Economic & Political Weekly

Every once in a while, I notice popular and semi-popular journals in which ideas I find interesting are discussed. As I understand it, Economic & Political Weekly is an Indian journal. It was named Economic Weekly when it published Krishna Bharadwaj's 1963 review of Sraffa's book. I cannot speak to Indian politics. But I find two articles of interest in the 16 October number.

Ghose (2010) builds on Arthur Lewis's model of development. Lewis depicts undeveloped economies as exhibiting a kind of dualism in which capitalist and traditional (subsistence) sectors coexist. The traditional sector experiences disguised underemployment and can provide an infinite supply at labor at the going wage. Lewis mentions farmerss, casual workers, petty traders, domestic and commercial retainers, and woman in the household as sources of such a labor supply. Economic development is a matter of structural change in which the capitalist sector expands and replaces the traditional sector. My impression is that this distinction between structural change and a mere quantitative expansion used to distinguish the economics of development and of growth. Ghose suggests this perspective has been lost in development economics.

Sinha (2010) provides an appreciation of Sraffa's book. Sinha does not see Sraffa's prices of production as dynamically stable limit points of some sort of gravitational process governing market prices. Nor does he think an internal critique of neoclassical economics based on reswitching was central to Sraffa's project. He emphasizes Sraffa's standard commodity and likes Joan Robinson's reading of Sraffa as generalizing Ricardo's corn economy, in which the rate of profits is a physically specified ratio independent of relative prices. This reading resembles Bharadwaj's.

• Krishna Bharadwaj (1963) "Value through Exogenous Distribution", Economic Weekly (24 August): pp. 1450-1454. (Republished in Capital and Growth (edited by G. C. Harcourt and N. F. Laing), Penguin (1973))
• Ajit K. Ghose (2010) "Reinventing Development Economics", V. XLV, N. 42 (16 October): pp. 41-50.
• Ajit Sinha (2010) "Celebrating Fifty Years of Sraffa's Production of Commodities by Means of Commodities", V. XLV, N. 42 (16 October): pp. 61-65.

Bad Teaching By DeLong?

Brad DeLong has kindly made his lecture notes on General Equilibrium available online. I think he explicitly only asserts that equilibria exist (under certain conditions), not that any are necessarily stable. But I do not see how any student reading his notes cannot come to that conclusion. He never explicitly states that economists have found that General Equilibrium Theory imposes basically no limit on dynamics - this is an implication of the Sonnenschein-Mantel-Debreu results. I also don't care for DeLong's treatment here of Karl Marx, who was not writing about the allocation of given resources. (I think that a formalization of Marx's notion of prices of production is more like a Von Neumann ray without requiring labor markets to clear.)

Not being a teacher, I'm willing to entertain discussion of simplifications in teaching beginners. I can see why Joan Robinson thought that General Equilibrium Theory doesn't stand up long enough to be knocked down. The complete model postulates that enough markets exist such that you can trade any commodity for any other commodity across all time periods and all states of nature. This is wildly non-descriptive of any actual capitalist economies. But I can see how the introductory teacher might not get to point where this objection makes any sense.

West, East, And South

Peter Nobel, who is descended from Alfred Nobel, has come out against the Nobel Prize in economics. I want to focus on this part of his statement:

"With no knowledge of economics, I have no opinions about the individual economics prize winners. But something must be wrong when all economics prizes except two were given to Western economists, whose research and conclusions are based on the course of events there, and under their influence."

My question is which two prize winners does Nobel have in mind? I think Leonid Kantorovich, the Soviet co-inventer of Linear Programming, is obviously one. Is the other Amartya Sen? I think one might contrast the West with both Eastern block countries and the global South. If one counts the South as non-West, then Peter Nobel's count is not quite correct. One would also have to count Arthur Lewis, for his contributions to development economics.

Papers To Read

I seem to be very slow to either read these or write up a detailed explanation:

