Wednesday, January 01, 2020

Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Thursday, July 04, 2019

On Milana's Purported Solution To The Reswitching Paradox

Carlo Milana has posted a paper on arXiv. I was prepared to accept this paper's claims. Economists have developed price theory. Referring to Sraffian "paradoxes" and "perverse" switch points is a matter of speaking. There does not exist separate Sraffian and neoclassical versions of price theory. For a result to be "perverse", it need only contradict outdated neoclassical intuition. But it is as much a part of the mathematical economics as any other result. (It is another matter that much teaching in microeconomics is inconsistent with the mathematics.)

In equilibrium, the price of the services of each capital good in use is equal to the value of the marginal product of that good, with all prices discounted to the same moment in time. This discounting implies that the interest rate appears in a formal statement of these equations. These equalities are very different from the claim that the interest rate equals the marginal product of (financial) capital. In limited cases, one can prove something like the aggregate equality. No such thing as a marginal productivity theory of distribution, however, is restored. Milana might cite Hahn (1982) on this background.

But Milana goes further. He claims that reswitching is impossible or, at least, examples up to now are erroneous.

I think Milana's basic mistake is exposed in Salvadori and Steedman (1988). (I go through one of their examples here.) The Samuelson-Garegnani model is not a model of two-(produced) goods. The model contains as many capital goods as there are techniques. Potentially, there can be a continuum of capital goods in the model. As such, it is meaningless to require the price of the capital goods used in each technique that is cost-minimizing at a switch point to be equal to one another. That is analogous to requiring the price of a ton of iron be equal to the price of a ton of tin.

For some reason, Milana does not discuss examples of reswitching in flow-input, point output models, such as in Samuelson (1966). Nor does he acknowledge, as I read him, valid examples in which the same n commodities are produced in all techniques, and all commodities are basic in all techniques. (Does he say anything at all about the distinction between basic and non-basic commodities?) At a non-fluke or generic switch point, in such a framework, the two techniques that are cost-minimizing differ in a process in exactly one industry.

Milana should read and reference Bharadwaj (1970), as well as Bidard and Klimovsky (2004) on fake switches in models of joint production. Other Linear Programming formulations are available for considering the choice of technique. Vienneau (2005) presents one. What does Milana have to say about the direct method for analyzing the choice of technique in Kurz and Salvadori (1995)? I briefly provide a survey of different analysis in Vienneau (2017), as well as an algorithm for finding the cost-minimizing technique? Are all these approaches in error?

References
  • Khrishna Bharadwaj. 1970. On the maximum number of switches between two production systems. Schweizerische Zeitschrift fur Volkswortschaft and Statistik (4): 401-428. Reprinted in Bharadwaj 1989. Themes in Value and Distribution: Classical Theory Reappraised, Unwin-Hyman.
  • Christian Bidard and Edith Klimovsky. 2004. Switches and fake switches in methods of production. Cambridge Journal of Economics 28:89-97
  • Frank Hahn. 1982. The neo-Ricardians Cambridge Journal of Economics 6:353-374.
  • H. D. Kurz and N. Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge University Press.
  • Carlo Milano. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital. arXiv:1907.01189
  • Neri Salvadori and Ian Steedman. 1988. No reswitching? No switching! Cambridge Journal of Economics 12: 481-486.
  • Paul A. Samuelson. 1966. A Summing Up. The Quarterly Journal of Economics 80 (4): 568–583.
  • Robert Vienneau. 2005. On labour demand and equilibria of the firm. The Manchester School 73(5): 612-619.
  • Robert Vienneau. 2017. The choice of technique with multiple and complex interest rates. Review of Political Economy 29(3): 440-453.

Saturday, June 22, 2019

Easy To Be Hard

Young Children Policing Group Members

This post presents examples of psychologists inducing stress in experimental subjects, some showing why we need Institutional Review Boards (IRBs). Some of the older studies involved so much suffering that experimental subjects suffered Post-Traumatic Stress Disorder (PTSD). I recall that at the end of the 1976 movie, The Tenth Level, about the Milgram experiment, starring William Shatner, the scientists are discussing what they would do if they were experimental subjects. Would they refuse to torture others? And one says to Shatner/Milgram something like, "It seems to me, you have already been tested and failed."

