Three Routes To The Choice Of Technique

1.0 Introduction
I think the analysis of the choice of technique in a steady state is a settled question. (The meaning of Sraffa's equations in wider contexts can be debated.) One strength of the analysis of the choice of technique is the existence of several methods of analysis, all reaching the same conclusion. If one wanted to overthrow this analysis, one would need to show that one is not attacking just one such method, but all of them - or at least as many as possible. This post illustrates this strength of the analysis by presenting three such methods.

2.0 Example Technology
I need an example technology (Table 1) to use in stepping through different methods for analyzing the choice of technique. Each process requires the inputs shown to be purchased at the start of the production period (a year) for each unit of output produced and available at the end of the year. Two processes are known for producing steel, and two other processes are likewise known for producing corn. The coefficients are fairly arbitrary. In this example, to produce any net output in a steady state, all commodities - that is, both steel and corn - must be produced.

Table 1: Constant-Returns-to-Scale (CRS) Production Processes

Inputs	Industry Sector
	Steel Industry		Corn Industry
	First Steel-Producing Process	Second Steel-Producing Process	First Corn-Producing Process	Second Corn-Producing Process
Labor (Person-Yrs)	3220/3321	13930/63099	3115/3321	1
Steel (Tons)	0	0	1/2	9/20
Corn (Bushels)	1/18	2752/7011	0	0
Output	1 Ton	1 Ton	1 Bushel	1 Bushel

The analysis of the choice of technique calculates which production process would be adopted for each combination of prices and interest rates. For this technology to be compatible with a steady state, at least one process for producing steel and one process for producing corn must be adopted. A "technique" consists of one process from each of the industries in this example. Table 2 defines the four techniques, each named with a greek letter. (I think this convention of using greek letters in this context may have been introduced by Joan Robinson.)

Table 2: Techniques and Production Processes

Technique	Steel-Producing Process	Corn-Producing Process
Alpha	First	First
Beta	First	Second
Gamma	Second	First
Delta	Second	Second

A technique, in this case, is expressed by a 2-element row vector of direct labor coefficients and a square Leontief Input-Output matrix. For example, the labor coefficients, a₀^α, for the first technique are:

a₀^α = [(3220/3321) (3115/3321)]

The Leontief Input-Output matrix, A^α, for the first technique can be expressed as two columns a_.1^α and a_.2^α:

A^α = [ a_.1^α a_.2^α]

The first labor coefficient and the first column in the Leontief Input-Output matrix come from the specified production process from the steel industry for that technique:

a_.1^α = a_.1^β = [0, (1/18)]^T

The second labor coefficient and the second column in the Leontief Input-Output matrix come from the specified production process from the corn industry for that technique:

a_.2^α = a_.2^γ = [(1/2), 0]^T

I leave to the reader how to completely specify a₀^β, A^β, a₀^γ, A^γ, a₀^δ, and A^δ.

3.0 Direct Method
Heinz D. Kurz and Neri Salvadori refer to this method for analyzing the choice of technique I describe here as the "Direct Method". Before proceeding, I need to introduce some notation. Let p be a two-element row vector of prices:

p = [p₁, p₂]

where p₁ is the price of a ton steel and p₂ is price of a bushel corn. Let w be the wage, assumed to be paid at the end of the year for each person-year of labor expended during the year. Let r be the rate of interest, also called the rate of profits.

I need to introduce a column vector to represent the numeraire. Let e₂ be the second column of the 2x2 identity matrix:

e₂ = [0, 1]^T

The assumption that e₂ is the numeraire implies the following equation:

p e₂ = 1

This specification of the numeraite implies that, p₂, the price of a bushel corn is unity.

The problem is to find a pair (p, w), given the interest rate r, such that

• No process can be operated with costs less than revenues.
• For any process that is operated, the costs do not exceed the revenues.

The first condition implies the following four inequalities must hold:

p a_.1^α(1 + r) + a₀₁^α w ≥ p₁

p a_.1^γ(1 + r) + a₀₁^γ w ≥ p₁

p a_.2^α(1 + r) + a₀₂^α w ≥ p₂

p a_.2^β(1 + r) + a₀₂^β w ≥ p₂

The conjunction of the requirement that steel be produced with the second condition implies that one of the first two inequalities must be met with a strict equality. The analogous requirement for corn production implies that at least one of the last two inequalities must be met with equality.

These specifications are easily graphed (Figure 1). Given the interest rate, the first two inequalities yield upward-sloping lines in the the figure. The last two inequalities yield the downward-sloping lines. The first condition implies the solution must lie on or above all of the lines in the figure. The second condition implies that the solution must lie on

• At least one of the upward-sloping lines
• At least one of the downward-sloping lines.

The only point that satisfies these conditions is graphed. It lies on the upward-sloping line corresponding to the first steel-producing process and the downward-sloping line corresponding to the second corn-producing process. Thus, this analysis shows that the beta technique is cost-minimizing at an interest rate of 100%. The solution wage and price of steel can be read off the figure.

Figure 1: Direct Method Illustrated At r = 100%

The direct method is easily generalized to any finite number of techniques. Each additional production process results in an additional line in the figure, upward-sloping for the steel industry and downward-sloping for the corn industry. The method also generalizes for any finite number of commodities. Each additional commodity results in the introduction of another dimension to the figure. Although the figure quickly becomes unvisualizable, the mathematics generalizes.

4.0 Indirect Method
The indirect method generalizes to cases in which an uncountably infinite number of techniques are available. It is based on constructing the wage-rate of profits frontier as the outer envelope of the wage-rate of profits curve for each technique (Figure 2). I illustrate how to construct the wage-rate of profits curve for the Alpha technique.

Figure 2: Indirect Method Illustrated

The condition that the same rate of profits be earned for each process comprising a technique yields a system of two equations:

p A^α(1 + r) + a₀^α w = p

One also has the equation setting the price of the numeraire to unity:

p e₂ = 1

For a given interest rate r, the above is a linear system of three equations for three variables (p₁, p₂, and w). One can solve the system to express each of these three variables as a function of the interest rate. The wage, for example, can be found as:

w = 1/(a₀^α [ I - (1 + r)A^α]^-1e₂)

One knows, from a theorem due to Perron and Frobenius, that the inverse exists between an interest rate of zero and some maximum interest rate.

Figure 2 shows the wage-rate of profits curves for each of the four techniques. The cost-minimizing technique at each rate of interest is the one with the highest wage. Points at which the rate-rate of profits curves for two or more techniques interesect on the outer frontier are known as switch points. The two switch points are shown in the example. The Gamma technique is cost-minimizing for a very low interest rate. For a somewhat larger interest rate, the Delta technique is cost-minimizing. Finally, the Beta technique is cost minimizing for larger interest rates. My exposition illustrates that the direct and indirect methods give the same conclusion. For example, the wage-rate of profits frontier shows that the Beta technique is cost-minimizing for an interest rate of 100%.

5.0 Cost Minimization Algorithm
This method I take from J. E. Woods. He provides an algorithm for finding the cost-minimizing technique(s), given the interest rate.

