Current Affairs

I may have something more to say in the coming weeks. But I thought I should note some of what the Post Keynesian economist Paul Davidson has to say about the subprime mortage crisis:

• Paul Davidson (2008)
  "How to Solve the U.S. Housing Problem and Avoid a Recession: A Revived HOLC and RTC", Policy Note, Schwartz Center for Economic Policy Analysis (January)
• Paul Davidson (2008) "Security, Liquidity, and Market Failure", Challenge, V. 51, N. 3 (May-June): 43-56

The Oneida Community: A 19th Century Commune

Figure 1: One View of The Mansion House

Figure 2: Another View of The Mansion House

Figure 3: Crafts On Display Inside Mansion House

Figure 4: Library Inside Mansion House

Figure 5: The Factory in Which Oneida Siver Was Manufactured

Figure 6: Another View of the Factory

Figure 7: Local Park Named After John Humphrey Noyes

"Malinvestment" in Ron Paul's Vocabulary

Ron Paul outlines mistaken Austrian Business Cycle theory:

"These governmental measures, combined with the Federal Reserve's loose monetary policy, led to an unsustainable housing boom. The key measure by which the Fed caused this boom was through the manipulation of interest rates, and the open market operations that accompany this lowering.

When interest rates are lowered to below what the market rate would normally be, as the Federal Reserve has done numerous times throughout this decade, it becomes much cheaper to borrow money. Longer-term and more capital-intensive projects, projects that would be unprofitable at a high interest rate, suddenly become profitable.

Because the boom comes about from an increase in the supply of money and not from demand from consumers, the result is malinvestment, a misallocation of resources into sectors in which there is insufficient demand.

In this case, this manifested itself in overbuilding in real estate. When builders realize they have overbuilt and have too many houses to sell, too many apartments to rent, or too much commercial real estate to lease, they seek to recoup as much of their money as possible, even if it means lowering prices drastically." -- Ron Paul, 23 September 2008

(As an aside, I am aware of some discussion on the community forums at mises.org of some version of my article.)

Barack Obama has also already gone into more technical detail, on another topic entirely, than I expect from presidental candidates. Last year at Google, Eric Schmidt asked him for "the most efficient way to sort a million 32-bit integers." Obama said, "The Bubble Sort would be the wrong way to go."

Conservatives As Cowards

The news reports a new scientific study showing that conservatives startle easier than liberals. This study was by John Hibbing, in the Political Science Department at the University of Nebraska at Lincoln, and others. Michael Greinecker has a more complete citation.

This is not an isolated study. Here's the abstract of another:

"Political scientists and psychologists have noted that, on average, conservatives show more structured and persistent cognitive styles, whereas liberals are more responsive to informational complexity, ambiguity and novelty. We tested the hypothesis that these profiles relate to differences in general neurocognitive functioning using event-related potentials, and found that greater liberalism was associated with stronger conflict-related anterior cingulate activity, suggesting greater neurocognitive sensitivity to cues for altering a habitual response pattern." -- David M. Amodio, John T. Jost, Sarah L. Master, and Cindy M. Lee (2007) "Neurocognitive Correlates of Liberalism and Conservatism" Nature Neuroscience, published online 9 September

And another:

"Analyzing political conservatism as motivated social cognition integrates theories of personality (authoritarianism, dogmatism—intolerance of ambiguity), epistemic and existential needs (for closure, regulatory focus, terror management), and ideological rationalization (social dominance, system justification). A meta-analysis (88 samples, 12 countries, 22,818 cases)confirms that several psychological variables predict political conservatism: death anxiety (weighted mean r = .50); system instability (.47); dogmatism—intolerance of ambiguity (.34); openness to experience (—.32); uncertainty tolerance (—.27); needs for order, structure, and closure (.26); integrative complexity (—.20); fear of threat and loss (.18); and self-esteem (—.09). The core ideology of conservatism stresses resistance to change and justification of inequality and is motivated by needs that vary situationally and dispositionally to manage uncertainty and threat." -- John J. Jost, Jack Glaser, Arie W. Kruglanski, and Frank J. Sulloway (2003) "Political Conservatism as Motivated Social Cognition", Psychological Bulletin, V. 129, N. 3: 339-375

Stigler On Neoclassical Economics

How economists perceive neoclassical economics may not be constant through time. Here is Stigler using the label in 1941:

"The basis of evaluation in this work is that body of contemporary theory which is given the nebulous description, neo-classical economics. This theoretical corpus stems directly from Marshall, but it has gained much in rigor at the hands of Walras, Wicksteed, and Edgeworth, and more recently the theory has been advanced by a host of economists too numerous even to mention. There is no unanimity regarding 'neo-classical' theory, but on the other hand, the divergences of opinion between competent students are certainly less than at any time since Mill. This statement is somewhat circular, it must be confessed, since a fundamental test of competence is the comprehension and acceptance of this theoretical system." -- George J. Stigler (1941), Production and Distribution Theories: The Formative Period, MacMillan, p. 8

"William Stanley Jevons is the forerunner of neo-classical economics. He did not so much depart from as supplement the classical theory, although the hasty lecteur can easily secure a contrary impression. Jevons, indeed, considered his theory to be revolutionary; he gave an impetus to and enthusiastic statement of the utility theory of value; 'his belief that all evil economic influences were incarnate in John Stuart Mill' is well known; and his mathematical mode of exposition was calculated to emphasize his apparent opposition to classical theory. But his theory of production and distribution ... is fundamentally classical. An indication of the orthodox nature of his approach is suggested by the fact that both Marshall and Edgeworth accepted his wage theory in toto." -- ibid., p. 13

My notes say I should find a passage using the label somewhere around page 266, in Stigler’s chapter on Wicksell. I don’t see this.

