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.

On "Substitutability"

"[The] validity [of the Cambridge Criticism of neoclassical theory] is unquestionable, but its importance is an empirical or an econometric matter that depends upon the amount of substitutability there is in the system. Until the econometricians have the answer for us, placing reliance upon neoclassical economic theory is a matter of faith. I personally have the faith; but at present the best I can do to convince others is to invoke the weight of Samuelson's authority." -- C. E. Ferguson (1969) [as quoted in Carter (2011)].

1.0 Introduction

In this post, I describe two different meanings of "substitutability", as used in the literature and economists' remarks on the Cambridge Capital Controversy¹.

2.0 Joan Robinson's Criticism

Imagine two island capitalist economies, Alpha and Beta, each in a steady state and with access to the same technology. Suppose for some reason, the distribution of income happens to be different in the two islands. Then the capitalists on the islands will, maybe, have adopted different techniques of production and be producing a different mixture of commodities for final output. Consequentially, the structure of capital goods, both in composition and in quantities, will differ between the two islands.

An (illegitimate) thought experiment is to imagine the distribution of income slowly changing from as it is on one island to the distribution on the other. One might mistakenly consider the capital equipment slowly changing through the composition appropriate to imaginary intermediate islands. This claim ignores the reality of what Joan Robinson called historical time. One is treating a process occurring in time as if it occurring in space, ignoring that past bygones are gone, and assuming no difficulties exist in getting into equilibrium.

Neoclassical² economists frequently ignore the structure of capital equipment and the plans of the entrepreneurs. One meaning of "substitutability" is the assumption that capital goods can be instantaneously taken apart and reassembled to be appropriate for whatever equilibrium is being considered. The tranverse from one equilibrium to another is abstracted from. Robinson satirized this meaning of substitutability by designating the capital good in, say, the Solow-Swan growth model with such names as "ectoplasm", "leets", and "mecanno sets". Post Keynesians, including Sraffians, are generally suspicious of this approach. (Any fans of Austrian school economists want to chime in in the comments?)

3.0 Substitutability and Smooth Microeconomic Production Functions

Another meaning relates to the smoothness of production functions. One might say substitutability exists when derivatives (including, second, third, etc. derivatives) exist for all production functions. That is, substitutability exists in these examples, but not in these ones. (But what would you say about this one, where the cost-minimizing technique varies continuously with the interest rate and output, and each capital good are produced with fixed-coefficients?)

As far as I know, capital-reversing, for example, is consistent with substitutability, in this sense of smooth production functions. I, too, will invoke the weight of Samuelson's authority, even though I reject it in the former case. I would like, however, to see an explicit numeric example.

4.0 Conclusion

I believe C. E. Ferguson was referring to my section 2 meaning of "substitutability". That is, when neoclassical economists claim that Sraffians rely on a lack of substitutability for their critique of neoclassical economics, they should not be objecting to a lack of differentiability of microeconomic production functions.

Footnotes

1. Other usages are ignored in this post. For example, J. R. Hicks' "elasticity of substitution", as used in his mistaken Theory of Wages (1932), is not treated here.
2. As far as I am concerned, "neoclassical" is a meaningful and appropriate word in this context.

References

• Scott Carter (July 2011). C. E. Ferguson and the Neoclassical Theory of Capital: A Matter of Faith, Review of Political Economy, V. 23, N. 3: pp. 339-356

Elsewhere, On Neoclassical Economics

• Noah Smith complains about the supposed overuse of the label.
• Alex Marsh comments.
• Matias Vernengo responds.
• Lars Syll responds, including in pictures. Also, see here.
• I wrote much of the wikipedia article, albeit not the introduction. And some stuff in it I now disagree with. I also wrote much of the Wikipedia article on Classical economics, and the subsection of that article is especially relevant to a Sraffian perspective on neoclassical economics.
• Daniel Kuehn shares some thoughts.
• David Ruccio comments.

Update: Added some links.

Haikus

These have been written by authors who have not acknowledged their authorship. (I have written many of them myself.)