1. Pick an initial technique. (For illustration, I start with the Beta technique in the example.)
2. Solve the equations specifying the wage-rate of profits curve for the selected technique. So you now have a price vector p and the wage w.
3. Using p and w, calculate the cost of producing a ton steel with each of the known production processes (Figure 3).
4. If the steel-producing process in the selected technique is cheapest, go to Step 6. Otherwise go to Step 5. (In the example, one would go to Step 5 for low interest rates and to Step 5 for higher interest rates.
5. Replace the steel-producing process in the technique analysed in Step 2 with the cheapest steel-producing process identified in Step 4. Solve the equations specifying the wage-rate of profits curve for the newly selected technique. Use the resulting p and w in Step 6. (In the example, one would calculate the wage-rate of profits curve for the Delta technique for a sufficiently low interest rate.)
6. Using the specified p and w, calculate the cost of producing a bushel corn with each of the known production processes (Figure 4).
7. If cost of producing corn could be found in Step 6 for the technique selected in Step 2 and the corn-producing process in that technique is cheapest, then stop. You have identified the cost-minimizing technique. Otherwise, replace the corn-producing process in the technique analyzed in Step 6 with the cheapest corn-producing process identified in Step 6. (In the example, the algorithm would terminate in one-pass for a sufficiently high interest rate, with the Beta technique identified as the cost-minimizing technique.)
8. Go to Step 2.

Figure 3: Costs of Producing Steel with Prices for the Beta Technique

Figure 4: Costs of Producing Corn with Prices for the Beta Technique

Figures 3 and 4 suggest that for a sufficiently low interest rate, the technique consisting of the second steel-producing process and the first corn-producing process, that is, the Gamma technique, is cost-minimizing. For a somewhat higher interest rate, the technique consisting of the second steel-producing process and the second corn-producing process, that is, the Delta technique, seems to be cost-minimizing. And, as noted above, the algorithm terminates with the Beta technique identified as the cost-minimizing technique at an even higher interest rate. In other words, the graphs suggest that the above algorithm converges to the same solution as the indirect method.

6.0 Conclusions
I have not exhausted the methods available for analyzing the choice of technique. For example, I have not formulated any Linear Programs above. Nor have I presented the diagram in my 2005 Manchester School paper. Furthermore, I have glossed over many interesting mathematical questions, such as proving the existence of solutions and proving that all methods give the same result. But this post is already too long.

References

• Heinz D. Kurz and Neri Salvadori (1995) Theory of Production: A Long-Period Analysis. Cambridge University Press.
• J. E. Woods (1990) The Production of Commodities: An Introduction to Sraffa, Humanities Press.

Great Female Economists

This is a selection. I always exempt those alive in making such judgements.

• Jane Marcet
• Harriet Martineau
• Rosa Luxemburg
• Mary Paley Marshall
• Beatrice Webb
• Charlotte Perkins Gilman
• Elizabeth Boody Schumpeter
• Joan Robinson
• Krishna Bharadwaj

Lost Knowledge In Economics

Economists' concerns can be expected to change as the world changes. In a serious scholarly discipline, however, such changes in emphasis should be theorized and argued. They should not be just a matter of fads and the following of changes in the political environment. I am not sure economics meets this standard. Anyways, here are examples I came up with today for exploring this question:

• Managerial theories of the firm (as developed by, e.g., Robin Marris)
• Markup pricing
• Sidney Chapman's theory of the length of the working day (as opposed to the textbook analysis of tradeoffs between leisure and commodities) (Derobert (2001), (Spencer 2003), and (Walker 2007)).
• Co-operatives (Kalmi 2007).
• Sidney and Beatrice Webb's analysis of labor markets (Kaufman 2008).

References

• L. Derobert. "On the Genesis of the Canonical Labor Supply Model". Journal of the History of Economic Thought, V. 23, N. 2 (2001): 197-215.
• Panu Kalmi. "The Disappearance of Cooperatives from Economics Textbooks". Cambridge Journal of Economics, V. 31 (2007): 625-647.
• Bruce Kaufman. "How a Minimum Wage Can Improve Efficiency Even in Competitive Labor Markets: The Webbs and the Social Cost of Labor". Andrew Young School of Policy Studies Research Paper Series, Working Paper 08-16 (July 2008).
• D. A. Spencer. "The Labor-Less Labor Supply Model in the Era Before Philip Wicksteed". Journal of the History of Economic Thought, V. 25, N. 4 (2003): 505-513.
• Tom Walker. "Why Economists Dislike a Lump of Labor". Review of Social Economy, V. 65, N. 3 (2007).

Coase Theorem Not About Markets

Mainstream economists tend to think of the "laws of demand and supply", for example, as applying to all of human history and independent of institutional structure¹. Geoffrey Hodgson has noted the difficulty of finding a definition of "markets" in mainstream economics.

To me, a market must allow for repetitive purchases and sales of a commodity where participants have information on, for example, prices from previous purchases and sales. A contract drawn up between two organizations to last for several years is a bilateral negotiation, not a market transaction, when neither organization is simultaneous to draw up parallel contracts with competing organizations².

One application of this idea is to labor unions. Maybe the difficulties mainstream economists have with defining "markets" is connected with their backward notions on labor unions, backward notions that others have recently pointed out³.

I was inspired to write this post by Hahnel and Sheeran's article. An train engine with tracks through a farmer's field is an example of application of the Coase Theorem. If vegetation isn't kept a certain distance from the rails, supposedly sparks from the train wheels are likely to start a fire and burn the crops. Do the farmers have a well-defined property right not to have sparks ejected on their fields? Or do trains have a well-defined right to emit sparks? Depending on the answers to these questions, the legal liability for maintaining the track and paying for any resulting fires is different. But, according to the Coase "theorem", if property rights are well-defined and no transaction costs exist, the farmer and the railroad will negotiate an efficient price for allowing the trains to emit sparks. Some conclude that it is government's job to ensure property rights are well-defined and perhaps lower transaction costs. Then the market will come to an efficient solution to the problem of externalities, however property rights are allocated.

Among other criticisms, Hahnel and Sheenan point out that the conclusion is a non-sequitur. This is not an example of a market. I think their treatment of information asymmetries is a formalization of a point I first read from Michael Albert. The Coase set-up will encourage those with property rights to act as bullies, to threaten obnoxious behavior they wouldn't otherwise do, so as to extort payments from their victims.

¹ An interesting experiment would be to count the number of occurrences of the word "capitalism" in, say, the American Economic Review or the Journal of Political Economy in the last decade and contrast those counts with the same counts in, say, the Cambridge Journal of Economics, the Review of Political Economy, or the Review of Radical Political Economics.

² Even if you object to this usage of "market", you should see that the game theoretic models appropriate for a bilateral negotiation under various assumptions about available information is not the typical model of demand and supply schedules.

³ Haven't the criticized economists heard of the theory of the second best? I thought that the case of a large employer and a labor union was a canonical example.

