Faustian Agents

"Two souls, alas, do dwell within this breast. The one is ever parting from the other" -– Goethe

"He [i.e., Dickens] told me that all the good simple people in his novels, Little Nell, even the holy simpletons like Barnaby Rudge [Slater comments parenthetically that this must have been Dostoevsky's description, not Dickens' -- indeed] are what he wanted to have been, and his villains were what he was (or rather, what he found in himself), his cruelty, his attacks of causeless enmity towards those who were helpless and looked to him for comfort, his shrinking from those whom he ought to love, being used up in what he wrote. There were two people in him, he told me: one who feels as he ought to feel and one who feels the opposite. From the one who feels the opposite I make my evil characters, from the one who feels as a man ought to feel I try to live my life. Only two people? I asked." -- Fyodor Dostoevsky

I have previously described agents that assess an action by ranking outcomes among a number of incommensurable dimensions. By Arrow's impossibility theorem, such an agent in general cannot have a single aggregate ranking of the outcome of actions. I was able to list all best choices for my simple example. That is, for each menu, I listed best choices, with ties being possible. (By the way, a budget constraint is a menu.) If one wants to generalize this approach, one would need to specify methods for specifying best choices when listing all possible menus by hand becomes impractical. Pairwise voting is not a good idea, since the results depend on the voting order in which pairs are compared. Furthermore, one would not want to specify one such method, but allow for many different possibilities. Ulrich Krause has done this. He calls the method for choosing out of these rankings of different aspects an agent's "character". As I understand it, he allows for these rankings to change, based on the agents experience. And so he ends up with a formal model of opinion dynamics. I don't know if or how this relates to Akerlof's identity dynamics, but, I think, that would be an interesting question to explore. References

• K. J. Arrow (1963) Social Choice and Individual Values (2nd. Edition), John Wiley & Sons.
• Ulrich Krause (2010) "Collective Dynamics of Faustian Agents", in Economic Theory and Economic Thought: Essays in Honour of Ian Steedman (ed. by J. Vint, J. S. Metcalfe, H. D. Kurz, N. Salvadori, and P. Samuelson), Routledge.
• S. Abu Turab Rizvi (2001) "Preference Formation and the Axioms of Choice", Review of Political Economy, V. 13, N. 2: pp. 141-159.
• A. K. Sen (1969) "Quasi-Transitivity, Rational Choice and Collective Decisions", Review of Economic Studies, V. 36, N. 3 (July): pp. 381-393.
• A. K. Sen (1970) "The Impossibility of a Paretian Liberal", Journal of Political Economy, V. 78, N. 1 (Jan.-Feb.): pp. 152-157.

To read:

• G. A. Akerlof and R. E. Kranton (2010) Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being, Princeton University Press.
• J. B. Davis (2003) The Theory of the Individual in Economics: Identity and Value, Routledge.
• A. Kirman and M. Teschl (2004) "On the Emergence of Economic Identity" Revue de Philosphie Économique, V. 9, N. 1: pp. 59-86
• U. Krause (2009) "Compromise, Consensus and the Iteration of Means", Elemente der Mathematik, V. 64: pp. 1-8
• I. Steedman and U. Krause (1986) "Goethe's Faust, Arrow's Possibility Theorem and the Individual Decision-Taker" in The Multiple Self: Studies in Rationality and Social Change (ed. by J. Elster), Cambridge University Press.

Stephen Williamson, Fool or Knave?

Stephen Williamson quotes Narayana Kocherlakota, apparently a very stupid person:

"Kocherlakota says this...:

'But over the long run, money is, as we economists like to say, neutral. This means that no matter what the inflation rate is and no matter what the FOMC does, the real return on safe short-term investments averages about 1-2 percent over the long run.'

Again, uncontroversial." -- Stephen Willaimson

This, of course, is false. Communities of economists exist who set their theories in historical time and dispute that money is neutral in any run. I prefer to point to Post Keynesians, but Austrian School economists satisfy these criteria also. Furthermore, economists within such schools surpassed mainstream economists in the current historical conjuncture by having pointed out the possibility of the global financial crisis before its occurrence.

I think economists should strive not to tell untruths abouts what economists believe.

Why Income Inequality Leads To Recessionary Conditions

1.0 Introduction
Apparently, some have been discussing whether the gross increased inequality in the USA is connected with the depressionary conditions we are in. So I thought I would climb on my bicycle and do some arithmetic.

I take it as a stylized fact that an increase in inequality is associated with an increase in the average and marginal propensity to save.

There's something called the Harrod-Domar model of growth. I'm not sure I've ever read Domar. I've certainly read more of Harrod than I have of Domar. So in the sequel, I refer exclusively to Harrod.

Harrod defined three rates of growth: the actual rate, the warranted rate, and the natural rate. Increased inequality can result in the warranted rate exceeding the natural rate. Since the warranted rate is unstable and the actual rate cannot long exceed the natural rate, increased inequality is likely to lead to the actual rate of growth falling below and away from the warranted rate, that is, to depressions.

2.0 Harrod's Model
Harrod's model is fairly simple, but it raises deep questions.

2.1 The Actual Rate
Along a steady state growth path, the ratio, v, of the value of capital to the value of net income is constant:

v = K/Y,

where K is the value of the capital stock, and Y is the value of net income. v is known as the capital-output ratio. Thus:

dY/dt = (1/v) dK/dt

Investment, I, is defined to be the change in the value of capital with time. Hence,

(1/Y) dY/dt = (1/v) (I/Y)

The left-hand-side of of the above equation is, by definition, the rate of growth, g, of the economy. The equality of investment and savings is an accounting definition in a model with no foreign trade and no government. Therefore,

g = (1/v) (S/Y)

Define the savings rate, s:

s = S/Y

Then, a steady state growth ratio is the ratio of the savings rate to the capital-output ratio:

g = s/v

That is, the (actual) rate of growth is the quotient of the savings rate and the capital-output ratio.

2.2 The Warranted Rate
Suppose the savings rate and the capital-output ratio are as desired by income recipients (consumers) and firms, respectively. This defines Harrod's warranted rate of growth:

g_w = s_d/v_d

where the subscripts on the right hand side stand for "desired". The warranted rate of growth is being achieved when expectations are being realized and current actions are not setting up forces to disturb current expectations.

The warranted rate of growth extends Keynes' analysis to the long period. Consider the stability of a warranted growth path. If the actual rate of growth exceeds the warranted rate, capacity will be utilized at a greater rate than firms expected. They will increase investment faster than the warranted rate, and the rate of growth will deviate from the warranted rate even more. Likewise, if the actual rate falls below the warranted rate, firms will cut back on investment since the plans upon which their investment was made are not being realized. Hence, the warranted rate is unstable.

Harrod suggested that this instability of the warranted rate is more like an inverted flat-bottomed bowl than a knife-edge.

2.3 The Natural Rate
Suppose the labor force is initially fully employed. Let n be the rate of growth of the labor force:

n = (dL/dt)/L

Define the value of output produced per employed worker:

f = Y/L

Harrod-neutral technical change occurs when the value of output per worker grows at a constant rate, m, while the rate of profit stays unchanged:

m = (1/f) df/dt

Harrod-neutral technical progress implies that the productivity of labor is growing at the same rate in all industries.

Anyways, the following equation follows:

dY/dt = f dL/dt + L df/dt

Some algebra yields:

(1/Y) (dY/dt) = ( 1/L) (dL/dt) + (1/f) (df/dt)

The left hand side of the above equation is the rate of growth that keeps the labor force fully employed (or a constant percentage unemployed). Harrod calls this the natural rate of growth. Hence, assuming Harrod-neutral technological progress, the natural rate of growth is the sum of the rate of growth of the labor force and the rate of growth of labor productivity.

g_n = n + m

3.0 Conclusions
Notice that the determinants of the warranted rate of growth - the savings rate and the desired capital-output ratio - are taken as exogeneous constants. The determinants of the natural rate of growth - the growth of the labor force and Harrod-neutral technological progress - are also given. Hence, the warranted and natural rates can only be equal by a fluke.

Solow, following up on some work by Pivlin, suggested that the desired equality between the warranted and natural rates can be brought about by considering the capital-output ratio as a well-behaved function of the rate of interest. Divergences between the two rates can be corrected by variations in the distribution of income. This approach of neoclassical macroeconomics is exemplified in Solow's eponymous growth model, but it has been shown to be not well-founded in the Cambridge Capital Controversy.

