Applied Sraffianism

"These allusions give incidentally some indication of the disproportionate length of time over which so short a work has been in preparation... As was only natural during such a time period, others have from time to time independently taken up points of view which are similar to one or the other adopted in this paper and have developed them further or in different directions from those pursued here." -- Piero Sraffa

Despite my appreciation of Bliss' 1975 book, I think the following view dubious, uninformed, and authoritarian:

"A striking feature of the school to which Piero Garegnani belongs is its seeming lack of interest in the real world... Our world is changing rapidly and in ways that demand economic analysis of what is happening... Over the last 30 years so-called neoclassical economics has been extraordinarily productive... What has been the contribution of the post-Sraffa school in the same period? Nothing at all as far as I can see. This has been an exceptionally sterile approach. Where are the new ideas? Where are the illuminating insights into what is happening today?" -- Christopher Bliss (2009)

I have no problem with a researcher deciding to center their investigations into criticism and the history of economic thought. I think that when Bliss calls neoclassical economics "extraordinarily productive", he includes research that fails to test neoclassical economics and whose relationship to neoclassical economics can be doubted. Sraffian economics can easily exceed this standard.

I take the "others" Sraffa refers to above to be principally Wassily Leontief and John Von Neumann. So, for example, work with Leontief's Input-Output (I/O) analysis is applied Sraffian analysis. Interestingly enough, countries maintain their national accounts in a form supporting I/O analysis. (For the United States, see the benchmark input-output accounts available from the Bureau of Economic Analysis (BEA). For many developed countries, see the Structural Analysis (STAN) Database for data on Industry and Services available from the Organisation for Economic Co-Operation and Development (OECD).) For me, challenges in working with this data arise from statistical discrepancies, rectangular matrices that I expect to be square, components in value added that are neither wages nor profits, import and export flows, etc. But other economists, including some Sraffians have addressed these challenges in their own work.

I have listed selected applied Sraffa work on two topics.. Tony Aspromourgos (2004) lists Sraffian research applied to a larger range of issues.

References

• Tony Aspromourgos (2004). "Sraffian Research Programmes and Unorthodox Economics", Review of Political Economy, V. 16, n. 2: pp. 179-206.
• Christopher Bliss (2009). "Comment on 'Capital in Neoclassical Theory: Some Notes' by Professor Piero Garegnani".
• Thijs ten Raa (2006). The Economics of Input-Output Analysis, Cambridge University Press.
• John Von Neumann (1945). "A Model of General Economic Equilibrium", Review of Economic Studies, V. 13, N. 1: pp. 1-9.

"The Impossibility ... [Of] ... A Single Magnitude Representing ... The Quantity Of Capital"

Figure 1: From Sraffa's Production of Commodities by Means of Commodities

Suppose people save more. A neoclassical and Austrian school¹ idea is that then the supply of capital will have increased, in some sense. One would expect its price, the rate of interest, to be less, absent intervention by the monetary authorities. Entrepreneurs, if they were alert, would adopt more capital-intensive - that is - longer techniques of production. After these techniques came online, output per worker would be higher.

Suppose that the length of the period of production of a technique were defined in terms of purely physical data. Given a complete list of inputs and outputs, including the times at which they flow into and out of the production processes, one would be able to measure the (average) period of production of the technique composed of those processes. Then reswitching shows the above story cannot be universally valid.

Austrian-school economists and economists sympathetic to the Austrian school have had at least two reactions to this demonstration of the logical invalidity of the above story. One reaction is to assert that an aggregate measure of capital-intensity, such as a physical measure of the average period of production, is not needed for the story to go through. Supposedly, entrepreneurs shift resources, in response to low interest rates, to time periods further before the production of consumer goods. In the technical jargon, entrepreneurs tend to move resources towards producing goods of higher orders and away from producing goods of lower orders. I have shown² that this response fails to evade a critique based on reswitching.