"[John Bates] Clark independently discovered both the marginal utility and the marginal productivity theories. He is best known, of course, for his exposition of the marginal productivity theory; it is indicative that, even at present, many continental economists consider Clark’s theory to be the marginal productivity theory. His chief task, indeed, was that of popularization – a task that was filled with appropriate detail, emphasis, and lucidity.

On the other hand, Clark performed one function for which economics has less cause for gratitude. In all of his major works, although perhaps to a decreasing extent through time, he introduced what has been called a ‘naïve productivity ethics’ – his marginal productivity theory contained a prescription as well as an analysis. The dubious merits of this ethical system need not concern us, but it is a cause for regret that Clark’s exposition, more than that of any other eminent contemporary economist, afforded some grounds for the popular and superficial allegation that neo-classical economics was essentially an apologetic for the existing economic order. Clark was a made-to-order foil for the diatribes of a Veblen." -- ibid., p. 297

Empirical Applications of Marxism - A Reading List

I've decided that if I want use data from the National Income and Products Account (NIPA) to explore Marxist and Sraffian economics, I need a more detailed understanding. I should read, sometimes again, at least these references, which are mostly Marxist:

• Applications
• Cockshott, W. Paul and A. F. Cottrell (1997) "Labour Time versus Alternative Value Bases: A Research Note," Cambridge Journal of Economics, Volume 21, Number 4, p. 545.
• Cockshott, W. Paul and Allin Cottrell (2003) "A Note on the Organic Composition of Capital and Profit Rates", Cambridge Journal of Economics, V. 27: 749-754.
• Cockshott, W. Paul and Allin Cottrell (2005) "Robust Correlations Between Prices and Labour Values: A Comment", Cambridge Journal of Economics, V. 29: 309-316
• Han, Z. and B. Schefold (2003). "An Empirical Investigation of Paradoxes: Reswitching and Reverse Capital Deepening in Capital Theory", Cambridge Journal of Economics, V. 30: 737-765.
• Izyumov, Alexei and Sofia Alterman (2005) "The General Rate of Profit in a New Market Economy: Conceptual Issues and Estimates", Review of Radical Political Economics, V. 37, N. 4 (Fall): 476-493.
• Kliman, Andrew J. (2002) "The Law of Value and Laws of Statistics: Sectoral Values and Prices in the US Economy, 1977-97", Cambridge Journal of Economics, V. 26: 299-311
• Kliman, Andrew J. (2005) "Reply to Cockshott and Cottrell", Cambridge Journal of Economics, V. 29: 317-323
• Mohun (2005) "On Measuring the Wealth of Nations: the US Economy, 1964-2001",Cambridge Journal of Economics, V. 29: 799-815
• Mohun (2006) "Distributive Shares in the US Economy, 1964-2001",Cambridge Journal of Economics, V. 30: 347-370
• Moseley, Fred (1988) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67: A Critique and Update of Wolff's Estimates", American Economic Review, V. 78, N. 1 (March): 298-303
• Ochoa, Edward M. (1989) "Values, Prices, and Wage-Profit Curves in the U. S. Economy" Cambridge Journal of Economics, V. 13, No. 3, September 1989, pp. 413-429.
• Petrovic, P. (1991) "Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2: 93-112.
• Podkaminer, Leon (2005) "A Note on the Statistical Verification of Marx: Comment on Cockshott and Cottrell", Cambridge Journal of Economics, V. 29: 657-658
• Shaikh, Anwar (1984) "The Transformation from Marx to Sraffa", in Ricardo, Marx, Sraffa (Edited by E. Mandel and A. Freeman), Verso
• Shaikh, Anwar M. and E. Ahmet Tonak (1994) Measuring the Wealth of Nations: The Political Economy of National Accounts, Cambridge University Press
• Venida, Victor S. (2007) "Marxian Categories Empirically Estimated: The Philippines, 1961- 1994", Review of Radical Political Economics, V. 39, N. 1 (Winter): 58-79.
• Weisskopf, Thomas E. (1979) "Marxian Crisis Theory and the Rate of Profit in the Postwar U.S. Economy", Cambridge Journal of Economics, V. 3 (December): 341-378
• Weisskopf, Thomas E. (1979) "Marxian Crisis Theory and the Rate of Profit in the Postwar U.S. Economy", Cambridge Journal of Economics, V. 3 (December): 341-378
• Wolff, Edward N. (1979) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67", American Economic Review, V. 69, N. 3 (June): 329-341
• Wolff, Edward N. (1988) "The Rate of Surplus Value, The Organic Composition, and the General Rate of Profit in the U.S. Economy, 1947-67: Reply", American Economic Review, V. 78, N. 1 (March): 304-306
• Methodology
• Pasinetti, Luigi L. (1973) "The Notion of Vertical Integration in Economic Analysis", Metroeconomica, V. 25: 1-29.
• Pasinetti, Luigi L. (1977) Lectures on the Theory of Production, Columbia University Press
• Raa, Thijs Ten (2005) The Economics of Input-Output Analysis, Cambridge University Press
• Steedman, I. and J. Tomkins (1998) "On Measuring the Deviation of Prices from Values", Cambridge Journal of Economics, V. 22: 379-385