If the warranted rate is below the natural rate, a moderate increase in the saving rate is desirable if the economy is exhibiting boom-like conditions. This would bring the warranted rate towards the actual rate of growth while still keeping it below the natural rate of growth.

Notice that when the warranted rate exceeds the natural rate, the economy must sometime fall below the warranted rate. The natural rate sets a limit which the economy cannot long exceed. Because of the instability of the warranted rate, such an economy will experience frequent and perhaps prolonged recessionary conditions. Since increased savings intensify the discrepancies between the warranted and natural growth rates under these conditions, increased savings intensify the frequency and severity of recessions. That is, increased inequality can intensify the frequency and severity of recessions.

References

• A. Asimakopulos (1991) Keynes's General Theory and Accumulation, Cambridge.
  1991
• Roy F. Harrod (1948) Towards a Dynamic Economics, Macmillan.
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.

Barnett's Fried Apples

Ingredients

4 Tablespoons butter
1 #2 can sliced apples or 2 1/2 cups fresh apple
1/8 teaspoon salt
1/4 cup sugar
Cinnamon to taste

1) Peel and core apples.

2) Melt butter in iron skillet. Add apples, salt, sugar, and cinnamon. (I'm generous with the cinnamon.)

3) Fry until soft, between low and medium heat about 1/2 hour. (Do not fry dry.)

Makes approximately 3 servings. (I like them served with pork chops.)

That You Should Listen To Mainstream Economists...

... seems often to me to be the main point of many mainstream economists these days. I deliberately don't write, "Why you should listen..." Somebody as stupid as Kartik Athreya, a PhD. with the research department of the Federal Reserve Bank of Richmond, appears to be doesn't deal in arguments. I also see this sort of babble in recent posts by Frances Woolley, and Mike Moffat. (See also Nick Rowe's comments to those posts.)

(I, of course, have read papers making points along Colander's line.)

Jeffrey Miron And Propertarian Advocacy Taught At Harvard

Jeffrey Miron teaches EC1017 at Harvard. "A Libertarian Perspective on Economic and Social Policy" is the course title, and PDFs for the lectures are available for download.

Based on the notes for the three lectures I looked at, Miron supposedly derives propertarian policy from intermediate principles (e.g., "efficiency"), with little to no data on relative magnitudes. I don't care for this approach myself, never mind the policy conclusions. He seems to mention no names. The reading list (from Spring 2009) does not include his book (which I haven't read). Perhaps Miron's experience is that Harvard students can be counted on to bring up Rawls, Karl Popper's piecemeal social engineering, Alan Haworth, and even Nozick.

"When Adam Delved And Eve Span, Who Was Then The Gentleman?"

I had associated the title of this post with the 17th century and the period of the English Civil War. I think it occurs somewhere in Christoper Hill's The World Turned Upside Down: Radical Ideas During the English Revolution. Hill's book is an account of Anabaptists, Diggers, Levellers, Muggletonians, the New Model Army, Ranters, and Quakers - a very heady and confusing mix. So I was startled yesterday to read the phrase in Crispin: The Cross of Lead. This is a Newberry-prize winning children's book, by Avi. It is set in England in the 14th century. I think it conveys a good idea of the drudgery and isolation of village life at the time; the seemingly unchangable hierarchy; and the bustle, confusion, and filth of a city before modern plumbing. I also like that Christianity is presented as a form of life, a language that all we see cannot but help using. So is Avi's use of the phrase an anachronism? Hill may reference it, but, if so, the people of his time were harking back to a previous one. Apparently, the phrase is associated with John Ball, the leader of the 1381 Peasants’ Revolt. I know nothing about the Peasants’ Revolt, although Hill does refer to it in one line. But John Ball does appear in Avi’s book. Crispin, our thirteen-year old hero, overhears him conspiring. John Ball says:

"...that no man, or woman either, shall be enslaved, but stand free and equal to one another. That all fees, obligations, and manorial rights be abolished immediately. That land must be given freely to all with a rent of no more than four pennies per acre per year. Unfair taxes must be abolished. Instead of petty tyrants, all laws shall be made by consent of a general commons of all true and righteous men. Above all persons, our lawful king shall truly reign, but no privileged or corrupt parliaments or councilors. The church, as it exists, should be allowed to wither. Corrupt priests and bishops must be expelled from our churches.. In their place will stand true and holy priests who shall have no wealth or rights above the common man..."

Update: I've learned a new vocabulary word: A Jacquerie is a peasants' revolt, named after the French peasants' revolt of 1358.

Infinities Of Infinities

1.0 Introduction

This is mathematics, not economics. It is meant to be an introduction to how abstract mathematicians can be.

2.0 Some Definitions for Set Theory

Two sets are the same size if and only if they can be put into a one-to-one correspondence with each other.

A set S₁ is bigger than the set S₂ if and only if:

• A subset of S₁ can be put into one-to-one correspondence with S₂, and
• S₂ cannot be put into one-to-one correspondence with S₁.

A set is countably infinite if and only if it can be put into one-to-one correspondence with the set of natural numbers N = {0, 1, 2, ...}. (The integers and the rational numbers are both countably infinite.)

The power set P(S) formed from the set S is the set of all subsets of S. For example, the power set for the set {a, b} contains four elements:

P( {a,b} ) = {S | S ⊂ {a, b}.} = { ∅, {a}, {b}, {a, b} }

3.0 A Theorem

Theorem For all sets S, the power set P(S) is bigger than the set S.

Proof: First, show that a subset of P(S) can be put into one-to-one correspondence with S. Consider the set of singletons:

{ {a} | a is an element of S }.

Since each singleton {a} is a subset of S, the set of all singletons is a subset of P(S). And the set of all singletons maps one-to-one to S.

Next, show, by a proof by contradiction, that P(S) cannot be put into one-to-one correspondence with S. Suppose that there exists a one-to-one function f that maps S into P(S).

Notice that, for all a ∈ S, f(a) is a subset of S. For any given a in S, either

a ∈ f(a)

or

a ∉ f(a).

Define the set T to be the set of all elements in S that map under f to a set not containing themselves:

T = { a | a ∈ S and a ∉ f(a)}

Since f is one-to-one and T is a (possibly empty) subset of S, there exists, by hypothesis, an element b in S such that

f(b) = T.

Now consider whether or not

b ∈ T.

Suppose true. But, by the definition of T as the set of elements of S that are not elements of the subset of S that they map to, b cannot be in f(b), that is, T. But, if b is not in f(b), by the definition of T, b must be in T. So either way yields a contradiction. Thus, no such b can exist.

So I have shown that there does not exist an element b in S that maps under f to T. Yet T is in P(S). Thus, f cannot be one-to-one. Which was to be demonstrated.

4.0 Applying the Theorem to the Set of Natural Numbers

An interesting property of the above proof is that it applies to both finite sets and infinite sets. So start with N, the set of natural numbers. N contains an infinite number of elements. But, by the theorem, P(N), the set of all subsets of the natural numbers, is a set containing a bigger infinity. One can go on to form a set of infinite sets, each with a bigger size infinity:

U₀ = { N, P(N), P(P(N)), ..., Pⁿ(N), ...}

(Under the Zermelo Frankel axioms for set theory, the elements of a set do not need to all be of the same "type".) One can repeat the process of forming a sequence of power sets:

U₁ = { U₀, P(U₀), P(P(U₀)), ..., Pⁿ(U₀), ...}.

One can even imagine constructing a power set of all these difference size infinite sets in this sequence of sequences of sets:

P( { U₀, U₁, U₂), ...} )

The definitions of infinite sets need not stop here.

4.0 Conclusion
I don't find the above hard to follow if I think of it as merely a matter of syntactic manipulation of symbols. Do I have a clear idea of these infinities of different size infinities after every point in this sequence of definitions? Does anybody? This is not so clear to me.

Reference

• Paul R. Halmos (1960) Naive Set Theory, Springer Verlag

Onieda-Like Community Near Stroud, In Gloucestershire?

Martin Gardner once received a letter referring to "an Oneida-like community near Stroud, in Gloucestershire". The topic of the letter was something else, on visualizing four-dimensional space. Can anybody provide me with more information on this community?