References

• Michael Albert. "Nobel Nerve", Z Magazine (Nov. 1991).
• Robin Hahnel and Kristen A. Sheeran. "Misinterpreting the Coase Theorem" Journal of Economic Issues. V 43, N. 1 (March 2009): 215-238.
• Geoffrey M. Hodgson Economics and Institutions: A Manifesto for a Modern Institutionalist Economists, Basil Blackwell (1989).
• R. G. Lipsey and Kevin Lancaster. "The General Theory of the Second Best", Review of Economic Studies, V. 24, N. 1 (1956-1957): 11-32.

Geoff Harcourt In Audio And Video Formats

As I understand it, Geoff Harcourt is now living in Australia, after having recently moved home from Cambridge, England. While in Cambridge, he wrote The Structure of Post-Keynesian Economics: The Core Contributions of the Pioneers and, especially, Joan Robinson, the latter with Prue Kerr.

While there, Harcourt contributed his time to a few interviews and lectures. I have previously mentioned his November 2009 lecture to the Post Keynesian Study Group on the legacy of Joan Robinson. He also gave a May 2010 lecture, to the same forum, on the crisis in mainstream economics. Finally, one can find a two-interview on YouTube.

Figure 1: First Part of Geoff Harcourt Interview

Figure 2: Second Part of Geoff Harcourt Interview

H/T Daniel Kuehn for links to the You Tube video.

Letter To The Editor

Mike Cushman, the secretary of the London School of Economics University and Colleges Union (LSE UCU) writes to the Guardian:

"Philip Inman (Scene of the crime, G2, 18 February) describes the complicity of economics academics in the crash. They were responsible for providing an intellectual gloss for reckless and maybe criminal behaviour. ...They circulated their legitimising patina in the house journals of their club: the leading economics journals beloved of the US and UK business schools.

These journals, a key part of the conspiracy, continue to cast their shadow. It is almost impossible for economists to get employed or promoted in leading economics and management departments like LSE without publishing in these "A-grade" journals. ...It is the same self-referential circulation of authority that underpinned the collateralised debt obligations and other key instruments of the credit bubble. Essential research income is allocated through the Research Excellence Framework by reference to success in those same publications and adjudicated by those who edit and publish in those journals.

Scholars who will not act as shills for the banks and reinforce the Panglossian orthodoxies, and instead promote critical analyses, are rarely welcome in these journals and thus increasingly not welcome in universities... The REF (Research Exalting Finance) is a dangerous, flawed mechanism, at least in economics and management: an ideological straitjacket disguised as a fair and unbiased assessment." -- Mike Cushman

Mr. Cushman's claims are backed up by academic research on the history and sociology of economics. If I recall correctly, Geoffrey M. Hodgson and Harry Rothman¹, for example, demonstrate the self-referential and closed nature of the supposedly "leading" journals in economics.Frederick Lee² adds to the documentation of the unwillingness of mainstream economists to cite non-mainstream economists with empirically validated analyses of the British Research Excellence Framework (REF). In my reading of Lee, the REF is leading to less excellence in British economics, at least if your measure is an ability to understand actually existing capitalist economies.

¹ Geoffrey M. Hodgson and Harry Rothman. "The Editors and Authors of Economics Journals: A Case of Institutional Oligopoly?". Economic Journal, V. 109, Iss. 453 (Feb. 1999): pp. 165-186.

² Frederic Lee. A History of Heterodox Economics: Challenging the Mainstream in the Twentieth Century.

People I've Never Heard Of, Am Barely Aware Of, And Thought I Knew

News coverage of the Egyptian revolution introduced me to Gene Sharp, who I have never heard of before. Apparently he is at the Albert Einstein Institution, and protesters are taking recipes from his book, From Dictatorship to Democracy.

Nonviolent revolutions these days are somewhat anarchist¹. I am not well read on contemporary anarchists. I found out existence of Colin Ward when he died. I am vaguely aware of Murray Bookchin. I have had a copy of Bill Devall and George Sessions' book, Deep Ecology: Living as if Nature Mattered on my bookshelf for a decade. Going back further, I like Hannah Arendt's On Revolution and Crises of the Republic and Paul Goodman's
Growing Up Absurd.

I have been much influenced, of course, in my views on economics by Joan Robinson. I don't know if I've read these before, but I find her Tanner lectures, "The Arms Race," are available online². In fact, almost all of the Tanner lecture series can be downloaded. There's just too much to read there, but I will pick out Albert Hirschman's, since I have blogged before on his book drawing from those lectures.

Notes:

¹A crossword puzzle clue passed on by Will Shortz: "Disordered sort?" The answer is, "Anarchist."

² I was motivated to look up Robinson's Tanner lecture by listening to Geoff Harcourt's November 2009 presentation on Robinson to the Post Keynesian Study Group.

Stephen Smale Presciently On Global Financial Crisis?

I have argued before that weaknesses in mainstream economics exposed by our current macro-economic problems have been known for decades. I here note another example.

Stephen Smale is a Fields medal-winning mathematician who has advanced our understanding of chaotic dynamical systems. Smale has also contributed to mathematical economics. He wrote the following in 1976:

"A criticism commonly made of economic theory is its failure to make predictions of crises in the country or anticipate correctly unemployment or inflation. One must be cautious in the social sciences about looking towards physics for answers. However, some comparisons with the physical sciences seem profitable in connection with the above criticism. In those sciences, where theory itself is in a far more advanced state, limitations can be seen in a similar way. For example a given individual human body functions according to physical principles; however no physical scientist would predict a heart attack. The physical theory gives understanding of aspects of what goes on in the human body only under very idealized conditions. The physical theories eventually play some role in the education of medical doctors, who can then say some things, some times about a patient's susceptibility to a heart attack, preventive measures, and cures.

The economy of the world or even a nation is a very complex phenomenon, like a human body, involving a number of factors, both economic and political. It is no more reasonable to expect economic theorists to predict a nation's economic future than for a theoretical scientist to predict the future health of an individual...

...I would like to give some reasons why I feel equilibrium theory is far from satisfactory. For one thing the theory has not successfully confronted the question, 'How is equilibrium reached?' Dynamic considerations would seem necessary to resolve this problem. Another is the reliance of the theory on long range optimization.

In the main model of equilibrium theory, say as presented in Gerard Debreu's Theory of Value, economic agents make one life-long decision, optimizing some value. With future dating of commodities, time has almost an artificial role." -- Stephen Smale. "Dynamics in General Equilibrium Theory." American Economic Review V. 66, N. 2 (1976): pp. 288-294.

Celebrity Economists?

When I look at many economists who have won the "Nobel" prize, I often wonder, where is the empirical evidence for their theories? Are they making empirical claims that have passed potentially falsifying tests? It seems to me that both Solow and Lucas, for example, won prizes more on the basis that their work is frequently cited than for expanding our understanding of actually existing economies. Perhaps some, such as Leontief or Stone, won for work providing an accounting framework that is useful in organizing empirical data.

Hence, my title: a celebrity has been defined as somebody who is famous for being famous.

This is a topical post.I was inspired by this list of "top twenty" articles in the American Economic Review, selected by six senior economists.

