Friday, December 28, 2012

Functions For Fashion

How might a concern with being up on current fashions in mainstream economics models help perpetuate the current sociology of economics?

Economists could study various economies in various regions and at various stages of development, economic history, the history of economics, epistemology and methodology, various alternative theories (Austrian, Feminist, Institutionalist, Marxist, Post Keynesian, ...), and other social sciences. Studying varieties of mathematical models takes up their time and provides an excuse for remaining ignorant of so much.

If you want to argue against mainstream economics, a mainstream economist can dismiss you as ignorant of some model variation and as attacking a strawperson. Furthermore, this dismissal could be "justified" by just checking whether you have a degree from a small number of schools, and, if you do, just mocking you as not having fully learned what they are teaching. Thus, your time can be taken up with argument about whether you know what you are talking about. The mainstream economist never need get to the point of engaging a critique.

With all these varieties of models, surely one will do better than another in some specific historical circumstance or when applied to some specific time series. But likely another will do better in a different circumstance. Thus, one need never empirically assess mainstream economics as a whole in some prominent field or empirically compare and contrast a mainstream theory to a non-mainstream theory.

Monday, December 24, 2012

Economics Of The Steady State

A steady state is characterized by the economy having a constant rate of growth. I here select a number of expositions of analyses of steady state I have made on this blog:

  • The Harrod-Domar model of warranted and natural rates of growth.
  • Karl Marx's volume 2 model of simple and expanded reproduction.
  • An extension of the Kahn-Kaldor-Pasinetti-Robinson macroeconomic model of income distribution.
  • Explanations of aspects of the non-substitution theorem.
  • Neoclassical Overlapping Generations (OLG) models with intertemporal utility maximization.

Consider the hypothesis that a consumer's decision to save should be viewed as a choice between current consumption and future consumption so as to maximize an utility function. Except in the last case above, I have no need of that hypothesis. Alternative theories of value and distribution exist. (Does Nick Rowe imagine that I am in his intended audience for this post?)

Friday, December 21, 2012

Krugman Confused About His Profession, Preferences

Paul Krugman has explained on several occasions that he was inspired to become an economist by Isaac Asimov's Foundation triology. The collapse of a galaxy-wide civilization into an interim dark age, before the revival of a second galactic empire, provides the background setting of the novels. The organizing conceit is that Hari Seldon, the expert founder of the discipline of psychohistory, has figured out how to set up initial conditions such that the intervening and unpleasant dark ages will last for only a millennium, instead of 30 millennia. In Asimov's telling, psychohistory is an explicitly mathematical discipline.

It turns out that Asimov was not the only science fiction author in that era writing about mathematical psychology:

"So? The greatest mathematical psychologist of our time, a man who always wrote his own ticket even to retiring when it suited him..." -- Robert A. Heinlein (1958).

Heinlein's character has written a book titled, On the Statistical Interpretation of Imperfect Data, and his colleagues are at the Institute for Advanced Study, in Princeton, New Jersey.

When people referred to "Mathematical psychology" during the 1950s, what were they talking about? I suggest that they had in mind cybernetics, as invented by Norbert Wiener, and later developments. For example, consider the 1960 book, Developments in Mathematical Psychology, with contributions from R. Duncan Luce, Robert R. Bush, and J. C. R. Licklider.

Many have built on this work over the last half-century, in a variety of disciplinary settings. A few years ago, one could find the label Command, Control, Communications, and Intelligence (C3I) used to refer to much of this work. Departments and ministries of defense provided quite a bit of funding for research in these areas. And if you want to find current research on these topics, you could do worse than read such journals as IEEE Transactions on Communications, IEEE Transactions on Control Systems Technology, and IEEE Transactions on Signal Processing. These journals are all put out by the Institute of Electrical and Electronics Engineers (IEEE).

Thus, Paul Krugman wanted to be a electrical engineer, although he does not know it.

  • Isaac Asimov (1953). Second Foundation. [I happen to have this book in the trilogy handy.]
  • Robert R. Bush (1960). "A Survey of Mathematical Learning Theory", in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
  • Robert A. Heinlein (1958). Have Space Suit-Will Travel.
  • J. C. R. Licklider (1960). "Quasi-Linear Operator Models in the Study of Manual Tracking", in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
  • R. Duncan Luce (1960). "The Theory of Selective Information and Some of Its Behavioral Applications, in (ed. by R. D. Luce), The Free Press of Glencoe, Illinois.
  • Norbert Wiener (1948). Cybernetics: Or Control and Communication in the Animal and The Machine.