  • Yudkin, Van Bavel, and Rhodes: Almost the only somewhat happy story here. Toddlers are willing to close a fun slide, for themselves, to punish another child for misbehavior. The experiment illustrates costly third-party punishment.
  • Stanford prison experiment: A sample of college students are randomly divided up into pretend guards and prisoners. The guards quickly begin abusing the prisoners.
  • Jane Ellliot experiments: In order to understand segregation and prejudice, divides a class of school children into blue eyes and brown eyes. The blue eyes sit at the front and treated well; the brown eyes sit at the back and are badly treated. The next Monday, the situation is reversed. Quickly, the well-treated act as if they believe they are superior and the others inferior.
  • Robber's Cave experiment: A somewhat happy ending, I guess. Boys divided up into two competitive groups at summer camp quickly disdain one another. Given a problem that requires cooperation with the other group, they will work together.
  • Milgram experiment: Given an authority figure telling them that this is experiment on negative re-inforcement for learning, people are willing to increase electric shocks past the point of torture. Some refused.
  • Gibson and Walk experiment: As far as the baby is concerned, they are crawling over the edge of a cliff on air. Tests whether caution about heights is inherent. More about individual psychology than most of the rest in this list.
  • Asch experiment: On conformity. Subject goes last in a group noting which line was the same length as the a standard. The subject does not realize the rest are part of the experiment. Many were willing to go along with the obvious falsehood all the others said.
  • Little Albert experiment: A baby is conditioned, as with Pavlov's dogs, to be terrified of a white rat, rabbit, dog, and a sealskin coat. More about individual psychology than most of the rest in this list.

Randomized Control Trials (RCTs) provide a rigorous methodology, albeit they can present problems of generalization and external validity. Not all of the above are RCTs. They do illustrate that designing ethical RCTs can be difficult. I expect the above list of amazingly mostly abusive studies, even in psychology can be extended.

References
  • Yudkin, Danial A., Jay J. Van Bavel, and Marjorie Rhodes (2019). Young children police group members at personal cost. Journal of Experimental Psychology.
  • Haney, C., W. C. Banks, and P. G. Zimbardo (1973). A study of prisoners and guards in a simulated prison. Naval Research Review 30: 4-17.
  • Muzafer Sherif (1966). In Common Predicament: Social Psychology of Intergroup Conflict and Cooperation Houghton Miffin.
  • Milgram, Stanley (1963). Behavioral study of obedience. Journal of Abnormal Social Psychology 67: 371-378.
  • Gibson, E. J. and R. D. Walk (1960).Visual Cliff. Scientific American April.
  • Asch, Solomon E. (1955). Opinions and social pressure. Scientific American November.
  • Watson, John B. and Rosalie Rayner (1920). Conditioned emotional reactions. Journal of Experimental Psychology 3(1): 1-14.

Monday, June 17, 2019

Lewin and Cachanosky on Neo-Ricardian Economics [Citation Needed]

This post is about the misrepresentation of Sraffian capital theory in Lewin and Cachanosky (2019). I cannot recommend this short book. Presumably, it is meant as an introduction. But I do not see it as succeeding. I do not see what a more advanced audience would get out of it that is not available in a few recent papers by Lewin and Cachanosky.

Before proceeding to my main theme, let me note that I agree with some parts of this book, mainly where Lewin and Cachanosky draw on Ludwig Lachmann, to parallel themes in Joan Robinson's emphasis on historical time. They state that no physical measurement of capital exists and that capital is not a factor of production, with a demand function. They state, probably as influenced by Jack Birner, that Hayek never set out a coherent and internally valid theory of capital. His triangles are only useful as an expository device. I am also ignoring certain gaps. For example, the text at the bottom of page 30 suggests, incorrectly, that the economic life of a machine would be the same as its physical life in equibrium, where such disequilibrium phenomena as the introduction of new and better vintages and changes in tastes and technology do not arise.

Citations are needed for these passages:

"Lachmann's capital theory provides the definitive understanding of the nature and working of the capital structure for Austrians today. Rather than conceiving of production as involving a homogeneous mass of 'capital' as a stock (as in both the neoclassical and modern Ricardian conceptions), Lachmann sees it as involving an ordered structure of heterogeneous multispecific complementary production goods. This structure is ever changing as entrepreneurs combine and recombine productive resources in accordance with their assessments of profitability." -- Lewin and Cachanoksy, p. 35.

Where do the neo-Ricardians reject the analysis in Sraffa's book?

"The Keynesian revolution established macroeconomics as [a] legitmate sub-branch of economic inquiry focusing on the relationship betwenn aggregates... [The] neoclassical production function is the workhorse of much of modern literature...