(While I was writing this post, Merijn Knibbe posted similar thoughts.)

I append the article list for reference:

• Alchian and Demsetz (1972). "Production, Information Costs and Economic Organization".
• Arrow (1963). "Uncertainty and the Welfare Economics of Medical Care".
• Cobb and Douglas (1928). "A Theory of Production".
• Deaton and Muellbauer (1980). "An Almost Ideal Demand System".
• Diamond (1965). "National Debt in a Neoclassical Growth Model.
• Diamond and Mirrlees (1971). "Optimal Taxation and Public Production" (two parts).
• Dixit and Stiglitz (1977). "Monopolistic Competition and Optimum Product Diversity".
• Friedman (1968). "The Role of Monetary Policy".
• Grossman and Stiglitz (1980). "On the Impossibility of Informationally Efficient Markets".
• Harris and Todaro (1970). "Migration, Unemployment and Development: A Two-Sector Analysis.
• Hayek (1945). "The Use of Knowledge in Society".
• Jorgenson (1963). "Capital Theory and Investment Behaviour".
• Krueger (1974). "The Political Economy of the Rent-Seeking Society"
• Krugman (1980). "Scale Economies, Product Differentiation, and the Pattern of Trade.
• Kuznets (1955). "Economic Growth and Income Inequality".
• Lucas (1973). "Some International Evidence on Output-Inflation Tradeoffs".
• Modigliani and Miller (1958). "The Cost of Capital, Corporation Finance and the Theory of Investment".
• Mundell (1961). "A Theory of Optimum Currency Areas".
• Ross (1973). "The Economic Theory of Agency: The Principal's Problem".
• Shiller (1981). "Do Stock Prices Move Too Much to Be Justified by Subsequent Changes in Dividends?"

Elsewhere

• Russell Jacoby pans Erik Olin Wright's book Envisioning Real Utopias. I don't know much about Jacoby. I find his review encourages me not to read Wright. It would help, however, if Jacoby didn't cite Wright's use of the word "interstitial" as an example of boring cant, while praising Veblen, who also used the word.
• Victoria Chick and Ann Pettifor write about the 75th anniversary, on February 3 of Keynes' General Theory.
• Eric Schliesser, a philosopher, notes Greg Mankiw's refusal to acknowledge the existence of literature on his points, a topic I've mentioned before.

Daron Acemoglu

What do you think of Daron Acemoglu?

Since he is a mainstream economist at MIT, I should be inclined to take a critical stance to be consistent with my themes. Acemoglu has written so many papers that I do not feel that I can have a comprehensive view. Maybe I should read up on the summary that must have accompanied his 2005 John Bates Clark medal.

Acemoglu writes on political economy and political science topics I think of interest - for example, power, coercion, social networks, innovation, governance, and economic development. The conclusions he and his colleagues reach are not necessarily a whitewash of capitalism. I've been trying to read, for example, Glenn Ellison and Alexander Wolitzky's paper, "A Search Cost Model of Obfuscation", in which more-or-less competitive firms deliberately put clauses hard to understand in contracts, thereby making it difficult to compare products and to obtain, for example, payouts on warranties, insurance, etc. Most of the papers I've read by Acemoglu and his colleages seem to tell just-so stories with game theory, a branch of mathematics I think can be fascinating. Empirical accounts can be used to illustrate the theories, but I wonder whether the theories are passing potentially falsifying tests. As an exemplar, I take Acemoglu, Egorov, and Sonin's accounts of incidents in the history of the Soviet Politburo in their 2008 Review of Economic Studies paper, "Coalition Formation in Non-Democracies".

Entrepreneurial Profits In A Classical Model

I came upon this passage recently:

"Thus, in the short run, the entrepreneurs introducing new techniques would reap supernormal profits. [Suppose] there is continuous technical change in the system, which Marx assumes to be in the nature of capitalist competition and a requirement for the maintenance of the 'reserve army of labour', then there arises a permanent income category that cannot be accounted for by labour-time accounting... Though Pareto does not clearly separate such entrepreneurial income from returns to capital in general, or from the notion of productivity of capital, it is plain that he foreshadows the idea that was later developed by Schumpeter...as an explanation for positive profits in a capitalist economy." -- Ajit Sinha (Theories of Value from Adam Smith to Piero Sraffa, Routledge (2010) pp. 214-215.)

This suggests to me a puzzle: can I create a model in which entrepreneurs make profits even though the workers are paid what would be the entire net output if the technology in use during the period in which they are paid were to persist unchanged? This post demonstrates that Sinha's comment is well-founded.

2.0 A Model
2.1 The Technology
Consider a simple economy in which a single commodity, corn, is produced each year. Workers produce the annual output from inputs of (seed) corn and their labor. The technology is defined by:

• a₀(t): the labor (in person-years) needed as input per bushel corn produced in the tth year.
• a₁(t): the (seed) corn needed as input per bushel corn produced in the tth year.

The coefficients of production evolve as in the following two equations:

a₀(t) = e^-λ₀t

a₁(t) = c e^-λ₁t

where the positive constants λ₀ and λ₁ are the rate of decrease in the labor and (seed) corn inputs, respectively. I impose the condition that the quantity harvested must exceed the quantity of seed corn planted in the spring:

0 < c < 1

2.2 Quantity Flows
Let Q(t) be the bushels of corn produced during the tth year and available after the harvest at the end of year. Assume:

Q(t) = e^λ₀t

The labor employed each year is a₀(t)Q(t), that is, one person-year.The seed corn, K(t), required for planting at the start of the tth year is:

K(t) = a₁(t)Q(t) = c e^{-(λ₁-λ₀)t}

The seed corn decreases each year if and only if the rate of decrease of the labor input per bushel corn produced exceeds the rate of decrease of the seed corn input per bushel corn produced:

λ₁ < λ₀

The surplus corn harvest, Y(t), over the seed corn planted at the start of the year is:

Y(t) = Q(t) - K(t) = e^λ₀t(1 - c e^-λ₁t)

2.3 Prices, Wages, And Distribution
Assume the labor hired during a given year is paid at the end of the year out of the harvest. The Sraffian price equations for this model are:

a₁(t) + a₁(t) w(t) = 1

where w(t) is the wage per person year, and I have taken a bushel of corn as the numeraire. It is easy to solve this equation to find that the wage is the net output produced by the person-year employed:

w(t) = Y(t)

If the seed corn required for a constant labor force declines year-by-year, this model provides a source of entrepreneurial profit:

π(t) = K(t + 1) - K(t) = c e^{-(λ₁-λ₀)t}[e^{(λ₀-λ₁)} - 1]

What happens if the condition on technological progress is not met? I haven’t worked out this case, but two possibilities seem to me to arise. In the first case, workers cannot consume the entire surplus each year. Perhaps, the capitalists obtain some accounting profits on their capital and they save those profits as additions to the seed corn each year. In the second case, the number of hours worked decline.

No Crisis In Mainstream Economics...

...Instead, the situation is chronic. The long-festering situation of economics is seen in the constant literature on the "crisis" in economics, going back for maybe half a century.