Full Unemployment

I find amusing the political slogan with which I title this post. We want the engineers to do their job in applying control theory to stepping motors, in creating Artificial Intelligences, in developing techniques of information management, etc. such that nobody need work out of necessity. Maybe in some future day, machinery will produce all we need, including more machinery. When the economic problem is solved:

"Man will be faced with his real, his permanent problem - how to use his freedom from pressing economic cares, how to occupy the leisure, which science and compound interest will have won for him, to live wisely and agreeably and well." -- John Myanard Keynes (1930)

Marx and Engels envision a post-capitalist society:

"Where nobody has one exclusive sphere of activity, but each can become accomplished in any branch he wishes, society regulates the general production and thus makes it possible for me to do one thing today and another tomorrow, to hunt in the morning, fish in the afternoon, rear cattle in the evening, criticize after dinner, just as I have a mind, without ever becoming hunter, fisherman, shepherd or critic. -- Karl Marx (1947, p. 22)

Bruce Sterling (1989) imagines that, in such a world, one will cultivate ones taste for "The Beautiful and the Sublime". At any rate, in this pleasant world of tomorrow, all will be able to devote themselves to great cooking, fostering social relationships, art, or whatever one may choose.

Curiously enough, the classical tradition in economics, as exemplified, for example, in Sraffa or Von Neumann, provides tools for analyzing how prices might be formed in a post-scarcity world. For example, Joan Robinson, in her first essay in (Robinson 1962) has a section titled "A model for the future" with a subsection on "The Robots". This is a model of a (maybe impossible) capitalist economy. In my version, all production is carried out in automated factories, and these factories are owned by firms traded on a stock exchange. Everybody owns shares, and the trading of these shares sets up a tendency torwards a uniform rate of profits.

I have described before some formulation of a price system consistent with this institutional set up. For now, I want to describe prices when the managers of each firm in an industry have chosen a process for producing the firm's output. As usual, I assume, for simplicity that all processes require the same time to operate, say, a year. Inputs must be purchased at the beginning of the year, and outputs become available at the end of the year. A reference set of prices satisfies the following system of equations:

p A β = p B

where

• A is a square matrix; a_i,j is the quantity of the ith commodity used as input when the jth process is operated at a unit level.
• B is a square matrix; b_i,j is the quantity of the ith commodity produced as output when the jth process is operated at a unit level.
• p is a row vector of prices; p_i is the price of the ith commodity.
• (β - 1) is the rate of profits.

This formulation allows for robots to last for more than one year. The quantity of a dated robot enters as an input, and the output includes a robot one year older, as well as whatever other outputs are produced by that process. The use of such robots is a special case of the more general model of joint production encapsulated in the above system of equations.

Various conditions must be imposed on the coefficients of production A and B to ensure a solution simultaneously exists for prices and the dual problem of the choice of technique. Von Neumann, in fact, assumes that each commodity is either used as an input or produced as an output in a poisitive amount in each process. Joan Robinson assumes the existence of "some standard physical elements (say, nuts and bolts) that enter into the production both of robots and of salable goods." But I do not want to discuss more of the mathematics in this post.

References

• D. G. Champernowne (1945-1946) "A Note on J. v. Neumann's Article on 'A Model of Economic Equilibrium'", Review of Economic Studies, V. 13, N. 1: pp. 10-18.
• John Maynard Keynes (1930) "Economic Possibilities for our Grandchildren", in Essays in Persuasion, W. W. Norton & Company
• Karl Marx and Frederick Engels (1947) The German Ideology: Parts I & III, International Publishers
• Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan.
• Piero Sraffa (1960) , Cambridge University Press.
• J. v. Neumann (1945-1946) "A Model of General Economic Equilibrium", Review of Economic Studies, V. 13, N. 1: pp. 1-9.
• Bruce Sterling (1989) Crystal Express, Ace Books

Nortz's Johnny Cake

Ingredients

1/4 cup sugar
1/3 cup shortening
1 beated egg
1 cup sour milk
1 teaspoon baking soda
1 teaspoon baking powder
1 cup flour
1 1/2 cup cornmeal
1/2 teaspoon salt

1) Mix in above order, stirring thoroughly after adding each ingredient. Bake about 1/2 hour at 400 F.

2) Serve sliced with applesauce or maple syrup.

Makes approximately 10 servings. I usually make a double recipe when making my great-grandmother's Johnny cake.

Phenomenology

"One of the embarrassing dirty little secrets of economics is that there is no such thing as economic theory properly so-called. There is simply no set of foundational bedrock principles on which one can base calculations that illuminate situations in the real world." -- Brad DeLong

My title does not refer to an approach in continental philosophy associated with Husserl and Heidegger. Rather, I refer to a term used in physics and engineering by practitioners who know they are not trying to develop models derived from fundamental laws, but only modeling the phenomena.

I find it of interest that Brad DeLong has recently described economics as phenomenology. A noted "rocket scientist" on Wall Street came to the same conclusion:

"The techniques of physics hardly ever produce more than the most approximate truth in finance because 'true' financial value is itself a suspect notion. In physics, a model is right when it correctly predicts the future trajectories of planets or the existence and properties of new particles, such as Gell-Mann's Omega Minus. In finance, you cannot easily prove a model right by such observation. Data are scarce and, more importantly, markets are arenas of action and reaction, dialectics of thesis, antithesis, and synthesis. People learn from past mistakes and go on to make new ones. What's right in one regime is wrong in the next.

As a result, physicists turned quants don't expect too much from their theories, though many economists naively do. Perhaps this is because physicists, raised on theories capable of superb divination, know the difference between a fundamental theory and a phenomenological toy, useful though the latter may be. Trained economists have never seen a really first-class model. It's not that physics is 'better', but rather that finance is harder. In physics you're playing against God, and He doesn't change his laws very often. When you've checkmated Him, He'll concede. In finance, you're playing against God's creatures, agents who value assets based on their ephemeral opinions. They don't know when they've lost, so they keep trying." -- Emanuel Derman (2004) My Life as a Quant: Reflections on Physics and Finance, John Wiley & Sons.

I think one can read intimations of Soros' reflexitivity or Joan Robinson's historical time in the above quote. Derman is even more direct about a Post Keynesian concept elsewhere:

"Slowly it began to dawn on me that what we faced was not so much risk as uncertainty. Risk is what you bear when you own, for example, 100 shares of Microsoft - you know exactly what those shares are worth because you can sell them in a second at something very close to the last traded price. There is no uncertainty about their current value, only the risk that their value will change in the next instant. But when you own an exotic illiquid option, uncertainty precedes its risk - you don't even know exactly what the option is currently worth because you don't know whether the model you are using is right or wrong. Or, more accurately, you know that the model you are using is both naive and wrong - the only question is how naive and how wrong." -- Emanuel Derman (2004)

Jacob Schwartz (9 January 1930 - 2 March 2009)

Jacob T. Schwartz was a mathematician at the Courant Institute of Mathematical Sciences at New York University. He once gave a series of lectures on mathematical economics, published as Lectures on the Mathematical Method in Analytical Economics, Gordon and Breach (1961). This book, coming out a year after Sraffa's work, seems to very little known. Its findings parallel Sraffa's in many ways:

"Our interest...will...be...in the use of the input-output model as a framework for ...abstract economic analysis." (p. 8)

"If each time labor appears as an input in production we replace this input by the corresponding real wage bill, we come to a hypothetical situation in which the only inputs required for the production of commodities are other (non-labor) commodities. Thus we may, if it is convenient for one or another theoretical purpose, consider our model to refer to a self-enclosed world of material commodities, produced out of each other with no additional input." (p. 10)

"The proper conclusion at this point is that the rate of profit ρ is not successfully determined by the Walrasian theories from considerations of production coefficients, utility functions, and so forth. What our analysis shows, in fact, is that the determination of the rate of profit is not purely a question of economics at all, but is rather a social-political question involving, among other things, union-management relations, pressures, and counterpressures, etc. Thus an initial skepticism about classical equilibrium analysis is justified. What this analysis aims to give us is a set of prices. But all the price-ratios are already determined by a small part of the theory, to wit by the competitive equality of profit rates. All that remains to be determined on the score of prices, is the rate of profit - but, as we have just seen, the Walrasian determination of this rate is questionable... What are determined more successfully are the amounts of production - but this is more a humble matter of consumption habits at given prices than a highly recondite matter of consumption schedules at a variety of hypothetical prices." (pp. 196-197)