The second reaction is to define the average period of production as dependent on the interest rate, as well as physical properties of techniques of production. Thus, the average period of production for a given technique will be different at the interest rates associated with different switch points. Apparently, Edmond Malinvaud, drawing on some work of J. R. Hicks, made this argument in a 2003 paper about Knut Wicksell's contributions. Saverio Fratini, in his paper presented at the recent 50th anniversary conference on Sraffa's book, took the opportunity of Malinvaud's paper to argue that this reaction also cannot be sustained as a response to a critique based on reswitching and capital-reversing.

I associate this second reaction with Leland Yeager, who, in a couple of papers in the late 1970s, argued that waiting has the dimensions of the product of value and time (for example, dollar-years). I find it hard to find a valid non-tautological argument here. I think Fratini's paper could be revised to point out that he refutes Yeager, as well as J. R. Hicks and Edmond Malinvaud. I would like to be referenced too, although I don't know about the conventions of referencing working papers.

Footnotes
¹ Both William Stanley Jevons and Eugen von Böhm-Bawerk expounded this idea.
² Due to a recent hard-disk crash, I have lost originals from which I generated some PDFs, as well as reviewer comments on recent revisions.
References

• Saverio M. Fratini (2010). "The Hicks-Malinvaud Average Period of Production and 'Marginal Productivity': A Critical Assessment", Sraffa’s Production of Commodities by Means of Commodities 1960-2010, Roma, Italy (2-4 Dec.)
• Robert L. Vienneau (2010) "Some Capital-Theoretic Fallacies in Garrison’s Exposition of Austrian Business Cycle Theory"
• Leland B. Yeager (1976). "Towards Understanding Some Paradoxes in Capital Theory", Economic Inquiry, V. 14: pp. 313-346
• Leland B. Yeager (1979). "Capital Paradoxes and the Concept of Waiting", Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (ed. By Mario J. Rizzo), D. C. Heath and Company

Videos And Papers From 50th Anniversary Conference On Sraffa's Book

In comments on my previous post, a blogger from Revista Circus links to a presentation of Gary Mongiovi on Marxian exploitation. This is too modest. The blog has organized a plethora of videos, abstracts, and draft papers from the recently completed international conference in Rome on Sraffa's Production of Commodities by Means of Commodities:

• Pierangelo Garegnani's presentation and a paper on the present state of the capital controversy
• Fabio Petri's paper and presentation on bringing sense back to the theory of aggregate investment
• Franklin Serrano's presentation on elements of continuity and change in the international economic order: an analysis based on the modern classical surplus approach
• Gary Mongiovi's paper and presentation on the concept of exploitation in Marxian economics
• Heinz Kurz's paper and presentation on reviving the "Standpoint of the old classical economists": Piero Sraffa's contribution to political economy
• Tony Aspromourgos' paper and presentation on Sraffa's system in relation to some main currents in unorthodox economics
• Marc Lavoie's paper and presentation on should Sraffian economics be dropped out of the post-Keynesian school?
• Esteban Pérez Caldentey and Matías Vernengo's paper and presentation on Raúl Prebisch's evolving views on the business cycle and money
• Roberto Ciccone's presentation on public debt and the determination of output
• Antonella Palumbo's presentation on potential output, actual output and demand-led growth
• Heinz Kurz's closing remarks

Update: In the comments, Saverio Fratini informs us that all the available papers are accessible from the conference web site.

Michele Boldrin Confused About Marxian Exploitation, Marginal Productivity

Michele Boldrin has written a paper in which supposedly Marxian themes are treated in a Dynamic Stochastic Equilibrium Model (DSGE). He writes:

...there is 'exploitation of labor' also in standard neoclassical models of production. Within each firm, almost all workers (i.e. everyone but the marginal worker at the marginal plant) are 'exploited' in the sense that they are being paid a wage smaller than their marginal productivity. -- Michel Boldrin (2009) "Growth and Cycles, in the Mode of Marx and Schumpeter. Scottish Journal of Political Economy, V. 56, N. 4 (p. 432)

The above is mistaken on at least two points:

• The notion of exploitation is Joan Robinson's neoclassical idea from the period in which she developed the theory of imperfect competition; this idea is not Marx's.
• The above passage seems to take the value of the marginal product of labor as defined prior to prices, including wages. If so, Boldrin follows the mathematically mistaken teaching of some not-so-bright orthodox economists.