• Francis M. Bator (1958) "The Anatomy of Market Failure", Quarterly Journal of Economics, V. 72, N. 3 (Aug): 351-379. John Cassidy takes this paper as the authoritative definition in his book How Markets Fail: The Logic of Economic Calamities.
• Arindrajit Dube, T. William Lester, and Michael Reich (2008) "Minimum Wage Effects Across State Borders: Estimates Using Contiguous Counties", forthcoming in the Review of Economics and Statistics. Generalizes the natural experiment approach of Card and Krueger to look at all cross-state local differences in minimum wages in the United States between 1990 and 2006. They find no adverse employment effects from higher minimum wages in the ranges examined. You can watch a video interview with Dube here. (The Wikipedia page on minimum wages also lists meta-analyses, by Stanley and by Doucouliagos & Stanley, more recent than Card and Krueger's meta-analysis.)
• Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou (2009) "The Complexity of Computing a Nash Equilibrium", Communications of the ACM, V. 52, No. 2: pp. 89-97. Defines a complexity class between P and NP and proves that computing a Nash equilibrium is in that class. Thus, if P ≠ NP, Nash equilibria cannot be computed in polynomial time for arbitrary games. In other words, computing a Nash equilibrium in general is infeasible in practice. (Tim Roughgarden's "Algorithmic Game Theory" (Communications of the ACM, V. 53, No. 7 (Jul. 2010)) and Yoav Shoham's "Computer Science and Game Theory" (Communications of the ACM, V. 51, No. 5 (Aug. 2008)) are survey articles.)
• Colin F. Camerer (2006) "Wanting, Liking, and Learning: Neuroscience and Paternalism", University of Chicago Law Review, V. 73 (Winter). Argues that three neural subsystems in our brains process "wanting", "liking", and "learning" separately. I don't think this is quite what Ian Steedman and Ulrich Krause mean by a Faustian agent, but it seems to be related.

P.S. Commentator Emil Bakhum lists some objections to Sraffa's analysis from Alfred Muller. I do not agree that these objections correctly characterize Sraffa's analysis, a point to which I may return. I think I would like a more complete reference, although I might not be able to read it if it is in german.

A "Nobel" Prize For Epicycles In Labor Economics?

Peter Diamond, Dale Mortensen, and Christopher Pissarides won the "Nobel" prize in economics this year. I do not have Bill Mitchell’s expertise on search theory and labor economics. Nevertheless, I thought I’d record my reactions.

As I understand it, Diamond, Mortensen, and Pissarides think labor would be described by by the interactions of well-behaved supply and demand functions for labor if it were not for the heterogeneity of workers and jobs and the time to form matches between them. The orthodox theory would be wrong even if workers and jobs were homogeneous. So I find puzzling why I should approve of this year’s award. I think my opinion is consistent with some of Alessandro Roncaglia’s observations of trends in mainstream economics.

David Ruccio and Richard McIntyre & Michael Hillard (Hat tip to Nick Kraft) have been critical of this year’s award. Paul Krugman has praised it. Doubtless, one could find more praise in the blogosphere.

Grandpa's Giant Pancake

Ingredients

1/2 cup Flour
3 teaspoons baking powder
3 eggs
1/2 cup milk

(This is my uncle's recipe. My father uses 1 cup, 1 teaspoon, 1 egg, and 1 cup, respectively.)

1) Mix and stir. Pour in large, greased fry pan.

2) Cook on medium high heat until bubbles burst. Flip and cook other side.

My father eats this with lots of butter, not maple syrup. Makes 2 or 3 pancakes.

Weird Science III

I guess this is part of a series in which I describe oddities upon which I have stumbled. Here I focus on two phenomena in the measurement of gravity. Perhaps the theory of general relativity is wrong. (The link goes to an explanation of a different problem in physics). Of course, much more prosaic explanations are possible.

Maurice Allais, the recently dead "Nobel" laureate in economics, experimented with a paraconical pendulum during the 1950s. He discovered the Allais effect, which is a variation in the behavior of a pendulum during an eclipse. The plane of the pendulum rotated approximately ten degrees during the eclipse and then returned to the previously pattern. A number of scientists have tried to replicate this and similar effects with various experimental equipment during various eclipses. Some succeeded in replication and some failed. Allais’ explanation, apparently, was to revive the 19th century concept of the aether and argue that space is anisotropic.

Pioneers 10 and 11 were launched in 1972 and 1973, respectively. NASA was still in communication with them after they had passed beyond the orbit of Pluto and were more than 20 Astronomical Units away from the sun. (An AU is the average distance from the Earth to the sun.) Pioneers 10 and 11 have an anomalous acceleration towards the sun of an order of magnitude of 10^-7 centimeters per square seconds. In other words, as they move away from the sun, they are very slowly slowing down more than can be accounted for under the current (relativistic) understanding of gravity. Pioneers 10 and 11 are moving away from the sun at a rate of approximately 12 kilometers per second. (It dawned on me while writing the above that I am no longer sure how many planets are in our solar system.)