The Wage As The Independent Variable

1.0 Introduction
Piero Sraffa, in his critique of neoclassical theory, described a system of prices in which capitalist earn the same rate of profits in every industry. One can derive, in the pure circulating-capital version of this system, a trade-off between wages and the rate of profits.

The shape of this wage-rate of profits curve depends on the (possibly composite) commodity chosen for the numeraire. It is a straight line when Sraffa's standard commodity is used for the numeraire. If the wage-rate of profits curve were a straight line for all other numeraires, the labor theory of value would be be exactly true as a theory of relative prices, abstracting from deviations between market prices and prices of production and from the theory of joint production. This theorem of mathematical economics raises an empirical question. How far does the wage-rate of profits curve vary from a straight line for various numeraires?

P. Petrovic ("Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2 (1991): pp. 93-112) explored this question for 1976 and 1978 data from Yugoslavia. Petrovic found that the empirical wage-rate of profits curve never deviated much from a straight line, no matter what numeraire was chosen.

I was only able to partially replicate Petrovic's results with 2005 USA data. The 2005 USA wage-rate of profits curve drawn with a numeraire in the proportions of net output is indeed quite close to a straight line. But the 2005 USA wage-rate of profits curve can be quite convex or quite concave, depending on the choice of the numeraire. My methodology differed from Petrovic's in that I introduced a normalization of the numeraire quantity to fix the maximum wage at unity for each numeraire.

My estimate of the rate of profits in the USA is higher than I expected. I am beginning to think that my approach is too simple. Perhaps I need to account for depreciation, fixed capital, and the distinction between productive and unproductive labor. I may post more analyses in this series before revisiting my past results.

2.0 Derivation of the Wage-Rate of Profits Curve
Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition.

The Sraffa prices equations, in which wages are paid out of the surplus, are:

p A (1 + r) + a₀ w = p

where p is a row vector of prices, w is the wage, and r is the rate of profits. After some manipulation, one has:

a₀ [ I - A (1 + r)]^-1 w = p

The Hawkins-Simon conditions guarantees the existence of the matrix inverse for rates of profits between zero and some maximum rate of profits. Let e be a column matrix representing the numeraire. Multiply on the right by the numeraire:

a₀ [ I - A (1 + r)]^-1 e w = p e = 1

The wage-rate of profits curve is then:

w = 1/(a₀ [ I - A (1 + r)]^-1 e)

3.0 Empirical Results

Figure 1 shows the range of convexities, depending on the numeraire, of the wage-rate of profits curve in the USA in 2005. The straight-line wage-rate of profits curve is constructed using Sraffa's standard commodity as the numeraire.

Figure 1: Wage-Rate Of Profits Curve For Selected Numeraires

I examined a numeraire for each of the 65 industries in the 2005 Use Table. The numeraire corresponding to each industry consists solely of the output of that industry; the output of all other industries is zero in this non-composite numeraire commodity. The quantity of the selected numeraire commodity is set to ensure the maximum wage, corresponding to a rate of profits of zero, is unity. In other words, the numeraire quantity is normalized such that its embodied labor value is one thousand person-years, the unit in which the BEA measures labor.

Figure 1 shows wage-rate of profits curves for two of these 65 numeraires. The wage-rate of profits curve for the numeraire consisting solely of output of Warehousing and Storage industry has the highest positive displacement from the straight-line wage-rate of profits curve. The wage-rate of profits curve for the numeraire consisting solely of output of the Petroleum and Coal Products industry is the furthest below the straight-line wage rate-of profits curves. The wages-rate of profits curves for all other numeraires are closer to the straight-line wage-rate of profits curve.

