Tuesday, October 31, 2006

A Physicist Versus Neoclassical Economics

Over at the Financial Times, Philip Ball, "consultant editor of Nature", describes neoclassical economics as "baroque fantasies of a peculiar science". He illustrates why "neoclassical idiocies" matter with the Russian transition economy, repeats a thesis developed at length by Philip Mirowski, and references Paul Ormerod. So I find this all very interesting.

I found out about this from a Mark Thoma post, and lots of commentators responded to that post there.

Update: Another Mark Thoma post references a supposed response from David Altig to Philip Ball. Philip Ball has his own blog, on which he responds to letters to the Financial Times. Mark Thoma has even more.

Monday, October 30, 2006

Libertarianism Versus "Libertarianism"

One might meet, in certain precincts of the Internet, soi-disant libertarians. As far as I am concerned, "libertarians" of this stripe are victims of commodity fetishim, and they have stolen the label. Traditionally, a libertarian is an anarchist, that is a kind of socialist. For example, Maureen Stapleton plays a libertarian in Warren Beatty's movie Reds. Anarchists, generally, do not have Ludwig Von Mises in their pantheon of heroes.
"...readers should take ... particular warning that I am absolutely not against freedom. On the contrary, I am for it. Libertarians ... think they are for freedom but they don't know what freedom is. In reality, their doctrine is so contrary to freedom that it ought to be entitled 'anti-libertarianism'. The thief comes in innocent disguise, but the beautiful garment is stolen. (The Right are good at that sort of thing.) So, if you want to make your copy of this book read more accurately, you should delete 'libertarian' and 'libertarianism' throughout, substituting 'anti-libertarian' and 'anti-libertarianism' as you go. For 'anti-libertarianism', etc., you should substitute 'anti-anti-libertarianism'. Unfortunately, this would make the book cumbersome to read, so I haven't followed the advice myself except in my choice of title, where my subject is named according to its true nature." -- Alan Haworth, Anti-Libertarianism: Markets, Philosophy, and Myth, Routledge, 1994: 5
Haworth does have more substantial points. Warning: this is political philosophy for those who think "If a lion could speak, we would not understand him" is a thesis worth discussing and who are comfortable with thought experiments which might lead one to be willing to say that a rock feels pain. Nevertheless Haworth is quite readable. (As an example of unreadable philosophy strongly following the later Wittgenstein, I cite John Wisdom's Other Minds.) I realize that those interested in political philosophy and "Libertarianism" should also read Robert Nozick.

Sunday, October 29, 2006

Hanged By ROPE

Steven Pressman, the editor of the Review of Political Economy, following the advice of the referees, has rejected my paper, "Creating Two-Good Reswitching Examples". My paper is mathematically correct, but the reviewers had good reasons for rejecting it. One reviewer thought I did not make a point that I should have:
"As students of Hicks (1965), Spaventa (1968), and Garegnani (1970) know, it is easy to generate examples of reswitching if the 'machine' is unique to the technique. This means that whenever a process is changed in one sector, it must be changed in the other sector as well. One is not therefore dealing with variable proportions of physically unchanged inputs as one considers different techniques. Anyone committed to the latter view as the 'meaning of technical choice' might therefore be suspicious of reswitching results. It is all the more important for the author of this paper to emphasize the fact that a mere variation in the proportions of physically unchanged inputs is sufficient to generate reswitching when there are three inputs: labor and two produced goods in each sector. This is the strength of the argument, but the point is never made. Emphasizing it would make the paper much more interesting. Otherwise, why would an instructor, interested in teaching reswitching, not just use the Hicks/Spaventa/Garegnani model?"

I guess I went overboard in refusing to point out how reswitching has been used to critique (versions of) neoclassical theory. The above reviewer also noted that it is not so easy to create a reswitching example that satisfies the constraints I point out. Two reviewers, by recasting the problem, showed me that section two can be made simpler. Two reviewers also show me how to greatly simplify sections four and five. The first, second, and sixth sections will need to be rewritten to take account of changes in the other sections, if I rewrite this paper. However, I still feel justified in recommending the first, second, and sixth sections as a tutorial introduction to reswitching.

Naturally, I would prefer to have written a paper suitable for publication. And the ROPE reviewers took slightly longer than is promised by the journal. Nevertheless, I would like to express my appreciation for the reviewers' solid engagement with my paper and their thorough examination. If I am to rewrite this paper and submit if for publication elsewhere, I will find their comments extremely helpful. I'm not going to get right to that. I am first attempting to write a paper by focusing some of my examination of the relationship between capital-theoretic "paradoxes" and General Equilibrium theory.

Tuesday, October 24, 2006

After The Exposure Of The Cult Of Personality

One book in random stuff I've read: On Communism: In Defense of the New Course, by Imre Nagy (English Translation: Frederick A. Praeger, 1957). I do not claim any expertise on their lives and times. But I find intriguing communist reformers, like Nagy and Alexander Dubcek, who tried to make no-longer-actually existing socialism into a worthwhile system. I guess they sincerely wanted to live in a society in which the free development of each is the condition for the free development of all.

I think one can see in Nagy's book that his context is after Nikita Khrushchev's 20th Party Congress speech. Nagy frequently complains about some of his Hungarian comrades, who claimed to have signed onto reforms, but, according to Nagy, worked to undermine them. I also thought interesting Nagy's complaints that Hungarians had not seen increases in their standard of living, despite the economic growth over the period before his writing. Apparently, the growth had been unduly concentrated in heavy industry. Maybe Nagy would have had an opinion on my game.

I realize Nagy's book is a primary document, and he probably felt constrained in what he could argue. Apparently, he felt he had more freedom to maneuver than turned out to be the case.