References

• Maurice Allais (1986). "The Concepts of Surplus and Loss and the Reformulation of the Theories of Stable General Equilibrium and Maximum Efficiency", in Foundations of Economics (edited by Mauro Baranzini and Roberto Scazzieri), Basil Blackwell.
• John D. Anderson et al. (1998) "Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration", arXiv:gr-qc/9808081v2 (1 October)
• John D. Anderson et al. (2005) "Study of the Anomalous Acceleration of Pioneer 10 and 11", arXiv:gr-qc/0104064v5 (10 March)
• Gibor Basri and Michael E. Brown (2006) "Planetesimals to Brown Dwarfs: What is a Planet?", Ann. Rev. Earth Planet. Sci., V. 34: pp. 193-216
• M. E. Brown, C. A. Trujillo, and D. L. Rabinowitz (2005) "Discovery of a Planetary-Sized Object in the Scattered Kuiper Belt", The Astrophysical Journal, 635: L97-L100, (10 December)
• Chris P. Duif (2004) "A Review of Conventional Explanations of Anomalous Observations during Solar Eclipses", arXiv:gr-qc/0408023 v5 (31 December)

Stephen Williamson, Again Is He A Fool Or A Knave?

Stephen Williamson writes some ignorant balderdash about heterodox economics. At least two of his commentators recognize the quality of his remarks.

If Williamson had a clue, he would know some scholars distinguish between the heterodox/orthodox distinction and the mainstream/nonmainstream distinction. Following Davis's taxonomy, I would classify North and new institutionalist economics as "mainstream heterodox". I do not think of either Paul Krugman or James Tobin as non-mainstream.

Non-mainstream heterodox economics do not all reject or dislike mathematics. Williamson doesn't seem to know about the existence of sraffians. Of course, he doesn't list feminist economics as a target of his ill-informed calumny. I think most heterodox economists would agree that one can make true and insightful statements about economics without using mathematics. One capable of a moment's reflection can see that that doesn't imply no mathematics can be be useful for economics. Williamson seems to think that the point of using mathematics is to seperate oneself from the hoi polloi. It is no legimate criticism of a paper that a graduate student can write out the model in twenty minutes. The questions one should ask oneself, in this case, are "Does this paper provide empirical and policy guidance for understanding some aspect of Japan's economy?" and "Is this paper original?"

Consider such journals as the American Economics Review or the Journal of Political Economy. And consider the Cambridge Journal of Economics, Metroeconomica, or the Review of Political Economy. The first set contains examples of mainstream economics. The second set of journals publish non-mainstream heterodox economists. An outsider will find journals in both set contain a mixture of natural language and mathematics. They both have both theoretical and empirical papers. The academics are not all from one university, they argue with one another, and they seem to have a variety of sources of funding. Clearly, non-mainstream heterodox economists are not "fringe" in the same sense that most are who argue for astrology, creationism, or a flat earth theory.

Some Reports

I haven't had time to read these:

• 2010 Ibrahim Index of African Governance: Summary (More here and here)
• Shadow Banking, a Federal Reserve Bank of New York Staff Report (h/t Kasey Dufresne)
• Findings Regarding the Market Events of May 6, 2010, a report by the staffs of the Commodity Futures Trading Commission (CFTC) and the Securities and Exchange Commission (SEC) on the flash crash (press release) (h/t Rajiv Sethi)
• Symantec's "W32.Stuxnet Dossier" and the Industrial Control Systems Cyber Emergency Response Team's "ICS-CERT Advisory ICSA-10-272-01 - Primary Stuxnet Indicators"

Inside Job

National Public Radio broadcast an interview last evening with Charles Ferguson, the director of the soon-to-be-released documentary, Inside Job. It is apparently about recent financial shenanigans on Wall Street and the proximate causes of the global financial crisis. The director seemed to be struck about how unlikely it is that top financiers would be heading off to prison. He also was astonished about the pervasive advocacy and lack of ethics he found among economists. He mentioned economists writing articles to promote some industry and not disclosing funding, serving on corporate boards, and acting as expert witnesses in court cases.

NPR played a clip where Glenn Hubbard, the dean of the Columbia University School of Business, a former chair of the Council of Economic Advisors, and a Visiting Scholar (if you can call it that) at the American Enterprise Institute, basically threw Ferguson out of his office. Hubbard apparently did not want to talk about his outside sources of income.

Update: In the comments, Tomboktu links to the NPR piece. Elsewhere, Chris Bertram links to a piece by Charles Ferguson in the Chronicle of Higher Education.