Wednesday, December 19, 2012

Money Missing From Mainstream Economics

"In practice, of course, the purists were unable to deliver, and the new tricks involve the 'modern macroeconomists' in ad hoc assumptions of their own that are at least as objectionable as the Keynesian macroeconomic generalizations that [Michael] Wickens objected to. We have already encountered one example, the 'Gorman preferences' needed to make the representative agent at least minimally plausible... Two others are equally incredible. The first is the 'no-bankruptcies' assumption in Walrasian models and the related 'No Ponzi' conditon that is imposed on D[ynamic] S[tochastic] G[eneral] E[quilibrium] models. This eliminates the possibility of default, and hence the fear of default (since these are agents with rational expectations, who know the correct model, and hence know that there is no possibility of default), and hence the need for money, since if your promise to pay is 'as good as gold', it would be pointless for me to demand gold (or any other form of money) from you. Money would be at most a unit of account, but never a store of value. The second is the unobtrusive postulate of 'complete financial markets', smuggled into Michael Woodford's Interest and Prices (Woodford 2003, p. 64), which means that all possible future states of the world are known, probabilistically, and can be insured against: this eliminates uncertainty, and hence the need for finance..." -- J. E. King, The Microfoundations Delusion: Metaphor and Dogma in the History of Macroeconomics (2012: p. 228)

Can General Equilibrium Theory find a role for money? Consider Frank Hahn's "On some problems of proving the existence of an equilibrium in a monetary economy" (1965). He considered the question posed above to be an unmet challenge at the time. Hahn did not think, for example, Don Patinkin's attempt to justify the use of money through the inconvenience of indirect transactions and through transactions cost fit comfortably in a General Equilibrium model. Hahn wanted to find a model in which the existence of money was essential, in some sense, in which an equilibrium with money differed from one without.

mainstream macroeconomists claim to base their approach on General Equilibrium Theory. Experts on GE (for example, Alan Kirman) have been saying for decades that this claim is dubious. The critiques that I am most aware of are based on price theory.

These modern macroeconomists claim to have available models incorporating money and finance. This availability does not mean that they are unwilling to deploy models without money in some contexts for some purposes. As far as I am aware, Woodford is widely cited and widely respected in current mainstream monetary economics.

I have wondered how and if mainstream macroeconomists address the problems highlighted by Hahn in incorporating money in General Equilibrium Theory. But I have not wondered enough to read much. If I take King as an authority, I can spare myself the trouble of establishing that mainstream macroeconomists are basically confused about their own monetary theory. Is this a sound conclusion?

(Colin Rogers is an expert on how the Cambridge Capital Controversies can be used to critique Wicksellian theories of money and of the natural rate of interest. Woodford and Rogers had an exchange of views in the Cambridge Journal of Economics a number of years ago.)

Sunday, December 16, 2012

Nick Rowe Knavery

So much nonsense packed into so few words:

"But the lefty Sraffian model has only labour and time as inputs." -- Nick Rowe

I do not know what politics has to do with it. I'd like to see some evidence of the political beliefs of, say, Neri Salvadori. When Sraffa states, in the preface of Production of Commodities By Means of Commodities, that "Others have ... independently taken up [similar] points of view," I think he includes John Von Neumann. Von Neumann wanted to wage an atomic war against the Soviet Union. I guess Rowe must think Von Neumann was a Trotskyite.

The Sraffa model, of course, includes non-produced inputs other than labor. "Land" is the title of Chapter 11 of Sraffa's book. I have attempted to explain some of the points in this chapter here and here. Heinz Kurz, Neri Salvadori, and Bertram Schefold are just some of the economists who have contributed to the literature building on Sraffa's analysis of land.

To address another Rowe misconception, Sraffians have also analyzed heterogeneous labor. In fact, "Heterogeneous Labor" is the title of Chapter 7 of Ian Steedman's book, Marx After Sraffa. I have an example with heterogeneous labor here.

The bit about time being an input in Sraffa's model is apparently some convex combination of a lie and begging the question. Sraffa explicitly states, in the title of his book, that he is considering production processes with inputs of commodities. These commodities include seed corn, iron, pigs, and so on. Although Sraffa assumes a yearly cycle of production for convenience, time is explicitly not an input in Sraffa's model. In fact, Sraffa can be said to have proven that "capital" cannot be reduced to time. In the case of joint production without land, the technique cannot even be reduced to labor inputs applied over time. (By the way, in the first chapter in her Essays in the Theory of Economic Growth, Joan Robinson explicitly analyzes an economy in which robots are produced by robots.)

Does anybody expect Rowe to acknowledge that he has no concern whatsoever over whether what he says is true or even makes sense?