John Maynard Keynes
Created Bretton Woods system
The theory works

Michal Kalecki
Macro with markup pricing
Empirical success

Nicholas Kaldor
Nonlinear business cycle
Generates chaos

Lorie Tarshis
Elements of Economics
Met McCarthyism

Richard Goodwin
Tenureless at Harvard
Among best of the best

John Kenneth Galbraith
The world listened
Not economists

Joan Robinson
Predicted stagflation
Bastard golden age

John Hicks
Renounced IS/LM
Post Keynesianism

Nicholas Kaldor
Defeated Milton Friedman
Endogenous money

Paul Davidson
Explains historical time
Nonergodicity

Post Keynesians
Kicked out of Rutgers
Alfred Eichner died

Wynne Godley
Invents Sectoral Balances
Predicts Crises

The genius of Keen
His splendid model
Remains unrecognized

Post Keynesianism
Destroyed Reinhardt and Rogoff
No surprises here

A Continuous Time System Block Diagram For Nicholas Kaldor

A System Block Diagram For A Business Cycle Model

In this model of business cycles, two state variables, Y(t) and K(t), represent national income and the value of the capital stock, respectively. These state variables are each specified by a differential equation. In the above block diagram, I have adopted a notation from Steve Keen. The triangles in the upper-right and lower right equate the integrals of their inputs, over time, to their outputs. In other words, the following differential equations obtain:

dY/dt = α[I(t) - S(t)]

dK/dt = I(t) - δK(t)

You can compare and contrast this continuous-time representation of a dynamical system with its analogous discrete-time version.

This is a multiplier-accelerator model that allows for the economy to normally be out of equilibrium. An economic interpretation¹ of the model is that entrepreneurs have some sort of common opinion about the level of economic activity they expect in this nation's economy. And they have an opinion about the total value of capital stock that they believe is needed to sustain that activity. When these expectations are realized, this dynamical system is in an equilibrium. The model shows that when the economy has more activity than expected, entrepreneurs tend to increase the capital stock more rapidly, and vice versa for when activity falls below the expected level. This tendency is a non-linear relationship. Maybe, the more extreme the difference between the actual level and the expected level is, the less likely entrepreneurs are to expect the actual level to continue.

Neither interest rates nor prices are modeled here. Such modeling might be justified by the claim that the income effects in the model overwhelm the effects of prices. At any rate, this model does not contain an aggregate production function. Capacity can be operated either above or below the rate that was desired when the capital equipment being evaluated was installed. If the value of the capital stock falls below the expected level, entrepreneurs tend to increase investment, and vice versa for when the value of the capital stock rises above the expected level. (I think of the depreciation of the capital stock shown in the model as an accounting heuristic, not a physical decay.)

I am not putting forth grand empirical claims. To me, this model is of mathematical interest. It illustrates how non-linear economic dynamics can be generated endogenously. A source of continuous external shocks is not needed².

Unlike in the discrete-time case, I do not see how the continuous-time model given here can generate chaos. Trajectories in the two-dimensional state space are smooth, with no gaps. They cannot intersect. So, I think, this continuous-time model can generate cycles, but not strange attractors³. Another difference between discrete-time and continuous-time systems revolves around the details of stability analysis⁴.

Anyways, the graphical specification of the Kaldor model, given in this post, is suitable for numerical exploration in Steve Keen's software, as I understand it.

Footnote

1. As I understand it, mainstream macroeconomists currently reject the rough-and-ready microfoundations I provide here. They insist on formal microfoundations, even though their preferred formal treatments are just nonsense.
2. Some more mainstream economists seem to be willing to make this points in Overlapping Generations (OLG) models. I am willing to explore the mathematics there, despite the absurdity of assuming investment is driven by intertemporal utility-maximization of consumption.
3. The logistic equation is an example of a one-dimensial, discrete-time, chaotic dynamical system. Off-hand, I cannot think of a continuous-time chaotic system with less than three dimensions.
4. In discrete-time systems, one analyzes the stability of a fixed point by analyzing whether the eigenvalues of the system, linearized around the fixed point, are inside or outside the unit circle in the complex plane. In a continuous-time system, one looks to see if the eigenvalues are to the left or the right of the complex axis, if I recall correctly.