Monday, October 23, 2006

Terence, This Is Stupid Stuff

Do mainstream economists respond to critics of their theory with instrumentalism, whether such a response engages the criticism or not? Consider an Amazon.com review of Philip Mirowski's More Heat Than Light: Economics as Social Physics, Physics as Nature's Economics:
Ideal versus real is the heart of this book

First off, the problem with this book is that people jump to conclusions too quickly. If I say that discrete math is not the same as continuous math, yet I go on to point out that the Z-Transform is analogous to the LaPlace Transform, there is an inherent ambiguity, a diaelectric, that seems contradictory but makes sense: all models are just that, models to reality. And reality cannot be modeled exactly (even the Theory of Relativity has flwas, which physicists are exploring today). In medice for example, Grey's Anatomy, a medical textbook, has been criticized for showing a 'perfect' anatomy that does not in fact exist in nature. Analogously, the old argument about which classical statute was 'better': classical Greek or Roman? Ideal or 'real'? (and if 'real', whose 'real'; the recent statute in Trafalger square showing a paraplegic pregnant woman comes to mind)?

The point being that classical economics is not perfect, nor is it flawed - it just is. Come up with a better model, and the economic world will beat a path to your doorstep.

BTW, I've not read this book. Please recommend this review if it's been helpful.

Saturday, October 21, 2006

Around And About

Tuesday, October 17, 2006

Should I Read Petri and Hahn?

Over on Crooked Timber, Michael Greinecker asserts without argument:
Sraffians are actually debating about non-problems. The standard GE model is a strict generalisation of the classic one. They simply don't get it, as they have proven at a conference on this very issue. The people who are really into aggregation problems are theorists like Kirman and Hildenbrand.
I find Petri (2004) cogent and well-argued. But given the references in the introduction to my draft paper, "A Model for Exploring Manifestations of Capital-Theoretic 'Paradoxes' in Temporary Equilibria", would I learn anything new by reading the proceedings in the volume edited by Petri and Hahn? This paper also shows why I don't find it convincing to say dynamic equilibria (which I take to be the same as temporary equilibria) are immune from Sraffian criticisms.

Reviews of Keen's Debunking Economics

I read some reviews as negative and some as positive. The negative reviews include both those who think neoclassical economics is basically inconsistent and incoherent (but think Keen fails to point out the errors well enough) and those who think otherwise. By the way, I argued with Keen about his presentation of the SMD theory before publication, even though I had never heard the label "Gorman form" then.
  • Balak, Benjamin (2005). Eastern Economic Journal: 148-150
  • Belenkiy, Ari (2005). Journal of Economic Behavior & Organization, V. 56: 129-139
  • Laibman, David (2003). Review of Radical Political Economics (Summer): 351-353
  • Misina, Miroslav (2005). Economic Journal (November): F419-F422
  • Murphy, Robert P. and Gene Callaham (2003). Review of Austrian Economics, V. 16, N. 4: 381-384
  • Myatt, Anthony(2004). Journal of Economic Education (Winter): 100-103
  • Nesiba, Reynold F. (2006). Review of Radical Political Economics (Winter): 154-157
  • Oleson, Ted (2003). Journal of Economic Issues: 228-231
  • Quiggin, John (2002). (?): 233-235
  • Whalen, Charles J. (2004). (?): 255-257

Sunday, October 15, 2006

Accumulate, accumulate! That is Moses and the prophets!

The data in Tables 1 and 2 are from Kenickell (2003), as quoted in Cagetti and De Nardi (2005). Table 2 is in 2001 Dollars. Raw data are from the Survey of Consumer Finances (SCF), I guess. Unlike the Panel Study of Income Dynamics (PSID), the SCF does not allow researchers to follow households over time, but is better in tracking the richest households. Cagetti and De Nardi survey a variety of publications by researchers examining trends in wealth ownership.

Table 1: Distribution of Wealth By Year

Table 2: Absolute Distribution of Wealth By Year
< $07.3%7.2%7.1%8.0%6.9%
> $1,000,0004.

The data show ownership of wealth is extremely concentrated in the United States. The top one percent own approximately a third, while the top five percent own more than half of total United States wealth.

Cagetti and De Nardi examine three types of models commonly used in mainstream economics:
  • Models with agents with an infinite lifespan
  • Overlapping generations models
  • Models that combine features from both the above types of models
Agents in the model are heterogeneous because different agents receive different shocks to, say, wages. Cagetti and De Nardi show that none of these model types is able to generate inequality as extreme as is seen in the data. (Cagetti and De Nardi do not put their conclusion so stark.)

Cagetti and De Nardi suggest extensions to these mainstream models to solve this empirical puzzle. But I do not know why one would not consider other types of models. I can think of other places to look.

I don't fully understand the literature Cagetti and De Nardi survey, but I read them as confining themselves to models with analytical solutions. I think agent-based simulations are an interesting approach. One uses simulation, when analytical solutions are not available, to understand long term dynamics in such models. These models are incompatible with methodological individualism inasmuch as model parameters include macroeconomic distributions over, say, tastes. Offhand, I have only one reference (Wright 2004) for such models, but I understand diverse researchers, for example, Alan Kirman have been exploring such models.

I consider the Kahn-Kaldor-Pasinetti-Robinson theory of income distribution to be a classic Post Keynesian approach. This theory has received increasing criticism within the Post Keynesian community. Nevertheless, one might consider trying to explore how analytical updates to this model fit the empirical data. Moore (1975) is a somewhat old exploration of the Kaldor-variant of this theory. Surely more could be done here.

One might also consider models with complex dynamics. Goodwin (1967 and 1990) provides some interesting models in this vein. Perhaps some work by Dumenil and Levy might be interesting here, too.

I'm not sure how to delimit the range of the outcomes of these models. I guess one would like to limit the parameters to empirically reasonable ranges. This, like Cagetti and De Nardi's, is not necessarily a simple research program.

