculture and in manufacturing.

Monday, November 17, 2008

Militant Voting

This post illustrates a phenomenon that is a possibility in pairwise voting. Consider a constituency of 30 voters deciding among six candidates for a given vacancy. (I take this example from Donald Saari.) Table 1 describes the preferences of these voters. For example, the first row shows that ten voters prefer Anne to Barb, and Barb to Carol, and so on.) The voters are asked to choose between successive pairs of candidates, as shown in Figure 1. In the first election, Debra defeats Elaine. But Carol defeats Debra in the next choice. And so on, until Flicka is the only choice standing, after a landslide victory. It seems that clearly Flicka is the consensus choice. Strangely enough, though, every voter prefers Carol, Debra, and Elaine to Flicka. The voting system doesn’t seem to allow for a true expression of the preferences of the members of the electorate.
Table 1: Voter Preferences
NumberPreference Ranking
10A > B > C > D > E > F
10B > C > D > E > F > A
10C > D > E > F > A > B

Figure 1: Pairwise Elections in Example

Militant was a Trotskyite tendency practicing entryism within the British Labour Party. They seemed to have figured out how to use party discipline to have their way in Liverpool in the early 1980s:
"All political parties on the Monday before the Council meeting on a Wednesday, have a caucus meeting to decide the line of approach at the Council. The agenda for the meeting comes out on a Friday. The ten or twelve Militant members ... meet on either the Friday or the Saturday and go through the agenda to look for important policy decisions and for important vacancies. They then have a meeting with the broad left of the Labour group on Sunday morning at Pirrie Labour Club ... those Militants turn up in their full strength. There are generally about twenty people and the ten or eleven Militants there. They carry the majority vote there that commits the broad left for the meeting of the Labour group. On the Monday night at the Labour group meeting of forty-two members the commitment that Militant have made themselves, plus other people they've taken along at the meeting on Sunday morning, gives them a majority. ... so you find that of forty-two Labour councilors, ten Militants control the policy of the Labour group." -- Eddie Roderick, as quoted by Michael Crick
Crick says, "Roderick's analysis may be a rather simplified version." At any rate, Figure 2 illustrates how the Council seems to have made their decisions. Figures 1 and 2 look quite similar. Maybe Saari’s math describes more than a theoretical possibility.
Figure 1: Pairwise Voting on the Liverpool City Council

  • Michael Crick (1984). Militant, Faber and Faber
  • Donald G. Saari (2004). "Geometry of Chaotic and Stable Discussion", American Mathematical Monthly, V. 111, N. 5: 377-393

Sunday, November 16, 2008


Gualra has a blog, titled "Controversias Del Capital". It seems like the kind of thing I would read if I were able to read spanish. Gualra kindly alerts me to aspects of Kaldor's thought I neglected.

I don't understand Matthew Mueller. One reason I expect professors can know more than most students is that typically students have simply not lived enough years to have been able to read as much. But this does not seem to apply to Matthew. I think this post from Matthew agrees with my previous post on the same topic. But, as I recall, I was alerted to Horwitz's controversy with Post Keynesianism by Matthew's comments on some post over at the Austrian Economics. (Here's a short recommendation of both Matthew's and my blog.)

I laugh at Paul Walker's display of ignorance, to put it kindly. Gabriel Mihalache already points out some major problems with Paul's statements. General Equilibrium does not address a research problem in which Adam Smith was interested; tâtonnement decribes a centralized - not decentralized - process for setting prices; and general results do not show the tâtonnement process converging to a stable equilibrium. In his last comment, Paul makes mistaken claims about Walras. He does not seem to realize that Walras's system is mathematically contradictory. Walras takes endowments of all goods, including individual capital goods, as givens in solving for steady-state prices.

By the way, the email discussion list for the Societies for the History of Economics (SHOE) has replaced the list for the History of Economics Societies (HES).

Thursday, November 13, 2008

A Minsky Snapshot

Figure 1 is a screen snapshot of normalized data from Google trends. Terms such as "Austrian Business Cycle" and "Austrian Business Cycle Theory", according to Google, "do not have enough search volume to show graphs." Mayhaps Michael is correct, at least for the incorrect Austrian Business Cycle Theory.
Figure 1: Trends in Popular Minsky Citations

Tuesday, November 11, 2008

Keynes As "A Puzzling Mathematician"

Where do I recall the quoted phrase in the title from? It's not in Skidelsky:
"Keynes finally saw Roosevelt for an hour at 5:16 p.m. on Monday, 28 May [1934]. No one knows what they talked about. Keynes found the tête-a-tête 'fascinating and illuminating'; Roosevelt told Frankfurter that he had had a 'grand talk with Keynes and liked him immensely'. As always, Keynes paid particular attention to Roosevelt's hands - 'Rather disappointing. Firm and fairly strong, but not clever or with finesse'." -- Robert Skidelsky, John Maynard Keynes: The Economist as Savior: 1920-1937, Penguin (1992)
And it's not in Galbraith, at least here:
"The following year he visited FDR, but the letter had been a better means of communication. Each man was puzzled by the face-to-face encounter. The President thought Keynes some kind of 'a mathematician rather than a political economist.' Keynes was depressed; he had 'supposed the President was more literate, economically speaking.'" -- John Kenneth Galbraith, The Age of Uncertainty

Monday, November 10, 2008

SDM: Path-Dependence and Instability

I recently read Peter Dorman's "Waiting for an Echo: The Revolution in General Equilibrium Theory and The Paralysis in Introductory Economics" (Review of Radical Political Economics, V. 33 (2001): pp. 325-333). Dorman claims that, in teaching introductory microeconomics, General Equilibrium Theory (GET) is "one of the back-of-the-book chapters we rarely get to." And if GET is taught, the teaching fails to reflect a "virtual revolution in GET during the past quarter-century". His thesis is that these developments in GET can and should be taught in introductory microeconomics classes.

