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.

Prices Of Production And A Wheat Theory Of Value

1.0 Introduction
In this post, I describe a theory of prices that is an alternative to the neoclassical supply-and-demand theory of prices as scarcity indices. In this exposition, I consider the simple case in which the modeled economy does not produce a surplus. In this simple case, prices of production are in the ratios of labor values and of commodity values, for any specified commodity. This post illustrates this claim too.

I do not draw the conclusion from the equivalence illustrated here that labor values have no priority over commodity values. After all, the formal model illustrated here does not include a principal agent problem arising with labor.

2.0 Technology and Advanced Wages
Consider a simple economy in which only three commodities are produced, namely, wheat, iron, and pigs. Each commodity is produced by a specified process requiring (possibly zero) inputs of labor, wheat, iron, and pigs. Suppose these processes are observed to produce the quantities of outputs shown in Table 1 from the inputs shown there. In other words, these processes are observed to operate at the scale shown. No assumption about returns to scale is made here. In particular, it is not necessary for Constant Returns to Scale to prevail.

TABLE 1: Technique in Use

INPUTS	Wheat Industry	Iron Industry	Pig Industry
Labor	1 Person-Year	2 Person-Years	3 Person-Years
Wheat	230 Quarters	70 Quarters	90 Quarters
Iron	12 Tons	6 Tons	3 Tons
Pigs	12 Pigs		12 Pigs
OUTPUTS	450 Quarters	21 Tons	60 Pigs

Suppose wages are advanced at the start of the production period, and that these advanced wages consist of 10 quarters wheat and 6 pigs per person-year. Then one could specify the inputs to the production processes as consisting exclusively of wheat, iron, and pigs, with no labor input (as shown in Table 2). This is now the example from paragraph 2 of Sraffa's Production of Commodities by Means of Commodities. Notice that the outputs can just replace the inputs, including the advanced wages, with no commodity surplus being left over. Capitalists do not make an accounting profit in this economy.

TABLE 2: Production of Commodities by Means of Commodities

INPUTS	Wheat Industry	Iron Industry	Pig Industry
Wheat	240 Quarters	90 Quarters	120 Quarters
Iron	12 Tons	6 Tons	3 Tons
Pigs	18 Pigs	12 Pigs	30 Pigs
OUTPUTS	450 Quarters	21 Tons	60 Pigs

3.0 Prices of Production
With the social division of labor in this economy, firms in each industry at the end of the production period have an inventory of a single commodity. To continue production, they must trade some of that commodity for the other commodities they need as inputs. Prices of (re)production are time-invariant prices that allow these trades to occur and the economy to be smoothly reproduced through the actions of the agents in the economy. For this simple example, prices of production must satisfy three equations:

240 p_w + 12 p_i + 18 p_p = 450 p_w

90 p_w + 6 p_i + 12 p_p = 21 p_i

120 p_w + 3 p_i + 30 p_p = 60 p_p

where:

• p_w is the price of a quarter of wheat,
• p_i is the price of a ton of iron, and
• p_p is the price of a pig.

These equations are linearly dependent. Any multiple of a solution set of prices is also a solution. I arbitrarily pick a quarter of wheat as the numeraire. The solution set of prices is then $1 per quarter wheat, $10 per ton iron, and $5 per pig.

4.0 Labor Values
One can work out a consistent accounting in which the amount of labor time embodied in each commodity is measured. Labor values are found as the solution to the following system of three linear inhomogeneous equations in three unknowns:

1 + 230 v_w + 12 v_i + 12 v_p = 450 v_w

2 + 70 v_w + 6 v_i = 21 v_i

3 + 90 v_w + 3 v_i + 12 v_p = 60 v_p

where:

• v_w is the person-years labor embodied in a quarter of wheat,
• v_i is the person-years labor embodied in a ton of iron, and
• v_p is the person-years labor embodied in a pig.

This system of equations has a unique solution. The labor values for the commodities are 1/40 person-years per quarter wheat, 1/4 person-years per ton iron, and 1/8 person-years per pig.

5.0 Wheat Values
One can also work out a consistent accounting system in which the amount of wheat embodied in each commodity is measured. Wheat values for iron and pigs are found as the solution to the following system of two linear inhomogeneous equations in two unknowns:

90 + 6 w_i + 12 w_p = 21 w_i

120 + 3 w_i + 30 w_p = 60 w_p

where:

• w_i is the quarters wheat embodied in a ton of iron and
• w_p is the quarters wheat embodied in a pig.

The wheat values of commodities are w_i = 10 quarters per ton and w_p = 5 quarters per pig.

Calculating iron values for wheat and pigs and calculating pig values for wheat and iron are left as an exercise to the reader.

6.0 Contrast and Comparison
For any set of values (prices of production, labor values, or commodity values), one can find quantities of each commodities that are valued as equal for that set. Table 3 illustrates by showing the values of specified quantities of each commodity. In this example, the following equation holds:

10 quarters wheat = 1 ton iron = 2 pigs,

whether commodities are valued in terms of dollars, embodied labor, or any commodity value (such as wheat). The equivalence of all these values is a special case. This equivalence works out from considering a pure circulating capital case in which an economic surplus not paid out in wages is not produced.