By the way, some of these references can be downloaded from somewhere or other.

  • Cagetti, Marco and Mariacristina De Nardi (2005). "Wealth Inequality: Data and Models", Working Paper 2005-10, Federal Reserce Bank of Chicago
  • Goodwin, Richard M. (1967). "A Growth Cycle", in Socialism, Capitalism & Economic Growth: Essays Presented to Maurice Dobb (edited by C. H. Feinstein), Cambridge: Cambridge University Press
  • Goodwin, Richard M. (1990). Chaotic Economic Dynamics, Oxford: Clarendon Press
  • Kennickell, Arthur B. (2003) "A Rolling Tide: Changes in the Distribution of Wealth in the U.S., 1989-2001", Mimeo (Sep.)
  • Moore, Basil J. (1975). "Equities, Capital Gains, and the Role of Finance in Accumulation", American Economic Review, V. 657, N. 5 (Dec.): 872-886
  • Wright, Ian (2004). "The Social Architecture of Capitalism", arXiv:cond-mat/0401053v1 (Jan.)

Saturday, October 14, 2006

Romer (1990) Mistaken From First Numbered Equation On

The equilibrium interest rate is unequal to the marginal product of capital. As I have explained, this inequality results from non-zero price Wicksell effects. Typically, in the theoretically unfounded Solovian growth model, the output functions as the consumption good, and a unit of this good is taken as the numeraire. An implication of price Wicksell effects is physical capital goods cannot be measured in units of consumption goods, at least when they serve as arguments to a production function. That is, the amount of output depends on the number of shovels of a given quality, or whatever, that enter into production as inputs. The price of a shovel varies with interest rate. Such price variations do not change the physical relationship between inputs and outputs.

Paul Romer claims his 1990 model contains disaggregated capital:
"The unusual feature of the production technology assumed here is that it disaggregates capital into an infinite number of distinct types of producer durables." -- Romer (1990):S80
But he is mistaken. He gives the production function for final output as follows:
The first argument of the production function is the amount of human capital, strangely enough measured on a cardinal scale, employed in the manufacturing sector (as opposed to the research sector). The second argument is the amount of physical labor hired in the manufacturing sector. The remaining arguments are the quantities of the capital goods, each measured in numeraire units. That is, capital is measured in units of "foregone consumption". Apparently, Romer recognizes issues exist here:
"It is possible to exchange a constant number of consumption goods for each unit of capital goods if the production function used to manufacture capital goods has exactly the same functional form as the production function used to manufacture consumption goods." -- Romer (1990): S81
I saw that Romer (1990) was sensitive to a Cambridge capital critique, despite his erroneous claim to be representing capital as composed of diverse commodities, when I first read his paper several years ago. Kurz (2006) recently makes the same point, and apparently I want to see if Park (2006) has come out yet. Steedman (2003) criticizes the lackadaisical approach to measurement scale issues in new growth theory. So one's work can be lauded in mainstream economics, yet still contain technical flaws that were exposed long before and that invalidate one's results.
  • Kurz, Heinz D. (2006). "Whither History of Economic Thought? Going Nowhere Rather Slowly?
  • Park, M. (2006). "Homogenity Masquerading As Variety: The Case of Horizontal Innovation Models", Cambridge Journal of Economics (forthcoming)
  • Romer, Paul M. (1990). "Endogenous Technological Change", The Journal of Political Economy, V. 98, N. 5 (Oct.): S71-S102.
  • Steedman, Ian (2003). "On 'Measuring' Knowledge in New (Endogenous) Growth Theory", in Old and New Growth Theories: An Assessment (ed. by Neri Salvadori), Edward Elgar

Tuesday, October 10, 2006

On the Preface to Adam's Fallacy

I have just began reading Duncan K. Foley's Adam's Fallacy. I have long been taken by the contrast between popular views on Adam Smith, including those put forth by some economists, and what is said in the bits of Smith and historians of economic thought that I have read. Apparently Duncan Foley is modest about his knowledge of the literature of the history of economic thought, while aware of the popular impression:
"This is not, however, a book on the history of of economic thought proper. It uses a historical perspective as a happy way to organize a complex set of ideas into a coherent and understandable story. It reflects much reading and teaching of particular texts in the history of economic thought, but I am far from an expert or a deep scholar of this extensive and demanding subject. In places I have ventured beyond the texts of the authors in question and pursued my own imaginative reconstructions of debates behind the debates, and the sometimes unconscious ground from which political economic knowledge arose. This is my own take on economics, and exploits the great figures in the history of political economy shamelessly for my own ends. Be warned.

...what do I mean by 'Adam's Fallacy'? Adam Smith says many things in The Wealth of Nations that are not fallacious. For example, it is undoubtedly true that self-interest is a powerful motivating force for human beings (though far from being the only one). It is also true that harnessing the pursuit of self-interest through competitive capitalist markets can be (though it is not invariably) a powerful mechanism for fostering progressive technical change and producing material wealth. It would be far from correct to claim that all pursuit of self-interest through competitive markets is morally bad. By 'Adam's Fallacy' I mean something a little more subtle than those much-debated claims. For me the fallacy lies in the idea that it is possible to separate an economic sphere of life, in which the pursuit of self-interest is guided by objective lawas to a socially beneficent outcome, from the rest of social life, in which the pursuit of self-interest is morally problematic and has to be weighed against other ends. This separation of an economic sphere, with its presumed specific principles of organization, from the much messier, less determinate, and morally more problematic issues of politics, social conflict, and values, is the foundation of political economy and economics as an intellectual discipline. Thus to my mind Adam's Fallacy is the kernel of political economy and economics. A full understanding of the arguments of the great economists requires seeing them in the context of this dubious division. In fact, as I hope this book will demonstrate, political economy and economics is at its heart an attempt to come to terms with this dualistic view of social life.