"As our analysis in Lecture 16 shows, as long as we assume a fixed scheme of production the Keynesian conclusion that wage cuts by lowering wage-generated commodity demand must lower demand for labor is inescapable. The neoclassical contention thus depends on the possibility of shifts in the production scheme; a conclusion which the neoclassicist would be the first to emphasize, since the whole apparatus of neoclassical theory, revolving about the notion of marginal product accruing to an increment of each input facor, does in fact center on an analysis of variations in production. This means that the equilibrium analysis of Lecture 16 has come to such distinctly Keynesian conclusions as it has only by assuming away the basis for the neoclassicist's argument. At the present point, therefore, we shall attempt to generalize the analysis of Lecture 16 to include the possibility of shifts in the production scheme, hoping to estimate the extent to which such shifts are likely to affect our earlier conclusions." (p. 239)

"We may at this point remark once more that our analysis of prices shows that even in the framework of the present general model [with a choice of technique] price ratios are determined up to a single parameter from the conditions of production. As we have emphasized in the final paragraph of Section 1, Lecture 3, this conclusion constitutes strong presumptive evidence against theories which attempt to tie prices to consumer demand. More generally, we see that by allowing variation in the scheme of production, we in fact introduce no changes in the fixed-matrix Leontief model other than to make the Leontief matrices dependent on the [rate of profits]." (p. 248)

I prefer Sraffa's book partly on the basis of style.

Quantity Flows For Structural Dynamics

1.0 Introduction
This post presents an example of a model of structural economic dynamics. I consider what quantity flows would arise for an economy in which agents make decisions in which the economy smoothly reproduces. The solution for this exercise turns out to be dynamically unstable in the special case I use for illustration. I think this means that, if I solve this special case in a future post for one way of setting out the price system, the solution for prices will be stable. The model presented in this post illustrates the difficult discovery problems that are solved in successful economies.

2.0 Technology
This economy consists of two sectors. In the first sector, labor produces means of production with existing means of production. In the second sector, labor produces means of consumption with existing means of production. (I use steel as as a synecdoche for means of production and corn for means of consumption.) The technique in use in both sectors exhibits Constant Returns to Scale (CRS). Only circulating capital is modeled; the means of production are entirely consumed in producing the output. Table 1 shows the coefficients of production for the technique in use during the t-th year.

Table 1: The Technology

	Steel Industry	Corn Industry
Labor	a0,1(t) person-years	a0,2(t) person-years
Steel	a1,1(t) tons	a1,2(t) tons
Outputs	1 ton steel	1 bushel corn

The technique improves each year. That is, each coefficient of production decreases at a constant rate of 100 c_i,j percent per year:

[a_i,j(t) - a_i,j(t + 1)]/a_i,j(t) = c_i,j

The above difference equation can be solved in closed form. The coefficients of production evolve as:

a_i,j(t) = a_i,j(0) (1 - c_i,j)^t

A more complex formulation might have non-constant percentage rates of decrease in the coeffients of production. For example, the percentage rate of decrease might be larger if the level of output of an industry was larger. Then one would be modeling "learning by doing" or endogenous growth, following in the tradition of Nicholas Kaldor and Kenneth Arrow. (Mainstream economists would cite Paul Romer's confused balderdash.)

3.0 Conditions for Smooth Reproduction
Let q₁(t) and q₂(t) be the tons of steel and the bushels of corn, respectively, produced as output and available at the end of the t-th year. I want to consider the case in which the labor force is always fully employed, the proportions in which output is produced always turns out to be appropriate, and no excess capacity is ever created.

The gross output of corn each year is divided up between the workers and the capitalists and then consumed. The gross outputs of steel and corn in a given year determine, along with the coefficients of production, how much steel should have been produced in the previous year:

q₁(t - 1) = a_1,1(t) q₁(t) + a_1,2(t) q₂(t)

The amount of labor employed in the t-th year is:

L(t) = a_0,1(t) q₁(t) + a_0,2(t) q₂(t),

where L(t) is the person-years of labor employed. In a general formulation, one might model the number of workers growing each year, but with increased productivity being taken partly in the form of decreased working hours per worker. For simplicity, I here model the labor force as a given constant:

L(t) = L^*

The above equations specify a dynamic system. An initial condition needs to be specified for any solution path to be completely determined. I take the initial ratio of employment in the two sectors as a given parameter:

a_0,1(0) q₁(0)/a_0,2(0) q₂(0) = h

The model can be simplified by expressing one quantity flow in terms of other by use of the condition that labor is fully employed. Some algebraic manipulation yields a single difference equation for the output of steel:

q₁(t) = [a_1,2(t) L^* - a_0,2(t) q₁(t - 1)]/d(t),

where

d(t) = [a_0,1(t)a_1,2(t) - a_0,2(t)a_1,1(t)]

If the coefficients of production were constant, the above would be a linear difference equation. If I recall my mathematics correctly, linear systems either blow up; decay to an equilibrium; or, for coefficients meeting an exact balance, generate a constant wave.

4.0 The Solution of a Special Case
I tried a numerical experiment to increase my understanding of this dynamical system. Accordingly, I chose some specific values for the model parameters. Table 2 gives the initial coefficients of production. The difference equation for gross steel outputs is simplified in that the coefficients of production in a sector decrease at the same constant rate. I chose the following rates of decrease:

c_0,1 = c_1,1 = 1/20

c_0,2 = c_1,2 = 1/40

Let the labor force be unity:

L^* = 1

Finally, I carefully specified an initial condition:

a_0,1(0) q₁(0)/a_0,2(0) q₂(0) = 0.22335983

Table 2: The Initial Technology

	Steel Industry	Corn Industry
Labor	a0,1(0) = 1	a0,2(0) = 1
Steel	a1,1(0) = 1/10	a1,2(0) = 1/5
Outputs	1 ton steel	1 bushel corn

One can easily step through the first few years of the solution, thereby obtaining the start of a series for q₁(t) and q₂(t).The solution is dynamically unstable. I carefully chose the initial condition to get six years before the solution blows up. For the first five years, the output of steel grows over 3% and the output of corn grows over 14 1/2%, for a constant labor supply. This set of priorities is the reverse of what was typically achieved in no-longer actually existing socialism. When Imre Nagy, for example, tried to put Hungary on a new course, he was deposed. The distribution of labor, shown in Table 2, is not realistic for a developing capitalistic economy either. In practice, the labor force becomes steadily less concentrated in producing means of consumption and more in producing means of production. Still, I think, this model with a better choice of parameters and perhaps some generalizations can be quite interesting.

Figure 1: Dynamic Distribution of the Labor Force

References

• Karl Marx (1885) Capital, Volume 2
• Luigi L. Pasinetti (1977) Lectures on the Theory of Production, Columbia University Press
• Luigi L. Pasinetti (1983) Structural Change and Economic Growth: A Theoretical Essay on the Dynamics of the Wealth of Nations, Cambridge University Press
• Luigi L. Pasinetti (1993) Structural Economic Dynamics: A Theory of the Consequences of Human Learning, Cambridge University Press

To read:

• Dale W. Jorgenson (1960) "A Dual Stability Theorem", Econometrica, V. 28, N. 4 (October): pp. 892-899

Judt On The Influence Of The Austrian School

I continue to find writers characterizing Austrian school economists as influential.

I think some might quarrel with this description of the influence of the Austrian school on Chicago:

"We are the involuntary heirs to a debate with which most people are altogether unfamiliar. When asked what lies behind the new (old) economic thinking, we can reply that it was the work of Anglo-American economists associated overwhelmingly with the University of Chicago. But if we ask where the 'Chigago boys' got their ideas, we shall find that the greatest influence was exercised by a handful of foreigners, all of them immigrants from central Europe: Ludwig von Mises, Friedrich Hayek, Joseph Schumpeter, Karl Popper, and Peter Drucker." -- Tony Judt (2010) Ill Fares the Land, Penguin Press, pp. 97-98

I don't think differences in details (e.g., aggregation in economic models) adequately refutes Judt's point.