The remaining wage-rate of profits curve shown in Figure is drawn for a numeraire in the proportions of positive quantities in the net output (final demand) quantities in the 2005 Use Table. (Final demand quantities are net of the circulating capital goods replaced out of gross output; they still include, however, depreciation charges against fixed capital.) Among the components of final demand, imports and nondefense consumption expenditures from the Federal government can be negative. Thus, the final demand for the output of an industry can be negative, if, for example, more of that industry's output is imported than exported. The following industries have negative quantities in final demand:

• Forestry, fishing, and related activities
• Oil and gas extraction
• Wood products
• Nonmetallic mineral products
• Primary metals

Finally, Figure 1 shows a point for the year 2005. Wages, in numeraire units, are calculated from data on employee compensation, full time equivalent employees, and net output. The data on full time equivalent employees is included with data on gross output and was used to calculate labor values. I did not make any correction here for negative quantities in final demand. Compensation of employees is a component in Value Added in the Use Table. The other two components of Value Added are Taxes on production and imports, less subsubsidies and Gross operating surplus. The actual wage is 0.575 of the net output of a thousand person-years. The corresponding rate of profits is 53.3%. The wage, when net output is used as the numeraire lies 0.0766 numeraire units above the straight line wage-rate of profits curve, close to the maximum difference along these two curves of 0.0773 numeraire units.

Theoretically, the wage-rate of profits curve for numeraires other than the standard commodity can be of any convexity. Furthermore, the convexity can differ over different ranges of the rate of profits. One might find surprising how close the wage-rate of profits curve is to a straight line when net output is chosen as a numeraire. The rate of profits can be increased by an increase in productivity, which moves the wage-rate of profits curve outward. The rate of profits can also be increased by a decrease in the wage, that is, by increasing the exploitation of the workers.

Rejection By Review Of Political Economy

Rejection Letter By Steven Pressman
Dear Robert,

I have now received back two referee reports on your paper "Some Capital-Theoretic Fallacies of Austrian Economics". Unfortunately, neither of the referees liked your paper and both recommended that I reject the paper.

Given the two reports, I have no choice but to turn down your paper. Enclosed are the comments that I received from my referees. I hope that they are helpful to you in revising this piece and getting it published elsewhere.

Best wishes, Steve

One Referee Report
This paper revisits the Cambridge Capital Controversies (CCC) by presenting an internal critique of "Hayekian triangles" illustrating the existence of reswitching in Austrian capital theory and its importance for Austrian Business Cycle Theory (ABCT). On the basis of this criticism, it declares ABCT to be inadequate and in need of serious revision, if not outright rejection.

The strengths of this paper are that it revisits an important victory of early Post Keynesian/NeoRicardian economics and illustrates that the points raised then have not been addressed by recent Austrian writings on ABCT, even by some smart and well-read people, such as Roger Garrison. In the second half of the paper (starting page 10), the author goes on to give a capable demonstration of this failure, and (briefly) argues that the tired old defense that "no actual instances" of capital-reversing "have ever been identified" is an inadequate response -- theoretically or empirically. That these errors are still made by Austrian (and I might add Neoclassical) economists suggests that the lessons of the CCC remain unlearned. For this reason there is indeed value in raising these points again (As an aside, I would venture that only one or two of my economist colleagues could even tell you what the CCC was, much less recount its importance for the Neoclassical theory of income distribution, but I digress).

My problems with the paper are three-fold. First, I found the introduction both too lengthy and not lengthy enough. This is indeed a paradox, so let me explain. While I have not done so lately, I once spent a great deal of time reading and teaching the Reswitching literature, and I found this lengthy review to be somewhat hard to follow. The reason is that it was (as the author admits) rather one-sided, but consequently it seemed to jump from point to point. But, simultaneously, these ten pages were also too brief and too abstract to inform someone who has only a passing acquaintance with the issue and its most important debates and findings. As a consequence, these less informed readers might be inclined to "turn the page." My point is that the introductory material was too short to satisfy those of us who know this literature and would like a review, but too long to help someone understand it if they do not already know it. My suggestion would be to cut out much of the first half and simply start with Section 3 (page 10) and position the paper as a "Research Note", and simply reintroduce it as a more narrow contribution, for example a critique of Roger Garrison or Hayek. Those interested will jump in, those who are not will skip over it, but the fairly unproductive first half can then be reduced to some references to the core literature (Harcourt or Garegnani, etc.)

Second, I found the algebraic examples to be, I believe, overly difficult to follow. Why were the units expressed in 49ths? That is a hard number with which to conduct long division in one's head! This presents a barrier to a reader who wishes to puzzle through the examples in the Tables. Was there a rationale for this choice? If so, please state it. If not, please simplify the treatment so as to invite the reader to follow the narrative and better learn from the examples.

Third, and perhaps most distressingly, I am not convinced that the overall presentation is all that original. Perhaps I am misinformed in surmising this, and I am willing to be corrected. But I must confess that I did not get the sense that this paper showed me a new angle or insight on the reswitching theorem or its implications. Now, that does not in itself doom this paper, but I do think that it means that it needs to be "repackaged", perhaps along the lines suggested above in my first criticism -- that is to say as a narrower and more specific project, without the lengthy preamble, and making a simple and direct critique of recent Austrian writings on Capital Theory and the ABCT.