...is it true that Adam Smith committed this fallacy? A better qualified scholar of Adam Smith could make this case textually on the basis of The Wealth of Nations more persuasively than I can, starting from Smith's discussion of self-love as a powerful motivator of human action (Book I, chapter 2), continuing with his characterization of frugal wealth-owners as public benefactors (Book II, chapter 3), and culminating in his famous invocation of the 'invisible hand' (Book IV, chapter 2). But I would argue that it is more to the point that everyone who reads The Wealth of Nations comes away believing that Smith presents the world through the lens of what I have called his fallacy. Smith is too clever and too wily to present the fallacy in its barest form; his political economic world of self-regulating competitive self-interest actually depends crucially on innumerable value-laden political contingencies and institutions. Smith's qualifications of the principle of laissez-faire, for example, wind up presenting a reasonably balanced view of the interaction of politics and the economy. But the premise of Smith's book is that it makes sense to start with the examination of purely economic principles that arise from the interaction of self-interested individuals in the context of competitive markets for privately owned commodities. As I try to show in this book, his successors' investigations and discoveries are already inherent in Smith's conception of the political economic problem." -- Foley (2006: xii-xiv)
By the way, I read Albert Hirschman's The Passion and the Interests (Princton University Press, 1977) as arguing that Adam Smith brought about a simplification in how humans in society were viewed. I think Hirschman's argument is complementary to Foley's, but I need to read more of Foley's book to be convincing.

One can only be disappointed in Brad DeLong's misrepresentation of Foley's thesis. (See also.)

Monday, October 09, 2006

Edmund Phelps Wins "Nobel" Prize

Edmund Phelps wins the 2006 "Nobel" prize in economics.

A Philips curve augmented with inflation expectations is a theory of stagflation. I don't claim any prescience in having blogged on this topic just the other day.

Milton Friedman's theory of the natural rate of employment is closely related to Phelp's theory. Friedman's theory has never made much sense to me. I don't know what it means to talk about the rate of employment ground out by the Walrasian model of general equilibrium, when theory provides no reason to think such a rate will be unique. Furthermore, economists have found the Walrasian model to be logically inconsistent, while the very short run Arrow-Debreu model does not grind out rates of unemployment. Instead, it grinds out time paths of employment rates. I think the theory indicates such paths will not be empirically observed, anyways. Finally, due to hysteresis, the natural rate has turned out to be an empirical failure in giving policy guidance. (See Galbraith 1998 for more on at least some of these points.)

I'm getting used to the "Nobel" being awarded to authors who have at least some works I have read long ago. In this case, I can mention Phelps (1961), for example, which is closely related to Robinson (1962).

I sometimes run into some mainstream economists who whine about my attitude. Given this, I don't know what they are talking about.
  • Galbraith, James K. (1998). Created Unequal: The Crisis in American Pay, Free Press
  • Phelps, Edmund (1961). "The Golden Rule of Accumulation: A Fable for Growthmen", American Economic Review, V. 51, N. 4 (Sep): 638-643
  • Robinson, Joan (1962). "A Neo-Neoclassical Theorem" (in Essays in the Theory of Economic Growth), Macmillan

I'd Like To Hear Second Thoughts On The CCC From Joseph Stiglitz

Stiglitz's first thoughts can be seen in his 1974 review of Harcourt's 1972 survey book. About that time, Stiglitz also reviewed Pasinetti's presentation of the Kahn-Kaldor-Pasinetti-Robinson theory of growth and distribution. Neither Harcourt nor Pasinetti were happy with Stiglitz's respective review. Morishima (1977) is an outgrowth the JEP's editor becoming aware of Pasinetti's unhappiness.

I don't want to hear second thoughts from Stiglitz so much on the technical content below. I rather hear second thoughts on a point from the sociology of "knowledge". What determines how some views become worth considering in mainstream economics, while others are written out? I think Stiglitz might have something interesting to say on that based on his recent experiences, and I wonder if that could inform how he might look back at the Cambridge Capital Controversy.

Stiglitz writes:
"It is also true that with profit-maximizing competitive firms, in long-run equilibrium where all relative prices are constant, the rate of interest is equal to the own rate of return of every capital good (the marginal productivity of every capital good in terms of itself..." -- J. E. Stiglitz (1974)
I find Stiglitz less than forthright in failing to address the conception of capital as finance. Is Stiglitz clear that, in neoclassical theory, no theorem asserts the equality in equilibrium of the interest rate and the marginal product of (finance) capital? I think Stiglitz's formulation about own rates, as if that was a point in dispute, is likely to mislead readers.
"...At any moment, there is a given vector of capital goods and of labor. Under the extremely simplified models conventionally used, these endowments determine the marginal productivity of the different capital goods and the rate of interest. Given the savings behavior, this determines the change in the stocks of capital goods; eventually the economy converges to a state where the rate of interest is equal to the rate of growth divided by the savings propensity; still, at each moment, it is the 'capital goods-labor ratios' which determine the rates of return on the different capital goods." -- J. E. Stiglitz (1974)
(Notice Stiglitz does not say marginal productivities determine factor prices.) I think this emphasis on very short run equilibrium paths has not held up well; I see no reason to think a capitalist economy will follow such a path. Anyways, a consensus still does not exist on whether this approach is resistant to Cambridge capital critiques.

"All that [reswitching] implies is that the weak qualitative assumptions we conventionally make in economics - that is, convexity of the technology, with its implications of diminishing returns - do not have any strong implications for comparisons of economies in steady state: that is, reswitching establishes that the derivation of simple comparative dynamics propositions requires stronger assumptions than those required for the existence of competitive equilibrium and the derivation of qualitative properties concerning economies with given initial endowments...