Judt does read, for example, Hayek as more nuanced than some of his followers:

"The intellectual refugees - and especially the economists among them - lived in a condition of endemic resentment toward their uncomprehending hosts. All non-individualist social thought - any argument that rested upon collective categories, common objectives or the notion of social goods, justice, etc. - aroused in them troubling recollections of past upheavals... Men like Hayek or von Mises seemed doomed to professional and cultural marginality. Only when the welfare states whose failure they had so sedulously predicted began to run into difficulties did they once again find an audience for their views: high taxation inhibits growth and efficiency, government regulation stifles initiative and entrepreneuship, the smaller the state the healthier the society and so forth.

Thus when we recapitulate conventional clichés about free markets and western liberties, we are in effect echoing - like light from a fading star - a debate inspired and conducted seventy years ago by men born for the most part in the late 19th century...

It is perhaps worth noting here that even Hayek cannot be held responsible for the ideological simplifications of his acolytes. Like Keynes, he regarded economics as an interpretive science, not amenable to prediction or precision. If planning was wrong for Hayek, this was because it was obliged to base itself on calculations and predictions which were essentially meaningless and thus irrational. Planning was not a moral misstep, much less undesirable on some general principle. It was simply unworkable - and, had he been consistent, Hayek would have acknowledged that much the same applied to 'scientific' theories of the market mechanism...

In the United States, among a younger generation of self-confident econometricians (a sub-discipline of whose bostful scientificity both Hayek and Keynes would have had much to say), the belief that democratic socialism is unachievable and has perverse consequences has become something close to a theology. This creed has attached itself to every effort to increase the role of the state - or the public sector - in the daily lives of American citizens." -- Tony Judt (2010): pp. 102-104

Orthodox Economists As Knavish Lickspittles

Bill Mitchell says:

"The mainstream economists hide behind lies. Most of the time they claim their policy recommendations are derived from economic theory. The reality is that they are not and economists lie and obsfucate.

There are many situations where strident policy suggestions – like the austerity packages – cannot be based on the economic theory that they are associated with – on the theories that economists use to give an air of authority and legitimacy to what are otherwise demands based on their blind ideology.

Unfortunately, the public is not in a position to judge and get swamped by the arrogance of economists..."

The arrogance of orthodox economists plays out in many ways. Philip Mirowski, for example, notes:

"But economists could not begin to discuss the major difference between 1929 and 2008: this time around, professional economists had played a much larger role in producing the conditions leading to systemic breakdown, from theorizing the financial innovations and staffing the financial institutions to justifying the deconstruction of regulatory structures held over from the last Great Depression. The profession did not entirely succeed in distracting public attention from that fact, either." -- Philip Mirowski, "The Great Mortification: Economists’ Responses to the Crisis of 2007–(and counting)", The Hedgehog Review, (Summer 2010)

And there is the matter of funding of inconvenient researchers. So we see Mirowski writing, "My home institution declined to provide any support for this research." And Jacob Hacker and Paul Pierson write something similar:

"The authors received no financial support for the research and/or authorship of this article."

Greg Mankiw seems always willing to demonstrate that he is a varlet. In his post labeled, "The Root Cause of the Crisis", he kowtows to another fool:

"According to Raghu Rajan: Skill-biased technological change, followed by ill-advised policies."

If an economist were honest, he could hardly continue to cite skill-biased technological change as a cause income distribution in the United States.

Simple Pepper Steak

Ingredients

3 Tbsps olive oil
1 sliced onion
2 sliced (green & red?) peppers
1 lb sandwich steak
1/2 tsp. salt
1/4 tsp. black pepper
3 Tbsps (ginger-flavored?) soy sauce

1) Fry sliced peppers and onions in olive oil over medium high heat about 7 minutes. (Variant: add chopped garlic clove.) Drain oil and lower heat.

2) Meanwhile, cut meat into 1 inch squares. Season with salt and pepper.

3) Add beef to fry pan. (Variant: consider adding additional spices, e.g. 1 tsp. thyme leaves.) Add soy sauce. Cook on low to medium about 10 minutes, stirring frequently.

4) Serve over boiled white rice.

Makes 2 or 3 servings

Congressional Testimony on Building a Science of Economics

The United States House of Representatives has a Committee on Science and Technology, with a Subcommittee on Investigations and Oversight. On Thursday, 20 July, they heard testimony about macroeconomics from Robert Solow, Sidney Winter, Scott Page, David Colander, and V. V. Chari. You can download the hearing charter, prepared statements, etc. I guess V. V. Chari's role is to defend the orthodox.

'Libertarian' Used Correctly

"Less World! More Bank!"

I have been reading Phil Edwards' 'More Work! Less Pay!' Rebellion and Repression in Italy, 1972-7 (Manchester University Press, 2009). He occasionally uses the word 'libertarian', for example:

"the group re-emerged within the 'area' as the Collettivi Politici Operai (CPO; 'Workers' Political Collectives'), opening itself to left-libertarian as well as Leninist influences." -- Phil Edwards (p. 69)

and in translating:

"The first, numerically in the majority, is the 'creative' wing, libertarians with radical leanings ... These are the 'small-a' autonomists, who at one time or another fight for a 'better quality of life' ... The second large strand is that of the professors, the intellectuals, the theorists of the message ... The third strand, finally, is that of the 'capital-A' autonomists, or Autonomia operaia organizzata ['Organised Workers' Autonomy']" -- M. Monicelli, L'ultrasinistra in Italia 1968-1978 (1978, Phil Edwards' translation)

Apparently, the custom of street performances at protests emerged from the area of autonomia. Antonio Negri was a member of the CPO. Perhaps activists in Detroit might consider the establishment of social centers (centri sociali) by squatting in abandoned buildings.

And Every Stinking Bum Should Wear A Crown

Why so much inequality in the United States? I have been reading Hacker and Pierson (2010). (I haven't yet read the commentaries, available for the moment.) I think I have previously made many of their points, as shown below. Hacker and Pierson present some striking graphs taken from work by Piketty and Saez. I reproduce two.

Figure 1: Richest 1 Percent's Share of National Pretax Income (Excluding Capital Gains) (Based on Piketty and Saez)

Figure 2: Average Actual Tax Incidence for Top Incomes (Based on Piketty and Saez (2007))

Anybody who still thinks the mainstream story of skills-biased technical change is a reasonable hypothesis is a feckless fop.

Given contract law and property law, government cannot leave the economy to itself. Policy has been driving increased inequality.

Another driver of increased inequality is a change in ideas and social norms. These include faulty ideas on corporate governance, incorrect theories of factor markets, and performative models of finance.

How did ideas that never had sound empirical and theoretical backing become dominant? Part of the explanation must be a propaganda campaign by vile reactionaries, including the suppression of progress in explaining actually existing capitalist economies.

There is an aspect of cumulative causation here. A smaller government is associated with more inequality. And more inequality is associated with the rich and powerful promoting an exploded and evil ideology.

Increased inequality also leads to failures in aggregate demand. A steadily growing economy needs a certain balance to be maintained. The consequences of the failure to maintain such a balance since the end of the post war golden age are all around us.

Reference

Jacob S. Hacker and Paul Pierson, "Winner-Take-All Politics: Public Policy, Political Organization, and the Precipitous Rise of Top Incomes in the United States", Politics & Society, V. 38 N. 2 (2010): pp. 152-204

Elsewhere

• Cosma Shalizi states a simple ergodic theorem.
• Cosma Shalizi reviews Yves Smith's Econned: How Unenlightened Self-Interest Undermined Democracy and Corrupted Capitalism.
• Victoria Chick and Ann Pettifor argue that the United Kingdom needs more government spending.
• James Galbraith affirms that "There is no economic justification for deficit reduction."
• Updated: David Harvey gives an animated lecture on the causes of the global financial crisis. I like the use of Volume 2 of Marx's Capital.

But Maybe Everything That Dies Someday Comes Back

I think the following three events, at least, were important in the development of the post (second world)-war model of development:

• The 1942 issuing of the Beveridge Report
• The 1944 Bretton Woods conference
• The April 1955 Bandung conference

Shouldn't the documents issued by such conferences and the whole Beveridge Report now be online somewhere? The first 20 pages of the Beveridge Report are here. Extracts from those pages and from Part V are here (mirrored).