Mainstream Economists: When The Storm Is Past The Ocean Is Flat Again

Did economists predict the possibility of the global economic crisis before it occurred? Did they describe sources of instability as they were building up? I think the following three papers are good for exploring these questions:

• Dirk J. Bezemer (2009) "'No One Saw This Coming': Understanding Financial Crisis Through Accounting Models".
• James K. Galbraith (2009) "Who Are These Economists, Anyway?", Thought and Action.
• Andrea Imperia and Vincenzo Maffeo (2009) "As if Nothing Were Going to Happen: A Search in Vain for Warnings about the Current Crisis in Economic Journals with the Highest Impact Factors" 13th Conference of the Research Network Macroeconomics and Macroeconomic Policies: The World Economy in Crisis - The Return of Keynesianism, Berlin (30-31 October.

The answer I get from these articles is mainly negative for orthodox economics. Robert Shiller receives praise. He could be said to be a mainstream economist. But, as I understand it, his analysis was based on behavioral economics and the rejection of the Efficient Market Hypothesis. The empirical evidence suggests macroeconomists should expand research following Wynne Godley's stock-flow consistent models. Imperia and Maffeo point to those who argued that financial innovation was leading to increased debt, an attempt to compensate for reduced aggregate demand resulting from increased income inequality.

For A New Robinson And Eatwell

Michael Hirsh recently ("Our Best Minds Are Failing Us", Newsweek, September 16, 2010) lamented how unwilling mainstream economists are to change their thinking in light of the events of the last few years. Brian Milner, a columnist for The Globe and Mail has added to the chorus of complaints.

Perhaps an opportunity now exists for a new introductory textbook in economics that differs fairly comprehensively from mainstream textbooks. Never mind Colander’s approach of modifying his textbooks at most 15% from the previous editions so that mainstream economists will not reject it. Maybe some enterprising heterdox economist should write an uncompromising introduction to economics that is also up-to-date on current events. Years ago, I listed some textbooks. More textbooks have become available since then, for example, G. C. Harcourt’s The Structure of Post-Keynesian Economics: The Core Contributions of the Pioneers. I am not sure that Luigi L. Pasinetti’s Keynes and the Cambridge Keynesians: A ‘Revolution in Economics’ to be Accomplished counts as a textbook. I’m sure I’m leaving much out.

But I’m not sure the packaging on most of these is what I’d like to see tried. The textbook I have in mind should be fairly thick, have various boxed asides, and have problem sets after every chapter. (The problem sets could include essays questions and have less numerical examples than is common.)

Chicken Rice Pilaf

Ingredients

2 Tablespoon olive oil
2 smoked sausage, bratwurst, italian sausage, andouille, or other flavorful link sausage (optional)
1 onion
2 ribs celery
1 large green or red pepper
1 bay leaf
1 teaspoon thyme
1 teaspoon tumeric (optional)
6 chicken thighs, skin removed if desired (could be boneless) or 2 x 1 1/2 pounds bone-in, skinless chicken breasts
2 cups uncooked rice
3 to 4 cups canned or home-made chicken broth

1) Heat vegtable or olive oil over medium-high heat in a wide, deep pot (e.g., a Dutch oven). Cut sausage in half lengthwise, then in half lengthwise again. Dice into small pieces and add to pot.

2) Peel and dice onion, adding it to the pot as you do. Dice celery (including leaves) and pepper, adding them to the pot. (Based on what I've seen, one could also add a diced carrot.)

3) When all vegtables are added, cook about 5 minutes so they soften a little. Add bay leaf, thyme, tumeric if desired chicken (e.g., whole thighs) and rice. Add broth plus water to equal 4 cups. Season with a little salt and pepper.

4) Bring to a boil, cover, reduce heat to simmer and cook 30 or 40 minutes, or until chicken is cooked and rice is tender. (I'm thinking of trying it with frozen peas added with about 20 minutes left.)

Makes approximately 6 servings.

Elsewhere

• Bruce McFarling is blogging at Daily Kos. I like his take on the (US) Social Security non-crisis.
• Paul Davidson is now on the the Advisory Board for the Institute for New Economic Thinking.
• David Hendy, another member of INEF Advisory Board, has co-written a paper, "On the Mathematical Basis of Inter-Temporal Optimization", which argues that rational expectations is inapplicable to the sort of non-stationary time series that often arise in economics.
• I stumbled upon Daniel Gay's blog the other day. He has a book, Reflexivity and Development economics: Methodology, Policy and Practice, which sounds interesting from a Post Keynesian perspective.
• I've added Tony Myatt and Rod Hill's blog to my blog roll. They have a book, the Economics Anti-Textbook, too. (I'm not going to try to read either of these books soon.)
• "Magpie" has some comments on a couple of my old posts.

Nonergodicity And The Butterfly Effect

1.0 Introduction
Cosma Shalizi says, "It is not true that ergodicity is incompatible with sensitive dependence on initial conditions." This poses some questions for me: Can I give an example of a non-ergodic process that also exhibits sensitive sensitive dependence on initial conditions? Can I give an example of an ergodic process that exhibits sensitive dependence on initail conditions?