...Moreover, it is easy to develop, using steady-state analysis, all manner of paradoxes. For instance, the opening of free trade may actually lower steady-state consumption (this does not contradict the classical propositions concerning gains to trade). One can show that of all the feasible steady states in a life-cycle model, the one which maximizes steady-state utility is not sustainable by a competitive equilibrium (without appropriate lump-sum transfers), and conversely. (This does not contradict classical welfare propositions.)" -- J. E. Stiglitz (1974)
(I think the classical theory of free trade is more about the comparison of steady states than very short run paths with given initial endowments of capital goods.) I don't think this comment has aged well, either. Economists have not been able to state general assumptions that rule out capital-reversing - which is not the same as reswitching. Furthermore, if reswitching is so non-threatening, why hasn't it entered the mainstream introductory textbooks? Why are economics students at all levels not taught to be clear on the structures of their models and their implications? Surely, one should not still be able to surprise economists with paradoxes whose possibility was established decades ago?

  • Harcourt, G. C. (1972). Some Cambridge Controversies in the Theory of Capital, Cambridge University Press
  • Pasinetti, Luigi L. (1974). Growth and Income Distribution: Essays in Economic Theory, Cambridge University Press
  • Stiglitz, Joseph E. (1974). "The Cambridge-Cambridge Controversy in the Theory of Capital: A View from New Haven: A Review Article", Journal of Political Economy, (Cowles Foundation Paper 410), V. 4
  • Stiglitz, Joseph E. (1975). "Growth and Income Distribution: Essays in Economic Theory", Journal of Economic Perspectives, V. 13, N. 4 (Dec.): 1327-1328
  • Morishima, Michio (1977). "Pasinetti's Growth and Income Distribution Revisited", Journal of Economic Perspectives, V. 15, N 1 (Mar.): 56-61

Friday, October 06, 2006

An Explanation Of Stagflation

"A Bastard Golden Age
We must now consider another type of limit upon the rate of accumulation. Inflationary pressure, bringing financial checks into operation, may arise when there is no scarcity of labour - indeed a great mass of non-employment - if the real-wage rate refuses to be depressed below a particular level. A higher rate of accumulation means a lower real-wage rate. When the desired rate of accumulation is greater than the rate which is associated with the minimum acceptable real wage, the desire must be checked. A situation in which the rate of accumulation is being held in check by the threat of rising money wages due to a rise in prices (as opposed to rising money wages due to a scarcity of labour) may be described as a bastard golden age.

The rate of accumulation may be less or greater than the rate of growth of population, so that non-employment is increasing or diminishing. (In the latter case the system is heading towards a legitimate golden age.)

A bastard golden age sets in at a fairly high level of real wages when organized labour has the power to oppose any fall in the real-wage rate. Any attempt to increase the rate of accumulation, unless it is accompanied by a sufficient reduction in consumption out of profits, is then frustrated by an inflationary rise in money-wage rates. In such a situation, the rate of accumulation is limited by the 'inlation barrier'.

A low-level bastard golden age is seen when the real-wage rate is at the minimum level tolerable. (A low-level bastard golden age might have the same standard of life as obtains in a leaden age, but the mechanism of the system is different. In a leaden age the slow rate of accumulation keeps the standard of life to a minimum; in the bastard golden age the minimum standard of life sets a limit to the rate of accumulation.)" -- Joan Robinson (1962). "A Model of Accumulation" (In Essays in The Theory of Economic Growth, Macmillan)
I did not reproduce a footnote in which Robinson references Richard Kahn's "Exercises in the Analysis of Growth" (Oxford Economic Papers, June 1959). Kahn puts forth a similar theory.

I might have read somewhere that if somebody offers a theory that explains a phenomenon before it is observed, scientists will tend to take that theory up for closer examination. But that would have not been written about economics.

Wednesday, October 04, 2006

Interest Rate Unequal To Marginal Product Of Capital (Part 4 Of 4)

4.0 Conclusions
This series of posts has presented a simple explanation of the nonequality of the interest rate and the marginal product of capital, as that equality is understood in macroeconomic models. Thus, neoclassical microeconomics does not imply that equality. Various attempts to defend the macroeconomic models considered here have been examined and have been found wanting. An interesting aspect of this criticism is that it does not seem to be about index number problems. Nor has this argument depended on the phenomena of reswitching at all, and it depended on capital reversing only in criticizing Champernowne's chain index [15]. If the demonstration of the theoretical possibility of these phenomena are taken as central to the Cambridge Capital Controversy, then the implications of that controversy should extend beyond aggregate neoclassical theory [16]. As far as I can see, this argument is fairly well understood on the Cambridge, England side.

It is curious that economists continue to use aggregate production functions despite the clear warnings of this traditional argument. Many of those economists who follow Solow or Lucas do not seem concerned about their inadequate concept of capital. Although these researchers may be interested in technical improvements in their models, capital-theoretic problems do not seem high on their agenda. Furthermore, much of graduate education in economics seems to leave newly emerging economists unaware of capital-theoretic problems with their models. These young economists do not seem to possess the analytical tools that were forged in the CCC, such as the correct analysis of the choice of technique, a correct analysis of the relationship between the theory of rent and income distribution, or even how to analyze depreciation and the economic life of machines in a framework of joint production.

What explains this apparent continuation of the miseducation of economists that Joan Robinson decried over fifty years ago [17]? My hypothesis is partly ideological. Any advanced treatment of capital theory and the appropriate analytical tools [18] would expose the student to the Cambridge Capital Controversy. The student would then learn about some serious questioning of the internal consistency of many claims of neoclassical economists. There are obviously normative overtones to this controversy, for example, over the exploitative nature of profits and the capitalist system as a whole. Neoclassical economics might be claimed to currently fill the social role of "hired prize fighters" for capital, what Marx characterized as "vulgar economics" [19]. This social role is threatened by the CCC.