Marx On Ricardo

Karl Marx wrote a lot about David Ricardo's economics. Here is some of what he had to say in Theories of Surplus Value:

Ricardo starts out from the determination of the relative va1ues (or exchangeable values) of commodities by “the quantity of labour”.  (We can examine later the various senses in which Ricardo uses the term value.  This is the basis of Bailey’s criticism and, at the same time, of Ricardo’s shortcomings.)   The character of this “labour” is not further examined, If two commodities are equivalents—or bear a definite proportion to each other or, which is the same thing, if their magnitude differs according to the ||524| quantity of “labour” which they contain—then it is obvious that regarded as exchange-values, their substance must be the same.  Their substance is labour.  That is why they are “values”.  Their magnitude varies, according to whether they contain more or less of this substance.  But Ricardo does not examine the form—the peculiar characteristic of labour that creates exchange-value or manifests itself in exchange-values—the nature of this labour.  Hence lie does not grasp the connection of this labour with money or that it must assume the form of money.  Hence he completely fails to grasp the connection between the determination of the exchange-value of the commodity by labour-time and the fact that the development of commodities necessarily leads to the formation of money.  Hence his erroneous theory of money.  Right from the start he is only concerned with the magnitude of value, i.e., the fact that the magnitudes of the va1ues of the commodities are proportionate to the quantities of labour which are required for their production.  Ricardo proceeds from here and he expressly names Adam Smith as his starting-point (Chapter I, Section I).

Ricardo’s method is as follows: He begins with the determination of the magnitude of the value of the commodity by labour-time and then examines whether the other economic relations and categories contradict this determination of value or to what extent they modify it.  The historical justification of this method of procedure, its scientific necessity in the history of economics, are evident at first sight, but so is, at the same time, its scientific inadequacy.  This inadequacy not only shows itself in the method of presentation (in a formal sense) but leads to erroneous results because it omits some essential links and directly seeks to prove the congruity of the economic categories with one another.

Historically, this method of investigation was justified and necessary.  Political economy had achieved a certain comprehensiveness with Adam Smith; to a certain extent he had covered the whole of its territory, so that Say was able to summarise it all in one textbook, superficially but quite systematically.  The only investigations that were made in the period between Smith and Ricardo were ones of detail, on productive and unproductive labour, finance, theory of population, landed property and taxes.  Smith himself moves with great naïveté in a perpetual contradiction.  On the one hand he traces the intrinsic connection existing between economic categories or the obscure structure of the bourgeois economic system.  On the other, he simultaneously sets forth the connection as it appears in the phenomena of competition and thus as it presents itself to the unscientific observer just as to him who is actually involved and interested in the process of bourgeois production.  One of these conceptions fathoms the inner connection, the physiology, so to speak, of the bourgeois system, whereas the other takes the external phenomena of life, as they seem and appear and merely describes, catalogues, recounts and arranges them under formal definitions.  With Smith both these methods of approach not only merrily run alongside one another, but also intermingle and constantly contradict one another.  With him this is justifiable (with the exception of a few special investigations, [such as] that into money) since his task was indeed a twofold one.  On the one hand he attempted to penetrate the inner physiology of bourgeois society but on the other, he partly tried to describe its externally apparent forms of life for the first time, to show its relations as they appear outwardly and partly he had even to find a nomenclature and corresponding mental concepts for these phenomena, i.e., to reproduce them for the first time in the language and [in the] thought process.  The one task interests him as much as the other and since both proceed independently of one another, this results in completely contradictory ways of presentation: the one expresses the intrinsic connections more or less correctly, the other, with the same justification—and without any connection to the first method of approach—expresses the apparent connections without any internal relation.  Adam Smith’s successors, in so far as they do not represent the reaction against him of older and obsolete methods of approach, can pursue their particular investigations and observations undisturbedly and can always regard Adam Smith as their base, whether they follow the esoteric or the exoteric part of his work or whether, as is almost always the case, they jumble up the two.  But at last Ricardo steps in and calls to science: Halt!  The basis, the starting-point for the physiology of the bourgeois system—for the understanding of its internal organic coherence and life process—is the determination of value by labour-time.  Ricardo starts with this and forces science to get out of the rut, to render an account of the extent to which the other categories—the relations of production and commerce—evolved and described by it, correspond to or contradict this basis, this starting-point; to elucidate how far a science which in fact only reflects and reproduces the manifest forms of the process, and therefore also how far these manifestations themselves, correspond to the basis on which the inner coherence, the actual physiology of bourgeois society rests or the basis which forms its starting-point; and in general, to examine how matters stand with the contradiction between the apparent and the actual movement of the system.  This then is Ricardo’s great historical significance for science.  This is why the inane Say, Ricardo having cut the ground from right under his feet, gave vent to his anger in the phrase that “under the pretext of expanding it” (science) “it had been pushed into a vacuum”.  Closely bound up with this scientific merit is the fact that Ricardo exposes and describes the economic contradiction between the classes—as shown by the intrinsic relations—and that consequently political economy perceives, discovers the root of the historical struggle and development.  Carey (the passage to be looked up later) therefore denounces him as the father of communism.