TABLE 3: Value of Specified Quantities of Commodities

Quantities	Value in
	Prices of Production	Person-Years of Embodied Labor	Quarters of Embodied Wheat
10 Quarters Wheat	$10	1/4 Person-Years	10 Quarters
1 Ton Iron	$10	1/4 Person-Years	10 Quarters
2 Pigs	$10	1/4 Person-Years	10 Quarters

No Mistakes In Marx's Analysis Of Social Classes

Marx puts forth an analysis of social class in Volume 3, Chapter 52 of Capital. He poses his problem in five paragraphs. I find no mistakes in his answer in the succeeding paragraphs.

Alternative Economics In Mechanics' Institutes And Think Tanks

Various nonacademic institutions have helped shaped the development of academic economics. Fred Lee, in his recent history, describes some aspects of the culture of university economics departments:

"Intellectual bullying of heterodox-interested graduate students; denying appointments, reappointments, and tenure to heterodox economists; red-baiting; and professional ostracism/discrimination" (Lee 2009)

In the United States around 1945, some institutions outside universities provided intellectual support and culture for left-wing intellectuals, including economists. I refer to schools for workers supported to some extent by the Communist Party:

• School for Jewish Studies (New York)
• Jefferson School for Social Science (New York)
• Abraham Lincoln School (Chicago)
• Samuel Adams School (Boston)
• Boston School for Marxist Studies
• Tom Paine School of Social Sciences (Philadelphia)
• Walt Whitman School of Social Sciences (Newark)
• Joseph Weydemeyer School of Social Sciences (St. Louis)
• Ohio School of Social Sciences (Cleveland)
• Michigan School of Social Sciences (Detroit)
• Seattle/Pacific Northwest Labor School
• Tom Mooney/California Labor School (San Francisco)

Under Truman, these schools were listed by the Attorney General as subversive. With continued McCarthyist oppression, none existed by 1957.

On the other hand, extremely rich reactionaries paid economists to argue for right wing views. This funding went to both universities and to think tanks set up since the workers' schools were shut down. Some examples:

• Harold Luhnow, who made his fortune selling furniture, is important for the history at, among other places, the University of Chicago (Van Horn and Mirowski 2009)
• Jasper Crane, a former executive of the DuPont Chemical Company was a major funder at one point of the Mont Pélerin Society (Phillips-Fein 2009)
• Sir Antony Fisher, who introduced factory farming into Great Britain, set up the Institute of Economic Affairs in Great Britain (Blundell 2007, Mitchell 2009)
• Leonard Read led the Foundation for Economic Education
• Edward H. Crane founded the Cato Institute in 1977

Perhaps the long history of oppression of economists with certain views and funding of economists with others has had some influence on what ideas are developed. The above only provides a very limited glimpse of political interventions into academic economics. Much more can be found for those willing to look.

References

• John Blundell (2007) Waging the War of Ideas,Third and expanded edition, Institute of Economic Affairs
• Colleen Dyble (editor) (2008) Taming Leviathan: Waging the War of Ideas Around the World, Institute of Economic Affairs
• Frederic Lee (2009) A History of Heterodox Economics: Challenging the Mainstream in the Twentieth Century, Routledge
• Timothy Mitchell (2009) "How Neoliberalism Makes Its World: The Urban Property Rights Project in Peru", in The Road from Mont Pélerin: The Making of the Neoliberal Thought Collective (ed. by Philip Mirowski and Dieter Plehwe), Harvard University Press.
• Kim Phillips-Fein (2009) "Business Conservatives and the Mont Pélerin Society", in The Road from Mont Pélerin: The Making of the Neoliberal Thought Collective (ed. by Philip Mirowski and Dieter Plehwe), Harvard University Press.
• Rob Van Horn and Philip Mirowski (2009) "The Rise of the Chicago School of Economics and the Birth of Neoliberalism", in The Road from Mont Pélerin: The Making of the Neoliberal Thought Collective (ed. by Philip Mirowski and Dieter Plehwe), Harvard University Press.

Manifesto for Freedom of Economic Thought

The Paolo Sylos Labini Associazione is named after a great Sraffian economist. They are collecting signatures for a Manifesto for freedom of economic thought: Against the dictatorship of the dominant theory and in favour of a new ethic (Italian version).