"The construction of the production function does not even require this refutation via the phenonomenon of returning techniques ('reswitching'), because a production function for which the marginal product equals the factor price already becomes impossible if the wage curves of single techniques are not straight lines (except for a few unimportant cases; see Garegnani, 1970, Hunt and Schwartz, 1972). Contrary to the usual interpretations today, the debate about the possibility of returning techniques is important not only because it proves that the production function with its marginal products is nonsensical, but because, on a more general level, it can be shown that a demand function for capital...cannot be defined." -- Bertram Schefold (1989). Mr. Sraffa on Joint Production and Other Essays, Unwin Hyman: 292.
[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 diffent. 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.

[17] This miseducation is asserted on slightly different grounds in the following quote:
"Observe that even in neoclassical theory full employment alone is not enough to transform marginal-productivity relationships into a long-run theory of distribution. In long-run neoclassical theory, the capital:labor ratio is endogeneously determined, so that the wage rate cannot be determined solely by marginal productivity of labor at full employment - not even in Chicago. Instead, distribution must reflect household preferences with respect to present and future consumption.

Thus, it is fair to conclude that there are two marginal-productivity theories. The first is a relatively innocuous, general theory that involves nothing more controversial than competitive profit maximization - and provides correspondingly little contribution to the theory of growth and distribution under capitalism. The second is more powerful, and very special, providing by itself a theory of distribution, for the short run at least, whose 'only' defects are (1) that it assumes full employment and (2) that it begs the question of accumulation. The wonder is that it is precisely this theory that so many students come away with from their study of economics. Only slightly more wondrous is that by and large they believe it!" -- Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press: 330-331.
Neither version of marginal productivity theory need include the equality of the marginal product of capital and the interest rate in an aggregate production function framework.

[18] Syed Ahmad (1991). Capital in Economic Theory: Neo-classical, Cambridge, and Chaos, Edward-Elgar.

"In summary I believe that Marx's sociology of economic knowledge was quite an impressive achievement, in spite of being flawed by its reliance on functional explanations and the labor theory of value... The recent 'capital controversy' shows that these are not dead issues. Surely some cognitive confusion lay at the origin of the idea that 'capital' can be treated as a homogeneous 'factor of production,' for instance an inference from the fact that capitalists form a fairly homogeneous class. And conceivably the tenacity with which the neoclassical economists stuck to the notion of aggregate capital has something to do with non-cognitive interests. This, admittedly, is sheer speculation, and I may be quite wrong. Vested intellectual interests may suffice to explain the resistance. Be this as it may, the sociology of economic conceptions and economic theory is a field worth cultivating, if proper attention is paid to the many methodological pitfalls in this domain." -- Jon Elster (1985). Making Sense of Marx, Cambridge University Press: 504.

Tuesday, October 03, 2006

Interest Rate Unequal To Marginal Product Of Capital (Part 3 Of 4)

3.0 A Simple Two-Good Counterexample

The question investigated here is whether Equation 9 is an implication of neoclassical microeconomics. I claim Equation 9 is not an implication of neoclassical microeconomics.

It is sufficient to demonstrate this negative conclusion by describing an example compatible with neoclassical microeconomics, but in which Equation 9 does not hold. The existence of such a counterexample demonstrates the use in macroeconomics of models in which the marginal product of capital and the interest rate are equal cannot claim full generality. It is up to the users of such models to state their assumptions and justify their use of these special cases.

How is the counter-example constructed? Assume we observe that in our economy only two goods are produced, steel and wheat, each measured in their own physical units, tons and bushels, respectively. We also observe the physical quantity flows in each industry, which I am going to write in a somewhat cryptic manner. Define d(0) as in Equation 12:
Suppose the physical quantity flows, on a per worker basis, are as Table 1. All quantities in the table are positive and:
Notice that the sum of person-years across industries is unity, as promised. Also notice that the sum of the inputs of steel is equal to the steel produced by the steel industry. As a further clarification, we observe that these inputs are purchased at the beginning of the year, and the outputs become available at the end of the year. Furthermore, the steel input is totally used up in these production processes. The output of the steel industry just replaces the steel used up in the economy. The net output consists solely of wheat, which we observe to be a consumption good.

Table 1: Quantity Flows Per Worker
(Tons Steel)

Assume constant returns to scale. This means we can express the observed quantity flows as in Table 2. This explains the puzzling notation in Table 1. The parameters reflect unit (gross) outputs in both industries.

Table 2: Quantity Flows Per Unit Output
Labor Person-Years Person-Years
Steel Tons Steel Tons Steel
OUTPUTS1 Ton Steel1 Bushel Wheat

Notice nothing has been assumed about the available technology other than constant returns to scale and that these proportions are possible. Based on our observations of the quantity flows actually used in this little model economy, we can draw no conclusions about what outputs will be produced when the inputs of either industry are in different proportions. It might even be the case that wheat can be used as a capital good for some other technology, or that copper or some other capital good might be used at a different set of prices.

We have observed that tons steel per worker are used in the economy, but this is not the value of capital per worker, k, used in Equation 5. The units are different. If aggregate output per head, y, is measured in units of bushels wheat per capita, capital per head, k, must also be measured in bushels wheat per capita in the aggregate production function framework. We have to figure out how many bushels of wheat this quantity of steel represents. But that's what prices are for.

Suppose we observe that prices are unchanged over the year in which we are making our observations, and that the wage w is paid at the end of the year. Suppose that we also observe that competition has brought about the same rate of interest in both industries. Let wheat be numeraire. Then the following price equations obtain:
I have not specified enough equations to fully define the price system. Thus, we can solve for two of the price variables in terms of the third, say the rate of interest. Define d(r) as in Equation 16:
The price of a ton of steel as a function of the interest rate is then given by Equation 17:
Hence, the quantity of steel, when measured in bushels wheat, is:
This value quantity of steel varies with the interest rate.