I find the following, at least, of interest in this long passage:

• Marx here writes about "the connection as it appears in the phenomena of competition", "the external phenomena of life, as they seem and appear", "externally apparent forms of life". I think these phrases echo what Marx elsewhere describes as "vulgar political economy", commodity "fetishism", and the "illusions" created by competition.
• Marx criticizes Ricardo for only being concerned with "the magnitudes of values of commodities", not with the "peculiar character of labour that ... manifests itself in exchange values". I think this supports those who do not see a (great) contradiction between volumes 1 and 3 of Capital.
• Marx talks about the connection of labor values with money. I like interpretations or solutions of Marx's transformation problem that relate value to some abstract measure of the value of the output of a capitalist economy, namely:
  • Those based on Sraffa's standard commodity
  • Foley and Duménil's new interpretation, which focuses on the Monetary Expression of Labor Time (MELT).
• I quite like that "Halt!" I think it fair to say that Marx saw himself following and transcending Ricardo in exploring "the obscure structure of the bourgeois economic system", "the intrinsic relations", "the inner coherence, the actual physiology of bourgeois society".

Kalecki And Sraffa: Compatible?

Two Great Economists

1.0 Introduction

Michal Kalecki set out macroeconomic models in which markup pricing was common. Economists in this tradition rarely explore the effect of inter-industry flows on prices. Sraffians, on the other hand, usually specify prices, at least, to a first approximation, in a model of full competition. Can work in the traditions of Michal Kalecki and of Piero Sraffa be usefully combined?

2.0 A Model

Consider an economy in which n commodities are produced by n (single-product) industries. Inter-industry flows are described by a nxn matrix A, where a_{i, j} is the amount of the ith commodity used as input per unit output in the jth industry, at the given level of output of the jth industry. Labor inputs are described by the row vector a₀, where a_{0, j} is the quantity of labored hired in the jth industry per unit output, at the given level of output of the jth industry.

The positive constants m₁, m₂, ..., m_n represent barriers to entry among the different industries. The going rate of profits is earned in industries in which m_j is unity. Industries in which m_j exceeds unity have high barriers to entry. Perhaps a large scale of production is needed to operate profitably in such an industry. Industries with m_j less than unity are backwards, in some sense. At any rate, they earn less than the going rate of profits. These constants lie along the principal diagonal of the diagonal matrix M. That is, m_{i, j} is m_j, for i equal to j. And m_{i, j} is zero, for i unequal to j.

The row vector p represents prices, where p_j is the price of a unit quantity of the output of the jth industry. Suppose w represents the wage, and r represents The rate of profits.

The matrix A, the row vector a₀, the diagonal matrix M, and one of the distributive variables (say, the rate of profits r) are the given data for this model. The prices p and the remaining distributive variable (for example, wages w) are the unknowns to be found. One can set out the (modified) Sraffa equations for prices:

(p A M + a₀ w)(1 + r) = p

(I think models of full cost prices typically show markups being earned on both labor and material costs.) A numeraire should be specified. For example, one can set out the following normalization:

p₁ + p₂ + ... + p_n = 1

Likewise, the markups are only specified by the model, so far, up to a scalar multiple. I suggest the following normalization condition for markups:

m₁ x m₂ x ... x m_n = 1

Presumably this model can be extended, as in Sraffa (1960) to embrace fixed capital, land, joint production in general, and an analysis of the choice of technique.

3.0 Conclusion

The above has set out a model of prices of production. This model provides a framework for analyzing both the effects of inter-industry flows on prices and of markup pricing, arising from barriers to entry and other hindrances to full competition. The compatibility of some such model with both Kaleckian macroeconomics and the larger research agenda of Sraffa remains to be argued. Likewise, I have not shown the usefulness of this sort of model in empirical explanations of actual capitalist economies. One important issue in such discussions would probably be the applicability of models of prices of production to industries in which the planned operating level is less than full capacity.

This post should really have a bibliography, since the question of the compatibility of the economics of Kalecki and of Sraffa has been raised before. I gather that Paolo Sylos Labini, in some unpublished work in the 1960s, set out and analyzed a model rather like the above.