Despite the post title, I don't think a Fordist accumulation regime can be recreated. But we need a new mode of regulation with new institutions and transformative events to set up a system that works. The current one doesn't.

Impact of Capital Controversies On Labor Economics

I think some with some exposure to economics might not be impressed by the Cambridge Capital Controversy because of the abstractness of capital. "Capital" can refer to finance, and it can refer to the means of production. And even if one thought that interest rates were determined by supply and demand, what quantity would be supplied or demanded? Loanable funds? Savings? One might expect capital theory to be complicated, even in the view of the defenders of mainstream theory. So why, some might rationalize, should one be surprised by aggregation problems?

I like to emphasize the labor market. This market might seem more concrete to many. (This is one of the illusions created by competition.) Consider cases in which firms have adapted their capital equipment and production techniques to the prices prevailing on both product and factor markets. A logical implication of capital reversing is that, given the level of output, such firms employ more workers at a higher wage. (I have deliberately worded the above to avoid saying, "Increasing wages lead to greater employment" - which is a claim about dynamics.) The sort of example I have in mind doesn't seem to depend on aggregating labor. I often motivate discussion of these matters with the introductory neoclassical textbook story on minimum wages, which is theoretically unfounded and only taught by bad economists. (Nose counting as a refutation of the above statement is a fallacy.)

I realize lots of literature backs up my position; I am not being original. I like to cite Graham White (2001) and Tony Aspromourgos (2001). I recently stumbled upon another economist who forcefully states a similar position.

John Weeks has been updating his 1989 book, A Critique of Neoclassical Macroeconomics. Two parts of the update-in-progress are currently available online: part I, part II. I extract some random quotes from the relevant chapter in part II:

"Reswitching implies an unexpected conclusion: theory tells us that in general capitalists will not necessarily select more labour-intensive techniques when wages fall.

This result is a potential disaster for the neoclassical macro model and its parable about real wages and employment."

"In the introduction to this book a quotation from The Times was cited, which ventured the assertion that '...few economists would argue with the general proposition that lower real wages will mean higher employment...' If it refers to theoretically competent neo-classical economists, this statement is false."

"One can conclude that when referring to actual economic outcomes, there is no theoretical basis for the generalization that lower real wages will stimulate more employment. The opposite conclusion has equal theoretical merit. The neoclassical parable, upon which so many policy prescriptions are based, is a false guide to real economies."

References

• Tony Aspromourgos (2001) "Is Labour Cheapening a Means to Reducing Involuntary (Labour) Unemployment?", History of Economics Review, V. 34: (Summer) pp. 7-18
• John Weeks (1989) A Critique of Neoclassical Macroeconomics
• Graham White (2001) "The Poverty of Conventional Economic Wisdom and the Search for Alternative Economic and Social Policies", The Drawing Board: An Australian Review of Public Affairs, V. 2, N. 2 (November): pp. 67-68.

Neoclassical Economics Overthrown A Half-Century Ago

Today the 50-year anniversary of the publication of Piero Sraffa's The Production of Commodities by Means of Commodities is being celebrated at Queen's College, Cambridge.

A Political Pamphlet

How many of you have worked through Paul Lafarge’s The Right To Be Lazy? Isn’t that against the spirit of the piece?

Manifestations of Sraffa Effects in General Equilibrium Models?

A Strange Attractor Arises From The Lorenz Equations

I think reswitching, capital reversing, and Sraffa effects may be the source of both dynamic and structural instabilities in General Equilibrium models. I am not so much interested in dynamics of a tâtonnement process in some sort of no-time before the beginning of time in the Arrow-Debreu model of intertemporal equilibrium. Rather, I find more of interest the dynamics of spot prices in models of temporary equilibrium.

My claim that the Cambridge Capital Controversy can be drawn on for examining the dynamics of certain economic models is not original. Barkley Rosser (1983) related reswitching to a cusp catastrophe. A cusp catastrophe, as I understand it, is a kind of structural instability. Overlapping Generation Models (OLGs) provide my favorite neoclassical closure of Sraffian production models. Saverio Fratini (2007) has investigated cases in which reswitching gives rise to multiple stationary state equilibria in OLGs. I've convinced myself that whether multiple equilibria are associated with a "normal" or "perverse" switch point can depend on the form of the utility functions in OLGs.

An issue arises in showing that Sraffa effects are associated with the appearance of complex and chaotic dynamics in models of General Equilibrium. Researchers have already established that complex dynamics can arise in such models anyways, including OLGs, for other reasons. For example, John Geanakoplus states:

"Grandmont ..., following related work of Benhabib and Day ... and Benhabib and Nishimura ..., gave a robust example of a one-commodity, stationary economy ... giving rise to a three-cycle... Of course a cycle ... is also a cyclical equilibrium for the economy, hence there are robust examples of economies with cycles of all orders." -- John Geanakoplos (2008)

Geanakoplos is relying on Theorem 1 in Li and Yorke (1975). In the references, I give sources for identifying literature exploring the dynamics of General Equilibrium models, including OLGs, independently of considerations raised in the CCC.

The consequences of modeling the economy as potentially exhibiting complex non-linear dynamics are far reaching. Rajiv Sethi, in a series of blog posts, has pointed out some implications of a serious concern with non-linear dynamics for mainstream macroeconomics:

• An Outsider's View of Modern Macroeconomics
• On the Consequences of Nominal Wage Flexibility
• On Buiter, Goodwin, and Nonlinear Dynamics
• On Rational Expectations and Equilibrium Paths

I think one can show that Sraffa effects can give rise to complex dynamics in OLGs, even with the knowledge that OLGs can produce chaotic dynamics otherwise. I need to find an OLG model with perhaps a single good being produced in each period and in which complex dynamics do not arise for the specified form of the utility function. Then one should alter the production model to be a two or three-good reswitching example. Finally, one should establish complex dynamics arise in the resulting models. Even if this strategy is not successful, one pursuing it will have to explore and understand already existing models with complex dynamics.

References

• Jess Benhabib (2008) "Chaotic Dynamics in Economics", in The New Palgrave Dictionary of Economics (Ed. by S. N. Durlauf and L. E. Blume), 2nd edition, Palgrave Macmillan
• Jess Benhabib (editor) (1992) Cycles and Chaos in Economic Equilibrium, Princeton University Press
• Saverio M. Fratini (2007) "Reswitching of Techniques in an Intertemporal Equilibrium Model with Overlapping Generations", Contributions to Political Economy, V. 26: pp. 43-59.
• John Geanakoplos (2008) "Overlapping Generations Model of General Equilibrium", in The New Palgrave Dictionary of Economics (Ed. by S. N. Durlauf and L. E. Blume), 2nd edition, Palgrave Macmillan
• John Guckenheimer and Philip Holmes (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag
• Yijun He and Willam A. Barnett (2006) "Existence of Bifurcation in Macroeconomic Dynamics: Grandmont was Right"
• Tien-Yien Li and James A. Yorke (1975) "Period Three Implies Chaos", American Mathematical Monthly, V. 82, N. 10 (Dec.): pp. 985-992
• J. Barkley Rosser, Jr. (1983) "Reswitching as a Cusp Catastrophe", Journal of Economic Theory, V. 31: pp. 182-193
• Paul A. Samuelson (1958) "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money", Journal of Political Economy, V. 66, N. 6 (December): pp. 467-482
• Robert Shiller (1978) “Rational Expectations and the Dynamic Structure of Macroeconomic Models: A Critical Review”, Journal of Monetary Economics, V. 4: pp. 1-44.

Good For Me, Bad For You

I still hope to publish my critique of Austrian business cycle theory (most recent public version). In my introduction, I need to answer the question why anybody should care about criticism of Austrian business cycle theory or Austrian economics more generally. Mentions of Austrian economics in popular venues helps make my case. And some recent outbreaks are available.

On 8 May 2010, the Maine Republicans adopted a platform with these insane planks:

"V. To Promote the General Welfare

• Return to the principles of Austrian Economics, and redirect the economy back to one of incentives to save and invest.
• Cut spending, balance the budget, and institute a plan for paying down debt. Proclaim that generational debt shifting is immoral and unconscionable and will not be tolerated! ..."