The book The Crisis in Economic Theory (1981) is a timely example. It was edited by Daniel Bell and Irving Kristol, and Daniel Bell's obituary was published in the New York Times today. (See also this Crooked Timber post.) The editors wrote the introduction, and each wrote a chapter. Other contributions include Frank Hahn on general equilibrium theory, Israel Kirzner on the Austrian school, Paul Davidson on Post Keynesianism, and Edward Nell on a Sraffa-influenced interpretation of Marxist economics.

Blah, Blah, Jevon's Paradox, Blah, Blah, Backfire

Figure 1: The Carrier Dome, Named After A Manufacturer Of A/C Equipment No Longer In Syracuse, NY

The Jevon's paradox arises when increased efficiency in the use of a resource results in greater overall use of that resource. This is a severe example of "rebound", where the effects of increased efficiency are lessened by increased use. Jevon's wrote about Coal.

Some may have noticed David Owen's recent article in The New Yorker focused on air conditioning (A/C). By synchronicity, Computer, the flagship journal of the Institute of Electrical and Electronic Engineers (IEEE) Computer Society, also published an article on rebound about the same time. Tomlinson, Sliberman, and White recommend mindfulness in the pursuit of energy efficiency in Information Technology and reference a report from an organization in the United Kingdom. (I'm not as dismissive of the Jevon's paradox as my title may suggests; I just wanted a template to could apply to both articles.)

The New Yorker published three letters on their article. I select Amory Lovins' letter for not just because he is a well-known advocate of increased energy efficiency. He points out that much of the increased use of A/C that David Owens describes is due to increased wealth, not rebound. He uses the example of oil to assert that increases in efficiency could drop energy use in absolute terms, even with economic growth. Apparently, between 1977 and 1985, the United States Gross Domestic Product rose 27 percent and oil use fell 17 per cent.

For utility-sponsored research in the United States, I look to the Electric Power Research Institute (EPRI). I don't know if they have a take on the Jevon's paradox. I think Leontief Input-Output analysis and Luigi Pasinetti's structural economic dynamics provide empirical tools for investigating the question.

References

• Amory B. Lovins (2011) "Letter", The New Yorker (17 Jan.): p. 3.
• David Owen (2010). "The Efficiency Dilemma", The New Yorker (20 & 27 Dec.): pp. 78-85.
• Steve Sorrell (2007). The Rebound Effect: An Assessment of the Evidence for Economy-Wide Energy Savings From Improved Energy Efficiency, UK Energy Research Center.
• Bill Tomlinson, M. Six Sliberman, and Jim White (2011). "Can More Efficient IT Be Worse for the Environment?", Computer, V. 44, Iss. 1 (Jan.): pp. 87-89.

Krugman On The Importance Of Austrian Business Cycle Theory

Paul Krugman writes:

"Someone, I don’t know who at this point, sent me to this post by Robert Murphy, which is the best exposition I’ve seen yet of the Austrian view that’s sweeping the GOP..."

I think the Republicans are not as coherent as Krugman makes them out to be. They are even less coherent than Austrian Business Cycle Theory.

I don't know that I will pursue trying to publish my rebuttal of Austrian Business Cycle Theory. Some have previously brought up my working papers in discussions of Krugman's blog and column. So far, I have not seen my name mentioned in discussions of this Krugman blog post.

ASSA, Not AEA In Denver?

Denver In Some Other Month

The proceedings of the recent American Economic Association annual conference are online. Preliminary versions of some of the papers are available for download.

I have trouble getting a sense of what mainstream economists are about from such a massive list. Doubtless I would find some of these papers of interest, despite the forbidding technical titles. I regret that downloads are not available for panel discussions (for example, "What's Wrong (and Right) with Economics? Implications of the Financial Crisis", "Lessons for Economics from the Great Recession", "Grand Challenges for Social Science...", "History, Crisis, Institutions and Economic Analysis", and "The Ethics of Professional Economic Practice"). (Actually, doing a search on the word "Panel" does cut down the list of titles to a manageable size that may give a feel to the direction of the profession.)

I also look in this list for economists of schools of thought and fields in which I'm interested. The Union of Radical Political Economics has only one session co-sponsored with the AEA. Steve Keen provides videos and download links. The History of Economics Society also has one co-sponsored session. As far as I can see, the Association for Evolutionary Economics (AFEE) and the International Association for Feminist Economics have no sessions. Brad DeLong's presentation is the only one with the word "Keynes" or "Keynesian" in the title. This sample should not lead one to conclude that heterodox economists were not represented in Denver, for they appear in the program of the Allied Social Science Associations. Explicitly identified heterodox economists just seem to be banished from the AEA, to the AEA's shame.

And The Life Of Man, Solitary, Poore, Nasty, Brutish, And Short

I am hostile to the notion of logically deriving an ideal society from first principles. Ideal norms can only be understood by us humans in a context that will evolve over time, not from some timeless, interest-free view from nowhere. Humans, in arguing about society, invariably base themselves on some partial perspective or faction. And to understand how to apply some principle articulated from some interest, one will have to draw on empirical results. (Is this an institutionalist, pragmatic view?)

Perhaps, nevertheless, some (not necessarily inconsistent) norms can be stated in keeping with these ideas. I suggest the following:

• Human society should be able to reproduce itself (Karl Marx).
• Unnecessary suffering should be alleviated (Karl Popper).
• Everybody should have the freedom to develop their capabilities to the best of their abilities (Aristotle, Marx).

Other norms don't seem to be compatible with my views on how to think about political philosophy. "People should be able to keep what they make" is a meaningless norm, maybe common among current intellectually and ethically impoverished mainstream economists.

Robert Nozick, as I understand him, begs a definition of natural rights. And then he argues for the following principles on that basis:

• A person who acquires a holding in accordance with the principle of justice in acquisition is entitled to that holding.
• A person who acquires a holding in accordance with the principle of justice in transfer, from someone else entitled to the holding, is entitled to the holding.
• Unjust acquisitions or transfer should be rectified

He ends up arguing for a more-or-less night-watchman state.

Perhaps these sorry days are ripe for an immanent critique of the idea of equality of opportunity.

I did not manage to mention above the Austrian-school economist Israel Kirzner's defense of returns to entrepeneurship with what he calls a "finders keepers" ethic. I have not read John Rawls.

Both Sides Now

Eric Schoenberg, of Columbia Business School, has a very confused response to the usual idiocy from Greg Mankiw. Schoenberg quotes Mankiw as saying

"under a standard set of assumptions... the factors of production [i.e., workers] are paid the value of their marginal product... One might easily conclude that, under these idealized conditions, each person receives his just deserts."

Schoenberg thinks the above is coherent. He merely questions whether the standard assumptions apply in our economy.

But marginal productivity is not a theory of the distribution of income, as I have demonstrated. It is a theory of the choice of technique. Income distribution can be anywhere on the factor price frontier and all agents will be receiving the value of the marginal product of the factors of production that they own. (I don't know if anybody in the comments at the Huffington Post points out that Mankiw does not know what he is talking about, even given all of his assumptions.)