"...its ability, using the marginal productivity theory, to explain the distribution of output (income) between capital and labor... During the 1960s and following, the neoclassical production function was the object of attack by the 'Cambridge Marxists' UK (neo-Ricardians) against the 'Cambridge Massachusetts' neoclassicals, on the presumption that it was essential to the validity of the marginal productivity explanation of the distribution of income ... and that demolishing the notion of capital upon which the aggregate production function depended, they would, at the same time, demolish the marginal productivity theory of distribution." -- Lewin and Cachanoksy, p. 46-47.

Where do the neo-Ricardians assert the non-existence of disaggregated, microeconomic neoclassical theory?

"These paradoxes consist of cases in which it is alleged, for example, ... a fall in the interest rate may first lead to the adoption [of] a more 'capital-intensive' productive technique, and then switch, paradoxically, to a less 'capital-intensive' technique, and then switch back again as the interest rate continues to fall. These are alternative techniques, characterized by their physical capital labor ratios. In other words, switches may occur, as well as reswitches and reversals..." -- Lewin and Cachanoksy, p. 68.

Even Joan Robinson's "real capital" is measured for a given interest rate. Techniques of production are characterized by a complete list of inputs and outputs. These inputs can include produced means of production, unproduced natural resources, and various kinds of labor. When deciding on which technique to adopt, managers of firms, in Sraffian and in any other reasonable analysis of a capitalist system, coompare costs and revenues, with inputs and outputs evaluated at prices.

"The neo-Ricardians identify all 'capital' as intermediate goods, such as machines, tools, or raw materials. They are goods-in-process from the original labor that constructed them, to the emergence of the final consumer good. So all capital goods (can be and) are reduced to dated labor. In this way, we get a purely physical measure of 'capital', one that, by construction, does not vary with the interest rate." -- Lewin and Cachanoksy, p. 69, footnote 3.

Where do the neo-Ricardians assert that, in all interesting cases of joint production, all intermediate goods can be expressed as produced by inputs consisting only of a stream of dated labor? Where do they put forth a measure of capital that does not vary with the interest rate?

"Also important, the neo-Ricardians identify the price of capital as the rate-of-interest which they regard as synonymous with the rate of profit. But neither is correct... The market interest rate is, indeed, the price of capital as we understand it. It is the cost of borrowing 'capital' for the employment of any valuable resource or for any other reason. It is the price of credit and is determined by the time prefernces of borrowers and lenders and the production possibilities available. (The neo-Ricardians have no discussion of what determines interest rates.)" -- Lewin and Cachanoksy, p. 72.

Post Keynesians have considered a theory of growth and distribution in which the interest rate is set by the monetary authorities and the rate of profits exceeds the interest rate by a conventional markup. They have considered other theories in which the wage is given by forces outside the theory of value. They have developed theories of inflation in which conventions on both the rate of profits and wages conflict. In the late 1950s and early 1960s, Richard Kahn, Nickolas Kaldor, Luigi Pasinetti, and Joan Robinson pointed out that savings propensities out of wages and profits constrained functional income distribution along a steady state growth path. Kaldor (1966), in this tradition, developed a model in which the interest rate and the rate of profits are distinguished. I provide two textbooks, in the references, that survey this large body of work.

Reference
  • Duncan K. Foley, Thomas R. Micl, Daniele Tavani (2019). Growth and Distribution, Second edition. Harvard University Press.
  • Peter Lewin and Nicolas Cachanosky (2019). Austrian Capital Theory. Cambridge University Press.
  • Stephen A. Marglin (1984). Growth, Distribution, and Prices, Harvard University Press.

Saturday, June 08, 2019

On Hicks' Average Period of Production

Figure 1: APP Around Switch Points
1.0 Introduction

I take it that the Austrian theory of the business cycle builds on Austrian capital theory. The following two claims are central to Austrian capital theory:

  • Given technology, profit maximizing firms adopt a more capital-intensive, more roundabout technique at a lower interest rate.
  • The adoption of a more roundabout technique increases output per worker.

Originally, Eugen von Böhm-Bawerk proposed a physical measure of the average period of production, but economists of the Austrian school have been distancing themselves from this position for well over half a century. I have argued that the first claim fails, even in a framework without any scalar measure of capital-intensity or the average period of production.

Recently, Nicholas Cachanosky and Peter Lewin, in a series of articles, have championed J. R. Hicks' measure of the Average Period of Production (APP), as a justification of the first claim. They note that the APP, as defined here, is a function of the interest rate. Hence, it cannot fully support Böhm-Bawerk's theory. Saverio Fratini has argued this justification does not work, since the second claim above fails, when this APP is used as a measure of capital-intensity. Lewin and Cachanosky, in reply, argue that Fratini does not properly calculate the APP, since it should be forward looking and apply in disequilibria.