Other Referee Report
The paper attempts to show by counterexample that Austrian Business Cycle theory is false. The counterexample is a model in which the interest rate is exogenous and marginal adjustments in response to the interest rate are impossible by assumption. The paper reaches its climax when the author shows that an important remark of Austrian economist Roger Garrison does not hold in the paper's model economy. Garrison's remark is:

"In response to a policy-induced reduction of the interest rate, one leg of the triangle (measuring the stage dimension of the structure of production) lengthens; the other leg (measuring the final output of the production process) shortens. The forced saving, i.e. the reduced output of consumption goods allows for expansion of the early stages of production. This is pure malinvestment."

Garrison could be wrong. But the context for the remark is an economy in which the interest rate is endogenous and marginal adjustments in response to the interest rate are possible. It is legitimate to restrict one's attention to two discrete techniques for an individual enterprise and ask which is preferred under different assumed interest rates. That exercise reveals the theoretical possibility of re- switching. But it is not legitimate to force Garrison's discussion of malivestment into that box.

I couldn't understand the author's model economy. Table 2 was a complete mystery to me. It is true that if iron and steel produce iron and steel, then it is not so clear what "order of good" means. But I cannot understand how the author divides his two output into (apparently) and infinite rank of orders.

The Austrians insist that "waiting" has two dimensions, time and money. He (she or they) even quote Hayek saying as much way back in 1941. I don't see that Austrian notion reflected in the paper's analysis, however. As well as I can make out, Cohen and Harcourt's toss off remark that Yeager didn't know what he was talking about is taken to settle the issue.

I think the Austrians are far more vulnerable on capital theory that they recognize. Thus, I would welcome a strong challenge to Austrian capital theory. If a strong challenge was mounted in this essay, it was beyond my ability to grasp it.

Blaug Versus Sraffians

Apparently, Gavin Kennedy delivered a paper, "Adam Smith's Invisible Hand: From Metaphor to Myth", at the 40th Anniversary Conference of the History of Economic Thought (HET). Kennedy reports the conference was held in Edinburgh on 3-5 September. And he uses a report on Marg Blaug's keynote address to express irritation at Sraffians:

"Professor Tony Brewer, University of Bristol, took over the chair, for Professor Mark Blaug's keynote address, which did not stir up the opposition I had expected, but then I did not know the economics of most of the participants, and I was relieved to find out that there were no vocal 'Sraffians' among the audience (the obscurity of the Sraffian economics monologue defies summary and any explanation for why it excites, or once excited, the in-group enthusiasm of a small cell in Cambridge).

Mark Blaug's paper was on 'The Trade-off Between Rigor and Relevance: Straffian economics as a case in point', and what a demolition job it was too, summed up neatly in the title." -- Gavin Kennedy

I was unable to find any other references to Blaug's address on the web. I am aware, however, that Blaug has been, for a number of years, griping about the formalist revolution that occurred in economics after World War II (e.g., Blaug 2003). And that he groups Sraffa's Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory with Debreu's Theory of Value: An Axiomatic Analysis of Economic Equilibrium as exemplars of formalism in economics.

Blaug has had something to say about Sraffians in the past. For example, he has written at least two pamphlets for the Institute of Economic Affairs. As I understand it, IEA is a right-wing think tank in Britain. Blaug (1975) is an attack on the Cambridge school, as it stood after the successes of the Cambridge Capital Controversies. In this attack, Blaug misunderstands Sraffa's mathematics in ways that he carries forward into his textbook. He also adopts the curious position that a demonstration, based on reswitching and capital-reversing, of the logical invalidity of neoclassical economics does not hold without the identification of empirical occurrences of the phenomena. Blaug (1988) is a review of The New Palgrave. Blaug claims that John Eatwell, Murray Milgate, and Peter Newman ("A Sraffian Trio") edited a "tendentious work":

"To have invited three Sraffians to edit a new Palgrave dictionary of economics is roughly equivalent to asking three atheists to edit an encyclopedia of Christianity" -- Mark Blaug (1988)

Since the incorrectness of most doctrines of orthodox economics are not recognized by many practitioners, editors of reference works have a problem. I welcome the recognition that belief in these doctrines are a matter of faith, although I am not sure Blaug is being fair to Christianity.

Sraffa had a revolutionary impact on how historians read Ricardo, in particular, and the Classical economists more generally. Recently, Blaug (1999) disputed the Sraffian interpretation of Classical economics. Kurz and Salvadori (2002), Blaug (2002), and Garegnani (2002) is a selection from the literature of responses and counter-responses to Blaug's article. The Sraffians seem to agree that Blaug disputes a straw person. In the Sraffian interpretation, the theory of value can be set out with rigorous mathematics. But the givens of the Classical theory of value are themselves explained within economics (in contrast to neoclassical General Equilibrium theory). Thus, the theory of value is only an element in an approach to a larger economics which investigates such issues as growth, development, population demographics, etc. Blaug failed to understand the instrumental role of the theory of value in the Sraffian interpretation. His criticism of the Sraffians for setting out the theory of value, in their understanding, without encompassing, for example, growth is simply misdirected.

Some Sraffians are competing with Blaug's Economic Theory in Retrospect (nth edition) in the market for textbooks on the history of economic thought. I gather that this market is shrinking, as mainstream economists purge the history of their field from the curriculum. Alessandro Roncaglia (2005) and Ernesto Screpanti & Stefano Zamagni (2005) are two textbooks from Sraffians.