The wage can also be found as a function of the rate of interest:
Equation 19 expresses the factor price curve [6] associated with the observed technique. A different technique, with its own factor price curve, may be preferred at a different rate of interest. All these curves can be graphed on the same diagram with the wage as the ordinate and the interest rate as the abscissa. The cost-minimizing technique(s) at any interest rate will correspond to the technique(s) with the highest wage at that interest rate [7]. The factor price frontier is thus formed from the outer-envelope curve of the factor price curves corresponding to each individual technique. Points on this frontier that lie on two or more curves for individual techniques are known as switch points. The optimal cost-minimizing technique is unique at interest rates for non-switching points.

Assume the observed technique is a non-switching point. In the case of a discrete technology, the factor price curve for the selected technique is tangent to the factor price frontier at this rate of interest. The desired derivative, dw/dr, in Equation 9 is the slope of the factor price frontier at the observed rate of interest. From this tangency relationship one can see that the slope can be found by differentiating Equation 19, the factor price curve for the observed technique (Figure 2).
Figure 2: Factor-Price Curve For Cost-Minimizing Technique
At Non-Switching Point
It seems useful to provide an aside on a correct understanding of marginal productivity relationships before proceeding with this differentiation. The analysis of the choice of technique in long run equilibrium through the construction of the factor price frontier is completely general in circulating capital models. It applies to a Leontief technique, a choice among several Leontief techniques, or continuously differentiable micro-economic production functions in which all inputs are specified in physical units (e.g. tons, bushels, person-years). In the last case, all points along the frontier are non-switching points, although the chosen technique varies continuously with the interest rate [8]. Price Wicksell effects, as explained in this essay, result in the difficulty in defining a unit of "capital" in any case. Marginal productivity is another method of analyzing the choice of technique in the continuously differentiable case. When correctly applied, marginal productivity does not determine the distribution of income, and no equation analogous to Equation 7 arises [9]. If my example is supplemented by the needed assumptions, one can show that the price of a ton of steel is equal to the value of the marginal product of (ton) steel in both sectors. Since time discounting is used in this relationship, the interest rate appears in the mathematical statement of these equalities. But these equalities clearly differ from Equation 7, for capital is measured in the same units as output in Equation 7. The two good model has other properties that differ from the simple one good model.

Now we can return to our problem of examining Equation 9 for this simple two-good model. From Equation 19, the slope of the factor price frontier is given by Equation 20:
We can now compare the value of capital with the additive inverse of the tangent to the factor price frontier. The right hand sides of Equations 18 and 20 do not look like additive inverses of one another. As a matter of fact, assuming a positive interest rate, the interest rate is equal to the marginal product of capital at any given interest rate if Equation 21 holds:
So if neoclassical theory is compatible with a steady state in which Equation 21 does not hold, macroeconomic models in which the interest rate is equated to the marginal product of capital are not the general case.

Equation 21 is quite interesting. It implies that equilibrium prices are proportional to labor values, as defined in classical economics. As a matter of history, the reliance of the labor theory of value on this sort of extremely special case was thought to be a major weakness. If neoclassicals find this condition too extreme for the labor theory of value, they can hardly find it general enough as a defense of neoclassical macroeconomics [10].

Perhaps the solution lies in adopting another method of evaluating the physical quantity of capital in the same units as net output. Champernowne has proposed a chain index measure of capital that will restore the macroeconomic equality [11]. However, this measure only works under special cases, too. Burmeister has shown that the macroeconomic equality can be established with this chain-index if and only if real Wicksell effects are always negative. However, as was shown by the Cambridge Capital Controversy, this assumption of "negative real Wicksell effects" is not a general case either. In fact, nobody has determined what are necessary assumptions on technology to ensure the desired conclusion will follow [12]. Finally, if this index is used to express an aggregate production function in per capita terms, the wage is no longer equal to the marginal product of labor as that marginal product is typically expressed in such functions [13].

But, some may object, aggregate production functions work empirically. So even though economists cannot state their assumptions, they may say, this empirical success justifies the continual use of aggregate production functions. This is an extremely weak defense. Income distribution has been stable over much of the period in which macroeconomists have been using aggregate production functions. Franklin Fisher has shown through simulation that the supposed empirical success of aggregate production functions can arise under these conditions even in cases where the needed assumptions do not hold. Thus, this supposed empirical success of aggregate production functions fails to test the models with the unstated assumptions of aggregate neoclassical theory or to test among alternative theories. In fact, economists who rely on this defense seem to be confusing their empirical results with another accounting relationship [14].


[6] See:
  • Heinz D. Kurz, "Factor Price Frontier," The New Palgrave.
[7] Textbook treatments of the connection between cost minimization and the factor price frontier can be found in (Woods 1990) or
  • Heinz D. Kurz and Neri Salvadori (1995). Theory of Production: A Long Period Analysis, Cambridge University Press.
[8] These properties of the factor price frontier in the "continuous substitution" case were brought out by Luigi Pasinetti in correcting a technical mistake by Robert Solow. See:
  • Luigi Pasinetti (1969). "Switches of Technique and the 'Rate of Return' in Capital Theory," Economic Journal: 508-513.
It seems worth pointing out, since many may be confused on this point, that reswitching and capital reversing are possible when the optimal technique varies continuously with the interest rate. See:
  • P. Garegnani (1970). "Heterogeneous capital, the Production Function and the Theory of Distribution," Review of Economic Studies, v 37, (June): 407-36.
[9] See:
  • Frank Hahn (1982). "The neo-Ricardians," Cambridge Journal of Economics, V. 6: 353-374.
[10] Hence, Paul Samuelson's defense of aggregate production functions is inadequate. This defense can be found in:
  • Paul A. Samuelson (1962). "Parable and Realism in Capital Theory: The Surrogate Production Function," Review of Economic Studies: 193-206.
[11] D. G. Champernowne (1953-1954), "The Production Function and the Theory of Capital: A Comment," Review of Economic Studies, V. 21: 112-35.