This post re-iterates Fratini's argument, with his example. I more closely follow Cachanosky and Lewin's approach, though.

2.0 Technology

Fratini considers a technology consisting of two techniques of production, Alpha and Beta (Table 1). Each technique requires three years of unassisted labor inputs, per bushel wheat produced at the end of the third year. Labor is advanced and paid at the end of the year. Labor is taken as numeraire. That is, the wage is assumed to be $1 per person-year. The price of a bushel wheat, p, is taken to be $12 dollars per bushel. As I hope becomes apparent, these assumptions generally characterize a disequilibrium.

Table 1: Inputs for Producing A Bushel Wheat
YearYears
Until
Harvest
Technique
AlphaBeta
13a3 = 1 Person-Yr.b3 = 2 Person-Yrs.
22a2 = 7 Person-Yrs.b2 = 2 Person-Yrs.
31a1 = 2 Person-Yrs.b1 = 8 Person-Yrs.

The output per worker, in a stationary state, is determined by the chosen technique. Suppose the Alpha technique is adopted. In any given year, 10 person-years are employed per bushel wheat produced. Two person-years are being expended to produce each bushel of wheat harvested at the end of the year, seven person-years are being employed to produce each bushel of wheat available at the end of the next year, and one person-year is employed per bushel wheat harvested even a year later. That is, output per worker, under the alpha technique, yα, is (1/10) bushels per person-year. Similarly, output per worker for the beta technique, yβ, is (1/12) bushels per person-year.

3.0 Net Present Value and the Choice of Technique

Suppose a wheat-producing firm faces a given annual interest rate, r. For convenience, define:

R = 1 + r

The discount factor, f, is defined to be:

f = 1/R = 1/(1 + r)

Consider a decision to choose a technique to adopt for next three years in producing wheat. Powers of the discount factor are used to evaluate the costs and revenues for each technique at the start of the given year. For example, the NPV of the alpha technique is:

NPV(α, f) = -a3 f - a2 f2 + (p - a1) f3

I have assumed that firms expect the given interest rate to remain unchanged for the decision period - a common convention. Revenues are positive, and costs (or outgoes) are negative.

Figure 2 graphs the difference between the NPV for the two techniques. A positive difference indicates that the alpha technique maximizes the NPV, while a negative difference arises when the beta technique is preferred. Which technique is chosen by cost-minimizing firm for each interest rate is shown. At switch points, firms are indifferent between the two techniques.

Figure 2: Difference in NPVs

Under the assumptions, NPV is always positive. (If the beta technique were adopted at an interest rate of zero, its NPV would be zero then.) If markets were competitive, the price of wheat would vary until the NPV was zero, given the interest rate. Fratini does indeed assume equilibrium and analyzes the choice of technique with backwards-looking calculations of costs, as Lewin and Cachanosky claim. But this makes no difference to his argument, so far.

4.0 The Average Period of Production

One might be interested in how NPV varies with the discount factor. The elasticity of the NPV, with respect to the discount factor, is a dimension-less number for assessing such sensitivity. Somewhat arbitrarily, I discount elasticity one period:

APP(α, f) = f [1/NPV(α, f)] [d NPV(α, f)/df]

Elasticity is the variation of NPV with variation of the discount factor, as a proportion of NPV.

APP(α, f) = [-a3 f/NPV(α, f)] x 1
+ [- a2 f2/NPV(α, f)] x 2
+ [(p - a1) f3/NPV(α, f)] x 3

The APP for a technique, at a given discount factor, is the weighted average of the time indices, looking forward, for a given income stream. The weights are the proportion of the income stream received in each period. All income is discounted to the start of the first year.

So the elasticity of the NPV of an income stream, with respect to the discount factor can also be expressed as the average period of production.

Notice that the APP is not defined in equilibrium. The denominators in the above terms are zero, and the APP could be said to be infinite. If only costs are used in the above calculations (thus, no longer of a NPV), the APP is well-defined, at least in the flow-input, point output case. Fratini (2019) does this.

One could also express the APP as a function of the interest rate:

APP(α, r) = [-a3 R2/NPV(α, r)] x 1
+ [- a2 R/NPV(α, r)] x 2
+ [(p - a1)/NPV(α, r)] x 3

where:

NPV(α, r) = -a3 R2 - a2 R + (p - a1)

I skip over some some algebraic manipulations above.