• Mark Blaug (1975) The Cambridge Revolution: Success or Failure?, Institute of Economic Affairs
• Mark Blaug (1988) Economics Through the Looking Glass: The Distorted Perspective of The New Palgrave Dictionary of Economics, Institute of Economic Affairs
• Mark Blaug (1999) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 31, N. 2: 213-236
• Mark Blaug (2002) "Kurz and Salvadori on the Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 34, N. 1: 237-240
• Mark Blaug (2003) "The Formalist Revolution of the 1950s", Journal of the History of Economic Thought, V. 25, N. 2: 145-156
• Pierangelo Garegnani (2002) "Misunderstanding Classical Economics? A Reply to Blaug", History of Political Economy, V. 34, N. 1: 241-254
• Heinz D. Kurz and Neri Salvadori (2002) "Mark Blaug on the 'Sraffian Interpretation of the Surplus Approach'", History of Political Economy, V. 34, N. 1: 225-236
• Alessandro Roncaglia (2005) The Wealth of Ideas: A History of Economic Thought, Cambridge University Press
• Ernesto Screpanti and Stefano Zamagni (2005) An Outline of the History of Economic Thought (Second edition)

If The Workers Were Able To Live On Air

"In so far as the development of productivity reduces the paid portion of the labour applied, it increases the surplus-value by lifting its rate; but in so far as it reduces the total quantity of labour applied by a given capital, it reduces the number by which the rate of surplus-value has to be multiplied in order to arrive at its mass. Two workers working for 12 hours a day could not supply the same surplus-value as 24 workers each working 2 hours, even if they were able to live on air and hence scarcely needed to work at all for themselves. In this connection, therefore, the compensation for the reduced number of workers provided by a rise in the level of exploitation of labour has certain limits that cannot be overstepped..." -- Karl Marx, Capital, Vol. 3, Part 3, Chap. 15, Sect. 2

Introduction
A maximum rate of profits arises in a model of the production of commodities by means of commodities. This maximum rate of profits is an upper limit on the rate of profits in any sublunary capitalist economy, where the workers produce commodities to consume and thereby reproduce their labor power.

This maximum rate of profits would be easily seen if the economy were a giant farm producing one commodity, corn, from inputs of labor and seed corn. The surplus would be the difference between harvested corn and the quantity of seed corn which needs to be set aside to continue production next year. The ratio of this surplus to the quantity of seed corn is the maximum rate of profits. The maximum rate of profits cannot be achieved because of the need to pay wages to the workers eats into this surplus.

Some of the simple lessons of the corn economy generalize to actual more-or-less capitalist economies, such as in the United States of America (USA). One can use the mathematics of eigenvalues and eigenvectors to set out the theory in this case.

2.0 The Standard System
Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition.

This data determines Sraffa's standard system, in which the gross output, the net output, and capital goods have specific properties. Let q* be an n-element column vector denoting the gross quantities output in each industry, that is to say, the gross output in the standard system. The column vector A q* represents the physical quantities of capital goods needed to produce the gross output in the standard system. Let y* be an n-element column vector denoting the net quantities output in each industry in the standard commodity. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output, in any proportions, are related as follows:

y* = q* - A q* = (I - A) q*

In the standard system, the ratio between gross output and the quantity of capital goods needed to produce the gross output is invariant among commodities:

q* = (1 + R) A q*

Or:

A q* = [1/(1 + R)] q*

As a matter of fact, [1/(1 + R)] is the maximum eigenvalue of A. The standard system is scaled such that the amount of labor employed in the standard system is unity:

a₀ q* = a₀ (I - A)^-1 y* = 1

y* is the standard commodity.

One chooses the maximum eigenvalue to ensure, under the Hawkins-Simon condition, the existence of a standard commodity in which all components are non-negative and at least some components are strictly positive. The commodities which enter the standard commodities are called "basic". They enter directly or indirectly into the production of all commodities. Those commodities with zero entries in the standard commodity are called "non-basic". Either non-basic commodities do not enter into the production of any other commodity. Or they enter into the production only of non-basic commodities. For each non-basic commodity, there exist some commodity such that the non-basic commodity does not enter, either directly or indirectly, into the production of that commodity.

To explicate the concept of a commodity entering indirectly into the production of another commodity, consider the output of the Motor Vehicles, Bodies And Trailers, And Parts industry, one of the 65 industries in the 2005 Use Table for the USA available from the Bureau of Economic Analysis (BEA). 0.18 units of the output of the Primary Metals industry enter (directly) into the production of each unit produced by the Motor Vehicles, etc. industry. (A quantity unit of any industry is one hundredth of the quantity output of each industry in the year 2000, where the quantity unit in each year is a chain index.) 0.15 units of the output of the Mining, Except Oil And Gas, industry is an input into each unit produced by the Primary Metals industry. Since Mining, Except Oil And Gas, enters into Primary Metals, and Primary Metals enters into Motor Vehicles, etc., then Mining, Except Oil And Gas, enters indirectly into the production of Motor Vehicles, etc. (0.040 units of Mining, Except Oil And Gas, also enter directly into each unit output of Motor Vehicles, etc..) Any number of steps can separate the indirect production of one commodity by another.