[12] See the reference in footnote 4.

[13] Salvatore Baldone (1984), "From Surrogate to Pseudo Production Functions," Cambridge Journal of Economics, V. 8: 271-288. Baldone also shows Burmeister's claims are problematic when used to compare quasi-stationary economies with a positive rate of growth, instead of just stationary economies.

[14] Anwar Shaikh (1990). "Humbug Production Function," The New Palgrave: Capital Theory, Macmillan.

Monday, October 02, 2006

Interest Rate Unequal To Marginal Product Of Capital (Part 2 Of 4)

2.0 Some Relationships Among Aggregate Variables
Consider a very simple capitalist economy in which the value of all net output is distributed as wages or (accounting) profits:
where Y is net output, W is total wages, and P is total profits. The term "profits" is used in some economic traditions to mean what some neoclassical economists call "interest". If this causes confusions, read "profit" as "interest" throughout this essay, except where "economic profit" is used.

If there is some homogeneous unit in which to measure the labor force (person-years), the wage w is related to total wages as in Equation 2:
where L is the number of person-years employed. Similarly, if the capital K used up in a year can be valued in the same units as output, total profits relate to the interest rate r as in Equation 3:
Equations 1, 2, and 3 are accounting identities, true by definition. No assumptions have been made yet about how any of these variables are determined.

Continuing with the manipulation of accounting identities, one can transform Equation 1 to Equation 4:
where y is net output per head and k is the value of capital per head. Note that the value of output per head, the wage, and the value of capital per head are all measured in the same units, say bushels of wheat. The interest rate is a percentage rate with no units attached (other than, perhaps, an implicit time dimension).

Some neoclassical economists relate net output to inputs of labor and capital by means of an aggregate production function, which, when written in per capita form looks like Equation 6:
The function f is supposed to satisfy certain assumptions that characterize Constant Returns to Scale and diminishing marginal returns to each factor. Given these assumptions and perfect competition, cost minimization (or the maximization of economic profit) is supposed to ensure the equilibrium conditions given by Equations 7 and 8:
Equation 7 shows the interest rate is equal to the marginal product of capital, while Equation 8 shows an equality between the wage and the marginal product of labor [3]. I intend to challenge Equation 7 in a framework that includes Equations 5, 6, 7, and 8.

The argument for the aggregate production function, when written in per capita form, is the value of capital per head. How can the value of capital per head vary? Consider a multi-commodity model in a steady state. Suppose the same technique is adopted at different interest rates. The corresponding price structure will vary with the interest rate. Even though the same capital goods may be used at different interest rates, the value of capital per head will differ with the interest rate. This variation in the value of a given set of capital goods with the interest rate is known as a price Wicksell effect.

Typically, though, the cost-minimizing technique will also vary with the interest rate. Consider the prices ruling at a given interest rate, where that interest rate is a switch point. That is, at least two techniques are cost minimizing at the given interest rate. We can then consider variations in capital goods resulting from a variation in the usage of two cost minimizing techniques. The resulting variation in the value of capital per head at the given prices is known as a real Wicksell effect. The chain-rule for differentiation shows how the price and real Wicksell effects combine to determine the total variation in the value of capital per head with the interest rate [4].

For completeness, I note there is a third manner in which the value of capital per head can vary, namely if the composition of final output varies, for example, due to a difference in the rate of growth. This possibility is not important to my argument.

Now I want to prove a theorem by some simple formal manipulations. Given Equation 5, the marginal product of capital is equal to the interest rate (Equation 7) if and only if Equation 9 holds [5]:

Proof: Equation 10 gives the total differential of both sides of Equation 5:
Thus, the interest rate is equal to the marginal product of capital (Equation 7) if and only if Equation 11 holds:
Equation 9 follows. Q.E.D.

A demonstration that the value of capital per head need not be equal to the additive inverse of the slope of the factor price frontier (Equation 9) demonstrates that the interest rate need not be equal to the marginal product of capital (Equation 7).

[3] A more general statement of these relations, abstracting from price Wicksell effects, is given by Equations 7' and 8' in terms of left-hand and right-hand derivatives:
In the discrete case without price Wicksell effects, the neoclassical aggregate production function is supposed to resemble the function in Figure 1.
Figure 1: Interest Rate Bounded By Marginal Products

[4] A good explanation of price and real Wicksell effects can be found in:
  • Edwin Burmeister, "Wicksell Effects," The New Palgrave.
Burmeister writes:
"The value of capital, however, is not an appropriate measure of the 'aggregate capital stock' as a factor of production except under extremely restrictive assumptions. Wicksell (1893, 1934) originally recognized this fact, which subsequently was emphasized by Robinson (1956)."

[5] Equation 9 follows from Equation 7' at a non-switching point in the discrete case. Consider a second set of values of y, w, r, and k, related as in Equation 5:
The difference between these two sets of values is given by Equation II:
Or, in obvious notation:
Assume Equation 7' holds. Two cases arise.

Case 1: . By diminishing marginal productivity, one also has . Ignoring higher order terms, the production function is:
From Equation 7', one has:
Substitute from Equation III:
A little algebra yields:
Take the limit as the value of capital per head approaches k from above (and therefore the interest rate approaches r from below):

Case 2: and thus Ignoring higher order terms, one has:
The inequality in Display V follows, once again, from Display 7'. An argument parallel to the first case yields the inequality in Display XI:
The left-hand and right-hand derivatives of the factor-price frontier are equal at a non-switching point in the discrete case. The two cases establish that that derivative is equal to the value of capital per head:
which was to be shown.