The above is not the definition of the APP in Fratini (2019), for example, in Equation 7. Where I have time indices of 1, 2, and 3, Fratini has indices of 3, 2, 1. I guess one can say that his definition of the APP is backwards-looking.

Fratini's argument still goes forward with Cachanosky and Lewin's (or Hicks') definition. One could present a mathematical proof that the APP is always increased around a switch point with a fall in the interest rate. But here I'll just graph it for the example. See Figure 1, at the top of this post. Around each switch point a lower interest rate is indeed associated with the adoption of a technique with a larger APP. But consider the switch point at an interest rate of 200 percent. The beta technique, adopted at a notionally lower interest rate, has a lower value of output per head.

4.0 Conclusion

The example illustrates that, around a switch point, a lower interest rate is associated with the adoption of a more roundabout technique, where roundaboutness is measured by Hicks' Average Period of Production. Incidentally, the example demonstrates that in a region where one technique is cost-minimizing the APP may decrease with the interest rate. But the adoption of a more roundabout technique can be associated with a decrease in output per worker. So much for Austrian capital theory and the Austrian theory of the business cycle.

Update (14 June 2019): Re-order numbers in table, as they are used in the calculations. References

Thursday, June 06, 2019

Refutation Of Austrian Business Cycle Theory

Those who understand price theory reject the theory of the Austrian Business Cycle (ABC). I am thinking here that its logical invalidity follows from post-Sraffian capital theory. It is also wrong because of its reliance on the concept of the natural rate of interest.

Some years ago, I tried to get published a demonstration that ABC theory was in error. I forget how many journals rejected it. Four or five articles here are from this series of revisions. The rejections from the journals more sympathetic to Post Keynesians generally said that everybody knows that ABC theory is wrong. The rejections from the journals more sympathetic to the Austrian school said that I ought to read more and more obscure literature. Some of this was helpful for my understanding of the history of ABC theory, but none really addressed my points.

Anyways, my favorite revision is the last. I think this is fairly good, but, as of now, do not intend to resubmit it anywhere. I find that recently some articles on the Cambridge Capital Controversies have been published in the Review of Austrian Economics.

References

Friday, May 31, 2019

Some Reviews of Quiggin's Economics in Two Lessons

I have been thinking of posting a review of Quiggin's book, but this is not it. I suppose I should mention that I am in the acknowledgements.

Quiggin has a response to a couple of the above. By the way, he had a paper, in 1987, on public choice.

I think any reviewer should note that Quiggin is extremely generous to Hazlitt's Economics in One Lesson. Hazlitt does not mention "opportunity cost". By focusing on this concept, Quiggin makes Hazlitt seem more coherent than he is. I agree with Quiggin that this coherence does not require Hazlitt to think the economy is always in equilibrium. It is consistent with prices providing signals, that, when entrepreneurs act on them, move the economy towards equilibrium. It is not consistent, as Quiggin notes in his book, with the economy persisting for a long time within the production possibility frontier, without any tendency to more towards the frontier.

It is no answer to or review of Quiggin's book to rattle on about Keynesianism or the logically incorrect AustrianBusiness Cycle theory. One has to also address Quiggin's points about externalities, information asymmetries, and the continual redefinition of property rights.

Furthermore, a fair reviewer would note that Quiggin does not recommend a mechanical calculation of, say, taxes and subsidies to correct market failures. Although, I guess, he does not mention "government failure" in his book, his consideration of policies is a lot more nuanced than that.

Furthermore, if one thinks the theory of public choice provides an answer to Quiggin, one should note that Hazlitt does not discuss these matters. Hazlitt was a propagandist and, for decades, should have not been taken seriously.

As far as I know, public choice is an application of neoclassical economics. Gloria-Palermo and Palermo (2005), as I recall this paper, argues that the Hayekian argument about the coordinating function of market prices does not provide a welfare criterion alternative to Pareto efficiency. I think I have such criteria in focusing on conditions for the continued reproduction of society, as opposed to the efficient allocation of given resources. One can also point to the Veblenian dichotomy, between instrumental and ceremonial aspects of institutions, as well as to the pragmatism of John Dewey. If I do review Quiggin's book, I want to point out how it is too accepting of Neoclassicism, as well as where it points beyond.

Reference
  • Sandy Gloria-Palermo and Giulio Palermo (2005). Austrian economics and value judgements: A critical comparison with Neoclassical Economics. Review of Political Economy 17(1): 63-78.