Summary of Some Empirical Results
I've implemented the above mathematics with 2005 data for the USA. Sixty two industries in the USA in 2005 are basic and enter into the standard commodity with positive components. The three non-basic industries are

• Hospitals and Nursing and Residential Care Facilities
• Federal General Government
• State and Local General Government

I think the non-basic property of the general government industries is an accounting convention. The industries Federal Government Enterprises and State and Local Government Enterprises are basic and enter into the standard commodity with positive values.

The maximum rate of profits in the USA in 2005 was approximately 106.4%.

OCC Varies Less Among Vertically Integrated Industries (Part 2)

I gave a hostage to fortune in the first part. That part notes the empirical claim that the Organic Composition of Capital (OCC) varies less among vertically integrated industries, as compared to non-vertically integrated industries. But I did not demonstrate this claim with actual data. This part retrieves this hostage by presenting empirical results.

The first part explained how to calculate the OCC for both non-vertically and vertically integrated industries, given Leontief Input Output tables. I performed these calculations with the Leontief Input Output table obtainable from the 2005 Use Table and other data available from the Bureau of Economic Analysis (BEA). Figure 1 shows these distributions of the OCC among the 65 industries aggregated by the BEA. Notice that the OCC does indeed seem to be more dispersed for non-vertically integrated industries.

Figure 1: Distribution of Ratio of OCC to Sum of Unity and Rate of Exploitation

In both cases, the distributions seem to be skewed and from a non-Gaussian distribution. Taking common logarithms yields the distributions shown in Figure 2. Table 1 presents summary statistics for these distributions. The absolute value of the coefficient of variation in the distribution of the OCC is indeed decreased by vertical integration. So these results replicate, for 2005 United States of America (USA) data, Shaikh’s and Petrovic’s earlier results for the USA in 1947 and Yugoslavia in 1976 & 1978, respectively.

Figure 2: Distribution of Common Logarithm of Ratio of OCC to Sum of Unity and Rate of Exploitation

Table 1: Logarithm of Ratio of OCC to Sum of
Unity and Rate of Exploitation

Statistic	Non-Vertically Integrated Industries	Vertically Integrated Industries
Number Industries	65	65
Mean	-0.0326576	-0.0770277
Standard Deviation	0.396980	0.225224
Coefficient of Variation (Absolute Value)	12.16	2.924

I suppose this analysis could be improved by performing formal statistical tests. In particular, one might use the Kolmogorov-Smirnov goodness of fit test to determine if the distributions of the OCC after a logarithmic transformation are Gaussian. I don’t know how to formally test for a change in the coefficient of variation. But, since the mean is so close to zero anyway, one might use an F test to contrast the variance in the distributions of the (transformed) OCC. I don’t plan on pursuing this line soon, though.

His Cousin Was A Socialist And A Great American

Francis Bellamy Family Gravesite, Rome, NY

Base of Pillar

Francis' cousin, Edward Bellamy, wrote Looking Backward: 2000-1887.

Relevance of Austrian Business Cycle Theory to USA Politics

Matthew Yglesias blogs "Live from the Paul-Dome":

"I never thought I’d hear an arena full of people cheering and clapping for 'the Austrian theory of the business cycle.'"

OCC Varies Less Among Vertically-Integrated Industries (Part 1)

1.0 Introduction
Anwar Shaikh claims that one can expect the Organic Composition of Capital (OCC) to vary less among vertically integrated industries than among non-vertically integrated industries. Shaikh shows his claim holds for the United States of America in 1947. Petrovic demonstrates the claim for Yugoslavia in 1976 and 1978.

This post lays out the theory formulating this empirical claim. Results replicating Shaikh's and Petrovic's test of the theory in new data are left for Part 2. I have yet to test the theory, and Part 2 remains unwritten for now.

2.0 Vertical Integration

Consider an economy in which each of n commodities are produced from labor and inputs of those n commodities. Let a_{0, j} be the person-years of labor used in producing one unit of the jth commodity. Let a_{i, j} be the physical units of the ith commodity used in producing one unit of the jth commodity. The direct labor coefficients are elements of the n-element row vector a₀. The remaining input-output coefficients are the entries in the nxn Leontief input-output matrix A, which is assumed to satisfy the Hawkins-Simon condition. The challenge is to express an empirical claim about the variability of the OCC in terms of this empirically-observable data.

Let q be an n-element column vector denoting the gross quantities output in each industry. The column vector A q represents the physical quantities of capital goods needed to produce this gross output. Let y be an n-element column vector denoting the net quantities output in each industry. The net output is available to be divided up between wages and profits after replacing the capital goods needed to reproduce the gross output. Net output and gross output are related as follows:

y = q - A q = (I - A) q

Or:

q = (I - A)^-1 y

The jth column of (I - A)^-1 represents the gross output in a vertically integrated industry producing a net output of one unit of the jth commodity. This interpretation becomes apparent when one considers a net output vector consisting of one unit of the jth commodity:

y = e_j

where e_j is the jth column of the nxn identity matrix.