Apparently, nobody has told these maniacs that Von Mises declares praxeology, that is, economic theory, to be Wertfreiheit, that is, value-free (Human Action, Chapter II Section 7).

And an unstable liar on Fox News has made Hayek's The Road to Serfdom the number one most popular book at times on Amazon. So Hayek is being discussed in the popular press and among academics who previously had taken no notice. By the way, other works of Hayek are more important for theories of the business cycle. In The Road to Serfdom, Hayek says his differences with Keynes are a matter of pragmatic judgment, not political principle:

"There is, finally, the supremely important problem of combating general fluctuations of economic activity and the recurrent waves of large-scale unemployment which accompany them. This is, of course, one of the gravest and most pressing problems of our time. But, though its solution will require much planning in the good sense, it does not - or at least need not - require that special kind of planning which according to its advocates is to replace the market. Many economists hope, indeed, that the ultimate remedy may be found in the field of monetary policy, which would involve nothing incompatible even with nineteenth century liberalism. Others, it is true, believe that real success can only be expected from the skillful timing of public works undertaken on a very large scale. This might lead to much more serious restrictions of the competitive sphere, and, in experimenting in this direction, we shall have carefully to watch our step if we are to avoid making all economic activity progressively more dependent on the direction and volume of government expenditure. But this neither the only nor, in my opinion, the most promising way of meeting the gravest threat to economic security. In any case, the very necessary efforts to secure protection from these fluctuations do not lead to the kind of planning which constitutes such a threat to our freedom." -- Friedrich A. Hayek, The Road to Serfdom, Chapter IX: Security and Freedom

The popularity of Austrian economics refracts and contributes to a policy environment in which bad ideas are being adopted with bad consequences.

Hyman Minsky On-Line

The Saint Louis Fed provides the following document:

• Hyman P. Minsky "Financial Instability Revisited: The Economics of Disaster"

I have commented on Minsky before. Those interested in Minsky's ideas might want to at literature available at the Levy Economics Institute.

Of Minsky's book, as I recall, I found John Maynard Keynes of most interest. I found Stabilizing an Unstable Economy dryer. That was more than a decade ago and maybe I would find it of greater interest now.

The Con Left In Economics?

The Spring 2010 issue of the Journal of Economic Perspectives has a debate among some mainstream economists on changes in economics since Edward Leamer's 1983 American Economic Review paper, "Let's Take the Con Out of Econometrics". Developments since then include more reliance on sensitivity analysis; randomized experiment designs, both in laboratories and in the field; natural experiments; and Instrumental Variables (IVs). Contributors to this symposium consist of Joshua D. Angrist & Jön-Steffen Pischke, Edward E. Leamer, Michael P. Keane, Christopher A. Sims, Aviv Nevo & Michael D. Whinston, and James H. Stock.

Correlation Between Increased Government Size And Equality

The Organization for Economic Cooperation and Development (OECD) has made some data available to everybody. So I thought I would replicate some of my previous analysis. In particular, income inequality is negatively correlated with the size of government (Figure 1). Income is measured by the Gini coefficient, and the size of government is expressed as a percentage of Gross Domestic Product (GDP).

Figure 1: Inequality Versus Government Size

The Gini coefficient is a measure of inequality, with a higher Gini coefficient denoting a more unequal distribution of income. It is defined as follows: sort the population in order of increasing income. Plot the percentage of income received by those poorer than each value of income against the percentage of the population with less than that value of income. This is the Lorenz curve, and it will fall below a line with a slope of 45 degrees going through the origin. The Gini coefficient is the ratio of the area between the 45 degree line and the Lorenz curve to the area under the 45 degree line. A Gini coefficient of zero indicates perfect equality, while a Gini coefficient of unity arises when one person receives all income and everybody else gets nothing. Consequently, the Gini coefficient lies between zero and one.

I take the data as given from the OECD. I'm not worrying about whether income is found per family, household, or individual. Nor am I worrying about whether government expenditures include transfer payments and include both state and Federal spending. I took data from the year 2000 because that seems to be the most recent year with data for both dimensions and in which the Gini coefficient is given for a definite year. The OECD lacks 2000 data in one or another dimension for Iceland, South Korea, Mexico, the Slovak Republic, and Turkey. The plotted points consist of data from Australia, Austria, Belgium, Canada, the Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand, Norway, Poland, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.

Among advanced capitalist nations, countries with bigger governments tend to have a more equal distribution of income.

Formalism in Economics

I think many mainstream economics equate formalism with use of equations. But analytical categories that are not easily set out as the value of a variable in a numerical equation can provide a kind of formalism. And, if you want mathematics, one could, I suppose, set out an ontology, using model theory, for such categories. (I'm not sure what would be the point of that.) To illustrate my claim, I point to two sets of triples that some economists have developed.

Structure, Organization, and Agency need to be analyzed if one wants to understand the provisioning process in capitalist economies. The interindustry dependencies shown in Input-Output tables, macroeconomic income flows, and money flows show some structures important for understanding capitalist economies. Business enterprises, government and quasi-government bureaus, and families are important organizations in such economies. Agency occurs, that is, decisions are made by individuals, in a context provided by such structures and organizations (Lee 2009).

Oligopoly involves a small number of firms maintaining special privileges in a market environment where other firms might enter (Rothschild 1993). Ever since the work of Joe Bain and Paolo Sylos Labini (Modigliani 1958), economists have analyzed oligopoly on the basis of Structure, Conduct, and Performance. The structure of a market is more or less stable in time, observable, and influences the conduct of market participants. Conduct includes the choice of which commodities to buy, the prices to post, decisions about advertisement, etc. Performance is a matter of comparing market results with some sort of ideally efficient results (Schmalensee 1987).

References

• Frederic Lee (2009) A History of Heterodox Economics: Challenging the Mainstream in the Twentieth Century, Routledge
• Franco Modigliani (1958) "New Developments on the Oligopoly Front", Journal of Political Economy, V. 66, N. 3 (June): pp. 215-232.
• Kurt W. Rothschild (1993) "Oligopoly: Walking the Sylos-Path", in Markets and Institutions in Economic Development: Essays in Honour of Paolo Sylos Labini (Edited by S. Biasco, A. Roncaglia, and M. Salvati), St. Martin's Press
• Richard Schmalensee (1987) "Industrial Organization", in The New Palgrave: A Dictionary of Economics (Edited by J. Eatwell, M. Milgate, and P. Newman), MAcmillan

Wittgenstein Online

According to this news story, the University of Bergen is providing online access, for anybody, to their archives of Wittgenstein's notes. The semantic web is made use of in their presentation.

I think I'll stick to dead tree editions of Tractatus Logico-Philosophicus, "Some Remarks on Logical Form", Philosophical Investigations, The Blue and Brown Books, Remarks on the Foundations of Mathematics, Philosophical Grammar, Philosophical Remarks, On Certainty, Culture and Value. And, I guess, there are even more posthumous works. But now, from your computer, you can check the work of G. E. M. Anscombe, Raymond Hargreaves, Anthony Kenny, B. F. McGuiness, D. F. Pears, Rush Rhees, Roger White, Peter Winch, and G. H. von Wright.

Lear Without The King

I have presented several models of a more or less capitalist economy smoothly reproducing.

Some have objected (for example, Jan Kregel (1985)) about the lack of money in these sort of models. Paul Cockshott and his colleagues provide a more recent example:

"For example, prices in neo-Ricardian models are also exchange ratios determined by solutions to static, simultaneous constraints. Similarly, historical time is absent, so there is no causal explanation of how or why a particular configuration of the economy arose. Money only plays a nominal not a causal role... neo-Ricardian theories tend to ignore ... actor-to-actor relations mediated by money, which unfold in historical time, and result in dynamic, not static, equilibria." -- Cockshott et al (2009)

I don't see why money cannot be included, in some sense, in a description of the transactions that must occur for the economy to reproduce. I think, for example, of Marx's account, in Chapter VI of Part I of Theories of Surplus Value, of Quesnay's Tableau.

Including money in the story, however, is not enough. Money and finance has to make a difference for the theory. Hahn points out an analogous problem with neoclassical general equilibrium. The way I view these models of reproduction, introducing money and finance should identify additional areas in which a capitalist economy can fail to reproduce smoothly.