By the way, Bill Mitchell has a recent post that wanders into my theme.

Canonical Statements Of Current Mainstream Price Theory?

I find puzzling where contemporary mainstream economists would point for good statements of a theory to explain prices in, say, the United States economy. I can think of a couple of possibilities.

The first would be General Equilibrium models in which a complete set of spot and future markets exist and in which goods are distinguished by location, date of delivery, and contingent events. Canonical statements of such a theory include:

• Gerard Debreu (1959). Theory of Value: An Axiomatic Analysis of Economic Equilbrium, Cowles Foundation Monograph.
• Kenneth J. Arrow and Frank Hahn (1971). General Competitive Analysis, Holden-Day.

But is this the current theory? Even though more textbooks have been written, the references would seem old to most young economists. The Sonnenschein-Mantel-Debreu results show that dynamic equilibrium paths are not limited by the theory. The theory does not allow for the existence of money to have any effect. Since the quantities of initial endowments are givens of the theory and any groping out of equilibrium, particularly with production going on, would change the data defining the equilibria, any time to reach equilibrium is too long. I think many mainstream economists would tell me General Equilibrium theory was abandoned in the 1980s.

Another possibility is models of temporary equilibrium. I look at the following as canonical statements of this theory

• J. R. Hicks (1946). Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory, 2nd edition, Oxford University Press.
• J. M. Grandmont (1977). "Temporary General Equilibrium Theory", Econometrica, V. 45, N. 3 (Apr.): pp. 535-572.

In this theory, only spot markets and maybe future markets for the numeraire commodity clear in equilibrium. The plans of different agents for future activities are not brought into agreement in equilibrium. Maybe this approach is related to Samuelson's model of overlapping generations. In addition to all the problems of General Equilibrium Theory, this approach has the difficulty of modeling how expectations alter, something that hardly seems observable or easy to model in a mechanical fashion.

Maybe game theory is the foundation of contemporary mainstream price theory. But cannot a game be found to rationalize almost any observed behavior? Is it not more a bag of tricks than a theory? Nevertheless, I have heard mainstream economists say good things about the following text:

• David M. Kreps (1990). A Course in Microeconomic Theory, Princeton University Press.

As I understand it, the dominant introductory graduate textbooks in mainstream microeconomics remain:

• Andreu Mas Colell, Michael D. Whinston, and Jerry R. Green (1995). Microeconomic Theory, Oxford University Press.
• Hal R. Varian (1992). Microeconomic Analysis, 3rd edition, W. W. Norton.

When I have perused these, I have found them to be more a collection of mathematics than a clear presentation of price theories. And I have found them very unclear on why the student should accept anything in them as applicable to actually existing capitalism.

Increase In The Feasibility Of Economic Planning

Mathematical programming is a key technique for economic planning. And we can solve linear programs much better now:

"Even more remarkable - and even less widely understood - is that in many areas, performance gains due to improvements in algorithms have vastly exceeded even the dramatic performance gains due to increased processor speed.

The algorithms that we use today for speech recognition, for natural language translation, for chess playing, for logistics planning, have evolved remarkably in the past decade. It's difficult to quantify the improvement, though, because it is as much in the realm of quality as of execution time.

In the field of numerical algorithms, however, the improvement can be quantified. Here is just one example, provided by Professor Martin Gröschel of Konrad-Zuse-Zentrum für Informationstechnik Berlin. Grötschel, an expert in optimization, observes that a benchmark production planning model solved using linear programming would have taken 82 years to solve in 1988, using the computers and the linear programming algorithms of the day. Fifteen years later - in 2003 - this same model could be solved in roughly 1 minute, an improvement by a factor of roughly 43 million. Of this, a factor of roughly 1,000 was due to increased processor speed, whereas a factor of roughly 43,000 was due to improvements in algorithms! Grötschel also cites an algorithmic improvement of roughly 30,000 for mixed integer programming between 1991 and 2008.

The design and analysis of algorithms, and the study of the inherent computational complexity of problems, are fundamental subfields of computer science." -- Report to the President and Congress - Designing a Digital Future: Federally Funded Research and Development in Networking and Information Technology, Executive Office of the President, President's Council of Advisors on Science and Technology (December 2010)

I don't know how such speedup was accomplished. I assume it cannot be merely a tradeoff between Dantzig's simplex algorithm and interior point methods (such as Karmarkar's algorithm). The simplex algorithm, for example, has never struck me, from what I recall, as naturally parallelizable. But parts of it can be done in parallel, I think. I think of choosing a pivot element, multiplying a vector by a scalar, and taking the inner product of two vectors as parallelizable operations. I think these improvements must have been accomplished by customizing an implementation with a well defined Application Programming Interface for a specific architecture.

(H/T: Noam Nisan)

Update: I've been reading Robert E. Bixby's "Solving Real-World Linear Programs: A Decade and More of Progress" (Journal of Operations Research, V. 50, Issue 1 (2002)). Apparently speedups were accomplished by algorithm improvements such as matrix operations that exploit the sparcity of the matrices, removing redundant constraints, aggregating decision variables under specified conditions, and many improvements I do not understand. The simplex algorithm, the dual simplex algorithm, and interior point methods all remain competitive on different problems. Bixby considers example problems with millions of decision variables and constraints. I think a couple of more orders of magnitude of improvements can be achieved with parallelization. Maybe somebody has tried that since Bixby's publication.

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.

Continued Balderdash From Liebowitz And Margolis

Joan Robinson, drawing on John Maynard Keynes, famously distinguished between models set in historical and logical time. Geoffrey Hodgson, now an institutionalist economist, has written extensively about evolutionary models in economics. Given my interest in such economists, I also find of interest how to formalize the notion that "history matters". I think mathematical models of nonergodic processes is one way of formally setting a model in historical time.

Brian Arthur and Paul David, two economists, have developed a parallel idea, that of path dependence. This post is about false statements Stan Liebowitz and Stephen Margolis like to make about this work. Liebowitz and Margolis quote Paul David:

"The foregoing account of what the term 'path dependence' means may now be compared with the rather different ways in which it has come to be explicitly and implicitly defined in some parts of the economics literature. For the moment we may put aside all of the many instances in which the phrases 'history matters' and 'path dependence' are simply interchanged, so that some loose and general connotations are suggested without actually defining either term. Unfortunately much of the non-technical literature seems bent upon avoiding explicit definitions, resorting either to analogies, or to the description of a syndrome - the set of phenomena with whose occurrences the writers associate path dependence. [Rather than telling you what path dependence is, they tell you some of the symptomology - things that may, or must happen when the condition is present. It is rather like saying that the common cold is sneezing, watering eyes and a runny nose.]" -- Paul David

Liebowitz and Margolis somehow think you will be persuaded to believe the following:

"So here we see David disqualifying, at least from others, any efforts to connect path dependence to observable phenomena. David would have path dependence discussed only in the context of the most severe abstraction, an immaculate concept immune from criticism: it is a dynamic stochastic process that is non-ergodic." -- Stan Liebowitz and Stephen Margolis

Notice Paul David never says that path dependence, under a rigorous definition, never will be manifested in observable empirical phenomena. Elsewhere Paul David notes that Markov processes can be non-ergodic, that is, path dependent. And he notes that economists have connect Markov processes, not all of which need be path-dependent, to observable penomena:

"Homogeneous Markov chains are familiar constructs in economic models of the evolving distribution of workers among employment states, firms among size categories, family lineages among wealth-classes or socio-economic (occupational) strata, and the rankings of whole economies among in the international distribution of per capita income levels." -- Paul David

Why are certain economists so willing to tell untruths?