The above analysis of vertically integrated industries allows one to specify the amount of labor and the capital goods employed in each vertically integrated industry. Consider the n-element row vector v defined as:

v = a₀ (I - A)^-1

The jth element of v represents the labor (in person-years) employed in a vertically integrated industry producing one unit of the jth commodity net. This element is the labor directly and indirectly embodied in one unit of the jth commodity. v is the vector of labor values for this economy. The capital goods used in producing any gross output vector is found by pre-multiplying that vector by the Leontief input-output matrix A. Define the matrix H such that each column is the product of A and the gross output of a vertically integrated industry producing a net output of one unit of the corresponding commodity:

H = A (I - A)^-1

Luigi Pasinetti calls the columns of H "the vertically integrated units of productive capacities." A column "expresses in a consolidated way the series of heterogeneous physical quantities of commodities which are directly and indirectly required as stocks, in the whole economic system, in order to obtain one physical unit of [the corresponding commodity] as a final good."

3.0 The Organic Composition of Capital
According to Karl Marx, the labor value of a commodity is the sum of the labor embodied in the capital goods used in the production of that commodity, the labor value of the labor power used in the production of that commodity, and the surplus value:

v_j = c_j + w_j + s_j

where

• c_j is constant capital expended in producing one unit of the jth commodity
• w_j is variable capital (that is, the labor value of capital spent on the wages of workers) expended in producing one unit of the jth commodity
• s_j is the surplus value obtained in producing one unit of the jth commodity.

For Marx, the labor value of constant capital appears unchanged in the product. The source of profits is the appropriation by the capitalists of surplus value produced throughout a capitalist economy.

The OCC is defined to be the ratio of constant capital and variable capital, both expressed in labor values:

occ_j = c_j/w_j

where occ_j is the OCC for the jth industry. Marxist economics would be much less problematic if the OCC were invariant across industries. The rate of exploitation e is another important parameter in Marxist economics. The rate of exploitation is the ratio of surplus value to variable capital in each industry:

e = s_j/w_j

The equality of the rate of exploitation across industries follows from an assumption of competitive labor markets, inasmuch as workers are free to transition among industries in seeking work. The OCC in each industry can be expressed as a function of the rate of exploitation and the ratio of constant capital to the remaining labor value of the product:

occ_j = (e + 1) c_j/(w_j + s_j)

The rate of exploitation can be treated as a nuisance parameter in exploring the empirical question raised in this post.

Consider non-vertically integrated industries, each producing a gross output of one unit of each commodity. The jth industry in this case employs a_{0, j} person-years of labor. That is, the labor value of the product from newly applied labor is merely the corresponding direct labor coefficient:

w_j + s_j = a_{0, j}

The columns of A represent the capital goods needed in each of these industries. The labor embodied in the capital goods for the jth industry is the dot product of the row vector expressing the labor values of a unit of each commodity and the column vector denoting the quantities of these capital goods. Thus, one has:

c = v A

On the other hand, consider vertically integrated industries, each producing a net output of one unit of each commodity. The amount of labor directly employed in the jth vertically integrated industry is v_j. The labor value c^*_j embodied in the capital goods for the jth vertically integrated industry are easily found:

c^* = v H

where the elements of c^* are the desired labor values.

The above observations can be brought together to summarize the empirical claim of interest here. The OCC in each non-vertically integrated industry is proportional to the ratio of the labor value of the capital goods used in that industry and the labor directly employed in that industry:

occ_j/(e + 1) = c_j/a_{0, j}

The OCC in each vertically integrated industry is also proportional to the ratio of the labor value of the capital goods used in that industry and the labor employed in that industry:

occ^*_j/(e + 1) = c^*_j/v_j

where occ^*_j is the OCC in the jth vertically integrated industry. The proportionality constant is the same function of the rate of exploitation in the above pair of equations. The empirical claim is that the expression on the right hand side varies less among industries for vertically integrated industries than among non-vertically industries. That is, the coefficient of variation is less among vertically integrated industries. Perhaps one should take a variance-stabilizing transformation, such as natural logarithms, before calculating the coefficient of variation.

References

• Luigi L. Pasinetti (1973) "The Notion of Vertical Integration in Economic Analysis", Metroeconomica, V. 25: pp. 1-29 (Republished in Pasinetti 1980)
• Luigi L. Pasinetti (Editor) (1980) Essays on the Theory of Joint Production, Columbia University Press
• P. Petrovic (1991) "Shape of a Wage-Profit Curve, Some Methodology and Empirical Evidence", Metroeconomica, V. 42, N. 2: pp. 93-112
• Anwar Shaikh (1984) "The Transformation from Marx to Sraffa", in Ricardo, Marx, Sraffa (Ed. by E. Mandel and A. Freeman), Verso