I think some progress has been made to meet this criteria. Sraffa, in an aside, recognized the importance of monetary institutions:

...And when the wage is to be regarded as 'given' in a more or less abstract standard, and does not acquire a definite meaning until the prices of commodities are dtermined, the position is reversed. The rate of profits, as a ratio, has a significance which is independent of prices, and can well be 'given' before the prices are fixed. It is accordingly susceptible of being determined from outside the system of production, in particular by the level of money rates of interest. -- Piero Sraffa (1960), paragraph 44

I think a conflict theory of inflation can be developed to explain the United States in the 1970s. Suppose both the general level of wages and the rate of profits are given in Sraffa's system. Then the system is overdetermined. Inflation is a means by which certain incompatibilities can be resolved. Since the level of output is consistent with unemployment ruling, here is a possible theory of stagflation.

Given the importance in the current crisis of finance going wrong, I don't think I've identified an adequate theory of money for Sraffa's system. Apparently, the most full development of Sraffa's remark is Pivetti's, which I haven't read. If I recall correctly, Rogers (1989) is more a destructive critique of the Wicksellian foundations of mainstream macroeconomics. Moore (1988), like Hyman Minsky's work, is more Post Keynesian than Sraffian economics. I could also stand to learn more about the circuitists, as well as recent being done at the University of Missouri at Kansas City.

References

• Basil J. Moore (1988) Horizontalists and Verticalists: The Macroeconomics of Credit Money, Cambridge University Pres
• W. Paul Cockshott, Allin F. Cottrell Gregory J. Michaelson, Ian P. Wright, and Victor M. Yakovenko (2009) Classical Econophysics, Routledge
• Frank Hahn (1965) "On Some Problems of Proving the Existence of an Equilibrium in a Monetary Economy" in Theory of Interest Rates (ed. by Hahn and Brechling)
• J. A. Kregel (1985) "Hamlet without the Prince: Cambridge Macroeconomics without Money", American Economic Review, V. 75, N. 2 (May): pp. 133-139
• Marguerite Kuczynski and Ronald Meek (1972) Quesnay's Tableau Economique
• Karl Marx Theories of Surplus Value
• M. Pivetti (1985) "On the Monetary Explanation of Distribution", Political Economy: Studies in the Surplus Approach, 1(2): pp. 73-103 [I haven't read this]
• M. Pivetti (1991) An Essay on Money and Distribution, Macmillan [I haven't read this]
• Colin Rogers (1989) Money, Interest and Capital: A Study in the Foundations of Monetary Theory, Cambridge University Press
• Piero Sraffa (1960) Production of Commodities by Means of Commodities, Cambridge University Press

Kurz And Salvadori Peeved With Mark Blaug?

Usually when Heinz Kurz and Neri Salvadori want to explain some economist is mistaken, they confine themselves to saying something along the lines of certain propositions "cannot be sustained". Recently, I stumbled upon a 2010 paper in which they answer Mark Blaug. I find their tone sometimes striking:

"A careful scrutiny of [Blaug (2009)] shows that Blaug reiterates once again his previous criticisms, adds a few new ones, but does not enter into a serious discussion of the replies to his earlier efforts... Answering him in detail would necessitate repeating again our counter-arguments. We spare the readers this and ask them to consult our earlier replies to Blaug."

"Blaug has already been given the opportunity in this journal to answer his critics; see Blaug (2002). Apparently, he feels that his rejoinder was not effective. This is hardly surprising because Blaug did not attempt to counter the objections of his critics.

Scrutiny of his new effort reveals that the situation has not changed. Once again Blaug merely reiterates his previous criticisms, adds a few new ones, but neglects to answer his critics. He seems to feel that repeating his story often will render it credible."

"If Blaug was concerned with an historical reconstruction of the case under consideration, he needs to spend some time in Trinity College Library, Cambridge (UK), as we did, in order to study Sraffa's papers and library and find out when Sraffa had arrived at which results, and why. He would then see that his above speculation as well as many other statements he put forward concerning Sraffa's contributions are without foundation; they are pure fiction. Historians of economic thought ought to be aware of the usefulness of archival work."

"In order to give credibility to his (in itself rather strange) complaint that 'Sraffians' have not contributed to certain themes or fields in economics, Blaug re-labels some authors: in case X has/has not contributed to field Y, he or she is not/is a 'Sraffian'."

"In the context of a discussion of the problem of the gravitation of market prices to their 'natural' or normal levels, he contends that while Kurz and Salvadori point out 'that little is known about the dynamic behaviour of even simple linear production models; nevertheless, they express the hope that the problem will be "settled in the foreseeable future" (Kurz and Salvadori 1998[a], 20)' (229 n.20). The reader who checks the source mentioned will not find this statement. Has Blaug got the page wrong? No, in the entire book the reader won't find the statement quoted. Has Blaug perhaps confounded some of our books? Yes, he has, but things are worse still. The only passage we are aware of having written that can be related to Blaug's criticism is contained in a book published in 1995. After having pointed out the extreme complexity of the issue at hand ('gravitation') and the dependence of the results obtained on the specific conditions assumed, we conclude: 'It should then be clear that there is no fear that the issue of gravitation will be settled in the foreseeable future' (Kurz and Salvadori 1995, 20; emphasis added). Hence we say exactly the opposite of what Blaug contends we are saying. This is not only annoying but also raises doubts about the seriousness of the entire enterprise. What is the relevance of a critique that lacks the elementary rigor of not misrepresenting (let alone reversing) the view of the people criticised? Misconstruction is an error surely worse even than historically unfaithful reconstruction?"

"None of Blaug's criticisms stands up to close examination. He attributes views to us (and to other authors) we (they) never advocated. He contends that 'Sraffian' authors have not written about certain problems, while referring to writings which show precisely the opposite. He commits a number of elementary blunders and mistakes the mathematical form of an argument for its content. He variously contradicts himself in the paper. He puts forward bold statements that are contradicted by the facts."

I have commented before on the specific Mark Blaug paper Kurz and Salvadori are rejecting; on the history of Blaug's incomprehension of Sraffianism; and even on the Institute of Economic Affairs, a right-wing think tank sponsoring some of Blaug's work.

References

• Mark Blaug (1975) The Cambridge Revolution: Sccess or Failure? A Critical Analysis of Cambridge Theories of Value and Distribution, Institute of Economic Affairs
• Mark Blaug (1985) Economic Theory in Retrospect, Fourth Edition, Cambridge University Press
• Mark Blaug (1988) Economics Through the Looking Glass: The Distorted Perspective of the New Palgrave Dictionary of Economics, Institute of Economic Affairs
• Mark Blaug (1999) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 31, N. 2: pp. 213-236.
• Mark Blaug (2002a) "Kurz and Salvadori on the Sraffian Interpretation of the Surplus Approach", History of Political Economy, V. 34, N. 1: pp. 237-240.
• Mark Blaug (2002b) "Misunderstanding Classical Economics: The Sraffian Interpretation of the Surplus Approach", in Competing Economic Theories: Essays in Memory of Giovanni Caravale (Edited by S. Nisticò and D. Tosato), Routledge
• Mark Blaug (2009) "The Trade-Off Between Rigor and Relevance: Sraffian Economics as a Case in Point", History of Political Economy, V. 41, N. 2: pp. 219-247.
• Pierangelo Garegnani (1987) "Misunderstanding Classical Economics? A Reply to Mark Blaug", History of Political Economy, V. 34, N. 1: pp. 241-254.
• Heinz D. Kurz and Neri Salvadori (2002) "Mark Blaug on the 'Sraffian Interpretation of the Surplus Approach'", History of Political Economy, V. 34, N. 1: pp. 225-236.
• Heinz D. Kurz and Neri Salvadori (2010) "In Favor of Rigor and Relevance. A Reply to Mark Blaug" (4 Feb).
• Carlo Panico (2002) "Misunderstanding the Sraffian Reading of the Classical Theory of Value and Distribution: A Note", in Competing Economic Theories: Essays in Memory of Giovanni Caravale (Edited by S. Nisticò and D. Tosato), Routledge

Geoff Harcourt On YouTube

A 2007 interview with Geoff Harcourt at Cambridge can be found on YouTube (Part 1, Part 2). Presumably, he was writing The Structure of Post-Keynesian Economics at the time.