References

• W. Brian Arthur (1989) "Competing Technologies and Lock-In by Historical Small Events", Economic Journal, V. 99, N. 1: pp. 116-131.
• W. Brian Arthur (2009) The Nature of Technology: What It Is and How It Evolves, The Free Press. [I haven’t read this]
• Paul A. David (1985) "Clio and the Economics of QWERTY", American Economic Review. V. 75, N. 2 (May): pp. 332-337.
• Paul A. David (2000) "Path Dependence, It's Critics and the Quest for 'Historical Economics'"
• Paul A. David (2007) "Path Dependence - A Foundational Concept for Historical Social Science", Cliometrica, V. 1, N. 2: pp. 91-114 (working copy)
• Stan J. Liebowitz and Stephen E. Margolis (2010) "How the Lock-In Movement Went off the Tracks"

Organized Labor Outmatched by Business in Class War in United States

On "A Splendid Contribution"

The appendix of Omkarnath's aprreciation of Bharadwaj's review of Sraffa's book contains an exchange of letters between Bharadwaj and Sraffa. Here's Sraffa's letter:

"As from Trinity College, Cambridge
Sabzburg, Austria
September 8, 1963

Dear Mrs. Bharadwaj,

Thank you so much for your kind letter, which I receive abroad, just as I am about to return to Cambridge.

I am delighted with your excellent article, which will be of great help to many who have been puzzled by my book. I have no doubt that you have correctly grasped the main lines of the argument and also guessed some of the directions in which, in my view the criticism of marginalism should be developed.

There are only one or two minor points in which I think your exposition is perhaps not as lucid as it is in general. One (p. 1452, col 3, first para), on deriving 'land theory of value'. I suppose this is an echo of Samuelson, but I do not see the implications. (I have the impression that you somewhat underestimate the historical importance of the labour theory of value: in my view much of modern theory is, whether consciously or not, a polemic against it.) Another one is p. 1453, col 1, from 'To a particular wage' to the end of the paragraph: I find this obscure and have some doubts about what I seem to understand. Also, a small point of disagreement is the very last words of your final footnote. I insist that the construction of a subsystem is a purely bookkeeping operation!

These, however, are very minor blemishes and the article remains a splendid contribution for which I am most grateful. I hope very much you will continue to work on these lines.

With kind regards,

Yours sincerely,
Piero Sraffa"

Sraffa criticizes three passages in Bharadwaj's review. I agree the second passage is not well written:

"To a particular wage, given in any standard, there may correspond several alternative rates of profits. This shows the absolute necessity of measuring the wage in terms of the Standard commodity, if unequivocal conclusions regarding the movements of the rate of profits given the wage rate are to be drawn. Measurement of the wage in terms of the Standard commodity gives us definite information regarding both the direction as well as the extent of change in the rate of profits, consequent upon a change in the wage rate. No other standard possesses this predictive value." -- Krishna Bharadwaj (1963)

The wage is only defined in terms of some standard. Once the standard is specified, a unique rate of profits corresponds to that wage, no matter what the standard. A different rate of profits may correspond to the same numeric value in a different standard. But one would not expect the same properties to be displayed by a substance at zero degrees Celsius and zero degrees Fahrenheit.

I think Sraffa's criticism of the third passage is a disagreement about the level of emphasis. Here is that passage:

"Nevertheless, while reading the paragraphs relating to the construction of the Standard system (pp. 23-4) and more particularly the subsystems (p. 89), one gets a feeling as though the assumption of constant returns-to-scale is necessary. Such doubts could easily be warded off since the Standard commodity is purely an auxiliary construction having no physical existence in production relations. Similar is the case of the subsystems which are used to derive the direct and indirect labour content of commodities (at zero profit rate)." -- Krishna Bharadwaj (1963)

References

• Krishna Bharadwaj (1963) "Value Through Exogenous Distribution", The Economic Weekly, (August 24): pp. 1450-1454.
• G. Omkarnath (2005) "'Value Through Exogenous Distribution': A Review Article in 1963", Economic and Political Weekly, (January 29): pp. 459-464.

Do Angeletos And La'O Know What They Are Talking About?

Some comic gives some stupid and vile economists an opportunity to comment on some of Cosma Shalizi's ideas [1]. (I find particularly stupid the commentator that cites Amazon, a Web 2.0 exemplar, for an example of agents interacting only through prices.) Eventually, one respondent says that George-Marios Angeletos and Jennifer La'O show how to embed animal spirits in Dynamic Stochastic General Equilibrium (DSGE) models. I'm not sure which paper they are talking about, but I did download their paper Sentiments (with accompanying slides.) I do not object to how Angeletos and La'O model shocks, although in this setting I don’t see why I should care.

I was quickly stopped in reading this paper at the first footnote:

"By 'mainstream' we mean the prototypical RBC and New-Keynesian models, as well as the more recent DSGE models. This excludes models with multiple equilibria or irrational agents, which we discuss in due course."

How are models with multiple equilibria non-mainstream? They continue in this vein throughout their paper:

"In our model, agents are fully rational; preferences and technologies are standard; markets are Walrasian; there are no nominal frictions, no externalities, and no non-convexities; the equilibrium is unique; and there is no room for correlation devices or lotteries. In these respects, our theory has squarely neoclassical foundations."

"This extrinsic uncertainty has very similar flavor as the one encountered in models with multiple equilibria: it captures the self-fulfilling nature of short-run fluctuations. Importantly, though, it does not rest on the severe externalities, non-convexities and missing markets that are most often needed to sustain multiple equilibria-nor does it come with the usual difficulties in conducting policy analysis."

It is my understanding that the Sonnenschein-Mantel-Debreu theorem is proved in a Walrasian model with no externalities, non-convexities, or missing markets. The excitement over the theorem comes from being derived with the same sort of assumptions that are used in Debreu's Theory of Value to derive the existence of an equilibrium. So I find it hard to believe the authors know what they are talking about when they suggest multiple equilibria are non-Walrasian or non-neoclassical.

By the way, I happen to have available a model with multiple equilibria. Figures 1 and 2 below illustrate. I'd like somebody to point out to me how agents in this model are not fully rational; how preferences and technologies are non-standard; or where nominal frictions, externalities, and non-convexities exist in this model. I suppose one can say some markets do not exist in an overlapping generations model. Agents cannot buy commodities or sell their labor before they are born or after they are dead. I did not think such an assumption made a model heterodox or non-neoclassical.