The Sonnenschein-Debreu-Mantel theorem is one of these developments. This theorem states that almost any excess demand curves in markets for individual goods can be justified by aggregating over individual excess demands. Theory imposes only Walras' law, homogeneity of degree zero, and a technical continuity condition. No other restrictions need arise on the shape of aggregate demand curves.

Why are the SDM results exciting? They imply the general possibility of multiple equilibrium and instability. Or at least, that's what I have taken from the literature. I first thought idiosyncratic Dorman's take on the SDM results. He says that they show the "path-dependence instability of general equilibrium" and the indeterminancy of equilibrium:
"In general equilibrium, each action that alters the distribution of resources among agents (and that would be just about anything) also alters the equilibrium vector of prices. It is not possible to identify an equilibrium seperate from the actions individuals take either in pursuit of in utter ignorance of it."
And he writes:
"The first task facing a principles instructor is to ignore the scholarly debate that has surrounded S-D-M. The original authors demonstrated that out-of-equilibrium exchanges altered the distribution of resources, and, since different individuals have different preferences, also altered the general equilibrium itself. Since then, researchers have been investigating the exact extent of preference differentiation under which this result would hold. This, it seems to me, is an utterly arid line of investigation, and it has no meaningful implications for nonspecialists."

I have heard of indeterminacy, but had not thought of it in the context of the SDM. As I understand the instability implications of the SDM results, they are explored in the context of tâtonnement dynamics. How then, can one talk about path dependence here?

I did come up with some justification after some thought. The SDM results show that any dynamics is possible in GET. And I know of an interesting example of chaos in which the sensitive dependence on initial conditions is connected to a particular fractal structure. Newton's method is a numerical method for solving non-linear equations. One can think of Newton's method as a dynamical system for iteratively mapping a point in the complex plane to a root of an equation, when the method converges. Polynomials, for example, have multiple roots. Color the plane by the roots to which Newton's method maps each point. All points that map to a given root are the same color. For certain simple polynomials, you will have drawn a fractal. (Google also gave me this.) Thus, in certain regions, any infinitesimal change in the initial conditions can cause this dynamical method to tend towards a different equilibrium. This property is independent of any claim that multiple equilibrium lie along a continuum.

Since, according to the SDM results, any dynamics is possible, I guess that some sort of dynamics like I have described for Newton's method is possible in GET. And so one can say that the SDM results show the possibility of path-dependence in economics.

Sunday, November 09, 2008

Sraffa at Corfu

"[O]ne should emphasize the distinction between two types of measurement. First, there was the one in which the statisticians were mainly interested. Second, there was measurement in theory. The statisticians' measures were only approximate and provided a suitable field for work in solving index number problems. The theoretical measures required absolute precision. Any imperfections in these theoretical measures were not merely upsetting, but knocked down the whole theoretical basis. One could measure capital in pounds or dollars and introduce this into a production function. The definition in this case must be absolutely water-tight, for with a given quantity of capital one had a certain rate of interest so that the quantity of capital was an essential part of the mechanism. One therefore had to keep the definition of capital separate from the needs of statistical measurement, which were quite different. The work of J. B. Clark, Bohm-Bawerk and others was intended to produce pure definitions of capital, as required by their theories, not as a guide to actual measurement. If we found contradictions, then these pointed to defects in the theory, and an inability to define measures of capital accurately. It was on this - the chief failing of capital theory - that we should concentrate rather than on problems of measurement." -- Piero Sraffa, Interventions in the debate at the Corfu Conference on the "Theory of Capital", 4-11 September 1958.

Tuesday, November 04, 2008

The Route To Normal Science

"Compared with physics, it seems fair to say that the quantitative success of the economic sciences has been disappointing. Rockets fly to the Moon; energy is extracted from minute changes of atomic mass. What is the flagship achievement of economics? Only its recurrent inability to predict and avert crises, including the current worldwide credit crunch...

...Crucially, the mindset of those working in economics and financial engineering needs to change. Economics curricula need to include more natural science. The prerequisites for more stability in the long run are the development of a more pragmatic and realistic representation of what is going on in financial markets, and to focus on data, which should always supersede perfect equations and aesthetic axioms" -- Jean-Phillippe Bouchard, "Economics Needs a Scientific Revolution", Nature, V. 455, 30 October 2008

Sunday, November 02, 2008

Peter Boettke With Nothing To Say

Peter Boettke goes on and on and on in this post. I'll confine my comments to Boettke's first numbered "point", even though I have views on some others. This point deals with Paul Davidson's review essay on O'Driscoll and Rizzo's The Economics of Time and Ignorance.

I believe Boettke's first point is an inadequate response to Matthew Mueller here and here. Boettke points out a verbal statement from Mises rejecting the claim that money is neutral. It never seems to occur to Boettke that Davidson's point might be that the logic of Mises and Hayek's positions requires them to accept the axioms of ergodicity (logical time), money neutrality, and gross substitution. Boettke cannot rationally challenge that view by citing statements where Mises or Hayek refuse to accept the first two axioms and therefore become inconsistent.

I am of the opinion that Austrian Business Cycle Theory is consistent with money non-neutrality only in the short run. Furthermore, Hayek's notion of intertemporal equilibrium is closely related to J. R. Hick's Capital and Value model of temporary equilibrium and to the Arrow-Debreu model of intertemporal equilibrium. Hicks came to recognize late in his life that his model could not be set in historical time. Hahn has pointed out the difficulties of introducing money in any essential way into the Arrow-Debreu model. I don't know that Austrians have ever grappled with these decades-old developments. I don't see that Boettke engages in arguments.