Boldrin continues his mistaken line:

From a Marxian view point, labor-saving innovations are the means through which capitalist exploitation can be perpetrated and maintained over time... -- Michel Boldrin (2009)(p. 435)

The above might or might be true of Marxian exploitation, but Boldrin is using a different definition. And again:

Asymptotically, all existing firms use the same, best, technology and the market wage corresponds to the marginal productivity of labor in the marginal technology, which is also the one everybody uses. Hence, exploitation of the workers has ceased. -- Michel Boldrin (2009)(p. 440)

John Roemer describes a source of profits in a model which could exhibit perfect free entry, constant returns to scale, and individual profit maximization:

"...the existence of postive-profit equilibria ... is to associated with the necessity of time in production, that capitalists must advance the costs of production before they receive the revenues from production. It is this temporal structure of production that gives rise to the economic necessity of a capital constraint, whether or not funds for production are limited to internal finance or are available on a capital market." -- John E. Roemer (1981). Analytical Foundations of Marxian Economic Theory, Cambridge University Press (p. 84)

As those familiar with Frank Hahn's critique of the "neo-Ricardians" know, this sort of model is consistent with every valid marginal productivity principle holding.

Man-Seop Park's criticizes new growth theory (from, for example, Paul Romer) on a number of grounds in a number of papers. One of these grounds is that such models ignore the presence of time in production, even when they depict a number of stages in production. I think Boldrin's paper may be weak on this ground.

Update: I thought a little more about this. Bouldrin considers the case in which the marginal plants in both the investment and consumer goods sector are both operated at less than capacity. In this case, the value of the marginal product of labor is positive (in the competitive case), and the marginal product of the capital good is zero.

I would rather consider the case in which both labor and the marginal plants are binding in both sectors. In this case, an additional unit of either labor or plant would contribute nothing to production. On the other hand, a marginal unit decrease in either labor or capital would decrease production by some specified amount. Thus, the value of the marginal product of both labor and the capital good (in the competitive case) would be an interval from zero to some positive amount. I think this case results in the familiar Sraffian wage-rate of profits curve in which wages can only be larger if the rate of profits would be smaller.

Robert Paul Wolff Blogging On Books On Sraffa And Marx

Here Wolff provides an overview of Marx, agrees with Morishima that Marx was a great economist, and mentions books by the analytical Marxists. Here he describes Sraffa's impact on interpretations of Marx and provides a list of books (which overlaps with my list of textbooks). Here he briefly overviews each of the books in his list, with the exception of Marglin's.

How Smaller Government Leads To Increased Inequality

David Ruccio hypothesizes that the current worldwide macroeconomic difficulties are related to increased inequality in the distribution of income in, say, the United States over the last few decades. I have been considering hypothetical mechanisms that expand on this idea. Previously I have put forth the Harrod-Domar growth model as a framework in which increased inequality leads to a tendency towards recessions. In this post, I focus on causation in the other direction. (A full analysis of the issues will likely describe a process of cumulative causation.)

Active macroeconomic fiscal policy is assisted if government spending is already a somewhat large component of a nation's economy. It is easier to raise government spending by some given fraction of national income if that change is a smaller percentage of current government spending. We have seen this issue in connection with the Obama administrations talk of "shovel-ready" projects and the stimulus policy. Perhaps this consideration even applies to automatic stabilizers.

So governments that are smaller with respect to their national economies might be expected to exhibit worse macroeconomic performance. And James Galbraith has shown quite some time ago that poor macroeconomic performance leads to increased greater inequality in wages.

Perhaps the above is part of the explanation for the empirical cross-section correlation between decreased government size and increased inequality. I think Hacker and Pierson give some explanation why increased inequality engenders political forces tending towards smaller government size.