Tuesday, December 11, 2012

Krugman Promoting Zombie Horror, Not SF Futures

Paul Krugman has been writing about robots lately. He explicitly cites J. R. Hicks' incoherent and mistaken 1932 book, The Theory of Wages. This is a classic statement of the neoclassical theory of factor substitution, of the choice of technique in allocating scarce factors among alternative uses.

If I want to analyze the adoption of new technology, I turn to:

  • David Ricardo's chapter, "On Machinery", in the third edition of his book.
  • The Von Neumann model of growth, which can be read as a model in which robots produce robots.
  • The Harrod-Domar model of the warranted and natural rate of growth, along with the definition of Harrod-neutral and biased technological change.
  • Joan Robinson's models of metallic ages.
  • Kaldor's growth models of various vintages and his definition of the technical progress function.

I am in agreement with Krugman on the importance of Hicks' book in the development of the neoclassical canon. And I recognize the existence of a problem in empirically distinguishing between the choice of technique and the adoption of new technology in Kaldor's model(s) of economic growth.

Update: Matias Verengo has two posts on this topic.

Monday, December 10, 2012

Anti-Reductionism: An Example?

"There are three good reasons to think that reduction will fail on any likely development of social sciences: (1) multiple realizations of social events are likely; (2) individual actions have indefinitely many social descriptions depending on context; and (3) any workable individualist social theory will in all likelihood presuppose social facts. Each of these claims, if true, rules out reduction as defined here." -- Harold Kincaid (quoted in J. E. King (2012)).

Kincaid is arguing against strong methodological individualism. To help explicate his first reason, I want to consider a different domain, biology, and some literature crossing over between biology and computer science.

I suppose I ought to first state the reductionist theory I want to oppose: The theory of evolution can be reduced to the biochemistry of DNA.

A large body of literature explores the logical structure of reproduction, including reproduction with mutations, independently of consideration of the structure of DNA. I think of Von Neumann's work on celluar automata, which, despite the publication date of the work Burks edited, pre-dates the discovery of the molecular structure of DNA. As I understand it, Von Neumann described a structure in which a part simultaneously functions as a blueprint for the next generation and as a component that is duplicated in reproduction.

Von Neumann described a celluar automaton with many states, but his logic can be implemented in a particular celluar automata with only two states, namely Conway's Game of Life. Plausibility arguments that this celluar automata can be used to form a universal computer were available before Paul Rendell implemented a Turing machine in the game of life. Basically, one can identify mechanisms for implementing a memory and an array of gates (for example, AND, OR, and NOT). The gates apply to bits flowing across a wire, in some sense. Jacob Aron has create another interesting pattern in the game of life relevant to my thesis, namely a self-replicating creature.

Some researchers have also explored the role of mutations in self-replicating automata. As I understand it, they typically assume the existence of an assembly language for a virtual machine. One can imagine small programs being executed in parallel in some sort of common memory. One needs some way of introducing random changes in some of the instructions over time cycles and a way of rewarding successful programs with, say, more energy, in some sense.

The different artificially alive creatures in these simulations do not reside in separate protected memories. They have the capability of overwriting one another and resisting such overwriting. Some have even arranged tournaments, called core wars, in these simulations. In some sense, the literature I am referencing includes some bits of recreational mathematics.

I have never seen much more than what the literature says in the little bit of exploration of the above I have done. I did once write an implementation of Conway's Game of Life in which the rules were configurable. I was able to create crystal-like growth, but nothing as interesting as in the original game.

I have pointed to some work exploring a logic of reproduction above the level of the biochemistry of DNA. DNA is one means of instantiating this logic. I have not pointed out any other non-virtual mechanisms for instantiating this logic. I do not know if mitochondrial DNA differs sufficiently from regular DNA to count. Silicon-based life forms on other planets is a standard trope in science fiction. Apparently, Reaves et al. (2012) show the supposed discovery of arsenic-based life forms in certain California lakes has not worked out. But does this anti-reductionist argument require the actual existence of another instantiation, or merely the demonstration of the possible existence of one?

  • J. E. King (2102). The Microfoundations Delusion: Metaphor and Dogma in the History of Macroeconomics.
  • Lenski, Richard E., Charles Ofra, Robert T. Pennock, and Christoph Adaml (2003). The Evolutionary Origin of Complex Features, Nature, V. 423 (May): pp. 139-144.
  • Poundstone, William (1984). The Recursive Universe. William Morrow.
  • M. L. Reaves et al. (2012). Absence of detectable arsenate in DNA from arsenate-grown GFAJ-1 cells.
  • Thearling, Kurt and Thomas S. Ray. Evolving Multi-Cellular Artificial Life.
  • Von Neumann, John (1966). Theory of Self-Reproducing Automata (ed. by A. W. Burks).