This post answers the former question. I consider Newton's method for finding roots of unity in the complex plane. The latter question is probably more important for Cosma's assertion. For now, I cite the Lorenz equations as an example of an ergodic process with the desired sensitive dependence.

Cosma's assertion, "It is not true that non-stationarity is a sufficient condition for non-ergodicity," directly contradicts Paul Davidson. I do not address that contradiction here.

2.0 Newton's Method
Newton's method is an algorithm for finding the zeros of a function. In this post, I illustrate the method with the function:

F(z) = z³ - 1,

where z is a complex number. A complex number can be written as a two-element vector:

z = [x, y]^T = x + jy

where j is the square root of negative one. (I've been hanging around electrical engineers.) Likewise, one can consider the function F as a vector of two elements:

F(z) = [f₁(z), f₂(z)]^T

The first component maps the real and imaginary parts of the argument to the real part of the function value:

f₁(z) = x³ - 3xy² - 1

The second component maps to the imaginary component of the function value:

f₂(z) = y (3x² - y²)

Newton's method is for numerically finding a solution to the following equation:

F(z) = 0

In my case, one is searching for the cube roots of unity. The method is an iterative method. An initial guess is refined until successive guesses are close enough together that one is willing to accept that the method has converged. A guess is refined by taking a linear approximation to the function at the guess. That guess is refined by solving for the zero of that linear approximation. The zero is the next iteration.

The derivative of a function, when evaluated at the current iterate, provides the linear approximation. The Jacobian is the two-dimensional equivalent of the derivative. The Jacobian, J, is a matrix with the following elements:

J_{i, 1}([x, y]^T) = df_i([x, y]^T)/dx, i = 1, 2.

J_{i, 2}([x, y]^T) = df_i([x, y]^T)/dy, i = 1, 2.

Newton's method is specified by the following iterative equation:

z_{n + 1} = z_n - J^-1(z_n) * F(z_n)

3.0 Numeric Explorations
Figure 1 shows a coloring of the plane based on the application of Newton's method. Each point in the plane can be selected as an initial point. The method is applied, and the point is colored according to which of the three cube roots of unity to which the method converges. Figure 2 shows an enlargement of the region around the indicated point in the northeast of Figure 1. Notice the fractal nature of the regions of convergence.

Figure 1: Fractal Basins of Attraction for Newton's Method

Figure 2: An Enlargement of These Fractal Basins

To exhibit sensitive conditions on initial conditions, I wanted to find nearby points whose trajectory diverges under this dynamical process. Table 1 lists six points selected from Figure 2. They fall into three groups, depending on which root they converge to. I claim that one can find at least three distinct points such that each pair is as close as one wants that each converge to a seperate root.

Table 1: Limit Points for Newton's Method

Initial Guess	Limit Point
0.3899 + j 0.6871	1
0.3938 + j 0.6780	(-1/2) - j (31/2)/2
0.3986 + j 0.6811	(-1/2) + j (31/2)/2
0.4010 + j 0.6868	1
0.3980 + j 0.6908	(-1/2) - j (31/2)/2
0.3943 + j0.6949	(-1/2) + j (31/2)/2

Figure 3 and 4 display the trajectories of the six points selected for Table 1. Apparently the function is very shallow in this region. I had not realized before these explorations that these sorts of trajectories go so far from the origin before returning to converge to a root on the unit circle.

Figure 3: Real Part of Some Time Series From Newton's Method

Figure 4: Imaginary Part of Some Time Series From Newton's Method

4.0 Conclusions
Cosma provides this definition, among others, of an ergodic process:

"A ... process is ergodic when ... (almost) all trajectories generated by an ergodic process belong to a single invariant set, and they all wander from every part of that set to every other part..."

This definition is appropriate for both deterministic and stochastic processes.

The three roots of unity constitute the non-wandering (invariant) set for the dynamical system created by the above application of Newton's method. A trajectory that has converged to one of the roots does not wander to any other root. So the process is non-ergodic. Yet which root a process converges to is crucially dependent on the initial conditions. A small variation in the initial conditions leads to a long-term divergence in trajectories. This is especially evident because of the fractal structure of the basins of attraction of the three roots.

I think of the above as close to recreational mathematics. I have not tied the above example into any economics model. Common neoclassical models, such as the Arrow-Debreu model of general equilibrium, fail to tie dynamics down. I find it difficult to see how one who has absorbed this fact and understands the mathematics of dynamical systems can find credible much orthodox teaching in economics.

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.)