Figure 1: Equilibrium Interest Rates as a Function of One Parameter in the Utility Function

Figure 2: Equilibrium Wages as a Function of Another Parameter

[1] Cosma Shalizi is on a team of three that has recently received a grant awarded by the Institute for New Economic Thinking.

A Slight Illness - The Doctor Jests, A King Today - Tomorrow He Is Dead

Has the global financial crisis discredited Dynamic Stochastic General Equilibrium (DSGE) models? It seems to me that that may be so, but I wonder if new criticisms of DSGE models have been put forth. It seems to me the fundamental flaws of such models have been unaddressed for decades. Cosma Shalizi describes these models in a critical way. Joseph Stiglitz is not impressed with them either:

"It is hard for non-economists to understand how peculiar the predominant macroeconomic models were. Many assumed demand had to equal supply - and that meant there could be no unemployment. (Right now a lot of people are just enjoying an extra dose of leisure; why they are unhappy is a matter for psychiatry, not economics.) Many used "representative agent models" - all individuals were assumed to be identical, and this meant there could be no meaningful financial markets (who would be lending money to whom?). Information asymmetries, the cornerstone of modern economics, also had no place: they could arise only if individuals suffered from acute schizophrenia, an assumption incompatible with another of the favoured assumptions, full rationality." -- Joseph Stiglitz

As I understand it, Smets and Wouters (2007) is an example of a DSGE model widely approved of by mainstream economists. Sbordone et al. (2010) is a recent presentation of an introductory DSGE. One can see that the output of these models is a set of stochastic processes meant to model certain time series available in empirical data. Nominal interest rates, (real) income, the inflation rate, the volume of one-period government bonds, employment, and nominal wages are all examples of such time series. The input into such models is another set of stochastic processes. These inputs are given names that suggest they are random terms in functions characterizing either government entities - e.g., monetary policy shock - or agents in microeconomic models. Examples of the latter kind of names are a household discount rate shock, productivity shock, markup shock, and firm discount rate shock. Stochastic processes are specified by parameters of certain probability distributions. As one can see from the names of these inputs, the agents are supposed to be optimizing, including across time. A story, expressed in mathematics and supposedly of microeconomic equilibrium, connects the inputs to the outputs in the model. That is, the DSGE models are supposed to have microfoundations.

But they do not have microfoundations. I look for a number of mistakes in such models:

• Are inputs into production function measured in numeraire units? (The numeraire is often taken to be a basket of consumer goods.) Joan Robinson (1953-54) explains why measuring the quantity of capital in production functions in numeraire units is an error. Notice this is not solely a question of the aggregation of capital. A model can have a continuum of capital goods, yet still exhibit this mistake.
• Are representative agents used? Kirman (1992) explains why the use of representative agents is unfounded.
• Is money modeled? Frank Hahn (1965) explains why money does not matter in General Equilibrium models, even though it does seem to matter for actually existing capitalist economies. Mainstream economists have a couple of strategies for introducing money in an ad hoc way into DSGE models. But I am not convinced the typical modeler has ever managed to address Hahn's point.
• Is the possibility of multiple equilibria taken seriously? Is it demonstrated that non-equilibrium dynamic processes converge to the modeled equilibrium? Richard Goodwin (1990) illustrates what a macroeconomics looks like that, in contrast to typical DSGE models, takes dynamics seriously. Kirman (1989) shows that ignoring muliple equilibria and stability issues was demonstrated to be unfounded by the Sonnenschein-Mantel-Debreu results. Shiller (1978) long ago raised the issues of multiple equilibria and convergence. Shiller was critiquing the tradition out of which DSGE models evolved.

I haven't read much in the literature of DSGE models. It seems to me, however, that these issues are routinely ignored by many mainstream economists. Perhaps a wider range of macroeconomic models should be considered by serious researchers.

References

• Ricardo J. Caballero (2010) "Macroeconomics after the Crisis: Time to Deal with the Pretense-of-Knowledge Syndrome", MIT Dept. of Economics, Working Paper 10-16 (September 27)
• Richard M. Goodwin (1990) Chaotic Economic Dynamics, Oxford University Press.
• Robert J. Gordon (2010) "Is Modern Macro or 1978-era Macro More Relevant to the Understanding of the Current Economic Crisis".
• Frank H. Hahn (1965) "On Some Problems of Proving the Existence of an Equilibrium in a Monetary Economy", in The Theory of Interest Rates (Ed. by F. H. Hahn and F. Brechling), Macmillan.
• Frank Hahn and Robert Solow (1995) A Critical Essay on Modern Macroeconomic Theory, MIT Press.
• Kevin D. Hoover (1988) The New Classical Macroeconomics, Basil Blackwell.
• J. E. King (2010) "Microfoundations for Macroeconomics? The Pre-History of a Dogma, 1936-1975", HETSA 2010, (June)
• Alan Kirman (1989) "The Intrinsic Limits of Modern Economic Theory: The Emperor has No Clothes", Economic Journal, V. 99, N. 35: Supplement: Conference Papers: pp. 126-139.
• Alan P. Kirman (1992) "Whom or What Does the Representative Individual Represent?", Journal of Economic Perspectives, V. 6, N. 2 (Spring): pp. 117-136.
• Joan Robinson (1953-54) "The Production Function and the Theory of Capital", Review of Economic Studies, V. 21, N. 55: pp. 81-106.
• Argia M. Sbordone, Andrea Tambalotti, Krishna Rao, and Kieran Walsh (2010) "Policy Analysis Using DSGE Models: An Introduction", Federal Reserve Bank of NY Economic Policy Review.
• Robert J. Shiller (1978) "Rational Expectations and the Dynamic Structure of Macroeconomic Models: A Critical Review", Journal of Monetary Economics, V. 4: pp. 1-44.
• Frank Smets and Rafael Wouters (2007) "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach", American Economic Review, V. 97, N. 3: pp. 586-606.
• Alessandro Vercelli (1991) Methodological Foundations of Macroeconomics: Keynes & Lucas, Cambridge University Press.

To read:

• Wynne Godley and Marc Lavoie (2007) Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, Palgrave MacMillan.

James Joyce On Identity Economics

I think that if one looked, one would be able to find in lots of depictions in literature of multiple selves. Here's an example:

"...he had heard about him the constant voices of his father and of his masters, urging him to be a gentleman above all things and urging him to be a good catholic above all things. These voices had now come to be hollow-sounding in his ears. When the gymnasium had been opened he had heard another voice urging him to be strong and manly and healthy and when the movement towards national revival had begun to be felt in the college yet another voice had bidden him to be true to his country and help to raise up her language and tradition. In the profane world, as he foresaw, a worldly voice would bid him raise up his father's fallen state by his labours and, meanwhile, the voice of his school comrades urged him to be a decent fellow, to shield others from blame or to beg them off and to do his best to get free days for the school. And it was the din of all these hollow-sounding voices that made him halt irresolutely in the pursuit of phantoms." -- James Joyce, A Portrait of the Artist as a Young Man

Does how artists depict human beings carry any weight for how economists choose to portray agent's choices? Should it?