Wynne Godley (1926-2010)

"Yet when, having produced a destructive critique of the neoclassical production function, [Sylos Labini] asks, 'When will economists finally accept their own logic?' I do believe he is not just sniping from the sidelines at the Neoclassical Paradigm (NCP), he is shaking at one of its foundation stones. For this reason my short answer to his question is 'Never' or at least 'Not until we have a new paradigm...' ...I am convinced that this concept of general equilibrium in a monetary economy [with markets for real product, the stock of money, labour, and the stock of bonds] constitutes the primal scene - the primitive imaginary vision of the world - out of which the whole of mainstream macroeconomics now flows. At one extreme are 'monetarists' of various hue who believe that the classical version of this simple model does, or should, or can somehow be made to describe the real world. Almost all other modern macroeconomists, while forming a huge spectrum, have as their essential activity the study what happens if parts of the machine do not function properly, e.g. are subject to rigidities or time lags. For instance, much work has been concerned with effects on the solution of this model if the various prices do not clear markets or clear them imperfectly. If wages are not flexible the labour market may not clear; this is what most students now understand as Keynesian economics. If the price of goods is not flexible, the market for goods may not clear, perhaps generating 'classical' unemployment. Now Sylos Labini (like Kaldor and Pasinetti in different ways) makes a devastasting case against the empirical relevance or even meaningfulness of the aggregate neoclassical production function. What I want to emphasize here is the system role which the production function fulfils and therefore just why the Sylos Labini critique is so important. What the production function does for all equilibrium systems - whether markets clear or not - is to bring labour into instantaneous equivalence with real product in such a way that alternative quantities of each can potentially be traded against one another. The production function is necessary for this equivalence so that labour can instantaneously be translated into the profit-maximising quantity of product which firms are therefore motivated to supply. Without the production function no neoclassical model will start up; the blood supply to its head is cut off... ...I have reached a point when I am prepared to make a declaration. I want to say of neoclassical macroeconomics what I have sometimes said of certain kinds of fiction; I know that the world is not like that and I have no need to imagine that it is. In particular, I do not believe that there exists a market in which goods in aggregate and labour in aggregate can be exchanged for one another provided only that the price of each is right in relation to some given stock of 'money.'" -- Wynne Godley (1993) "Time, Increasing Returns and Institutions in Macroeconomics: Essays in Honour of Paolo Sylos Labini", in Market and Institutions in Economic Development (ed. by S. Biasco, A. Roncaglia and M. Salvati), St. Martin's Press.

Godley goes on in this paper to outline a stock-flow consistent macroeconomic model with both real and monetary sectors.

The (??) Natural Rate of Unemployment

Milton Friedman defined the natural rate of unemployment, also known as the Non-Accelerating Inflation Rate of Unemployment (NAIRU), at least at the level of abstraction of this post:

"The 'natural rate of unemployment' in other words, is the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is embedded in them the actual structural characteristics of the labor and commodity markets." -- Milton Friedman (1968), as quoted in James K. Galbraith (1998)

Two mathematical mistakes are embedded in the above definition.

First, what does Friedman mean by the "Walrasian system"? At the time of his statement, the Arrow-Debreu model of intertemporal equilibrium was becoming the canonical statement of general equilibrium theory. But the Arrow-Debreu model is a very short run model, in which the initial quantities of capital equipment are among the given endowments. Consequently, a solution to the model yields neither a rate of employment nor a rate of unemployment, independent of time. Rather, these rates are time-varying. So he cannot mean to refer to that model.

Now, Walras himself presented a model with given quantities of capital goods and a supposed steady state set of prices and quantities. But this model was just logically inconsistent. In consistent long-run economic models the set of capital goods are found by solving the model, not taken as givens. Thus, the logic of such models is not about allocating given resources among alternative ends. To refer to such a model as "the Walrasian system of general equilibrium" is dubious.

Second, Friedman's definition relies on an implicit mathematical theorem: that the equilibrium solution of whatever model he is talking about is unique. But no reason exists for such a theorem to hold in either the Arrow-Debreu model or a long run equilibrium model with many markets. I have myself created a model with multiple equilibria.

Here, then, is another example of right-leaning economists giving decades of policy advice based on theoretical claims with no support in economic theory. Unsurprisingly, the policy did not work empirically either, as can be seen by looking at results in the 1980s and 1990s. (These claims are not new. James Galbraith made my second point long ago.)

Have mainstream economists ever addressed this failure? Did they not mostly just continue their mistake with Dynamic Stochastic General Equilibrium (DSGE) models?

References

• Milton Friedman (1968) "The Role of Monetary Policy", American Economic Review Papers and Proceedings (May): pp. 1-17
• James K. Galbraith (1998) Created Unequal: The Crisis in American Pay, The Free Press.

Performing Corporate Finance

1.0 Introduction

Economics can change the world, and not necessarily for the better. Mainstream economists often do not describe actual capitalist economies, but theorize an imaginary, supposedly ideal world in which everybody pursues their own self-interest, narrowly defined. Participants in this world are then sometimes encouraged by the theory to change institutions and their behavior to come closer to that imaginary world.

This post describes theories that encouraged corporations to become more vulnerable, by taking on large amounts of debt, and to become more short-run oriented, by focusing more on immediate stock market prices. I know about these two contributions to economics more from Bernstein and Cassidy's popularizations than the primary literature. I am deliberately treating some elements that I think have not much appeared in popular discussion since the advent of the global financial crisis.

2.0 Modigliani and Miller (M&M) and Capital Structure

The Modigliani and Miller theorem states that whether a corporation obtains financing with stocks or with bonds has no impact on its stock price. I gather that this follows from an arbitrage argument under admittedly unrealistic assumptions. An individual can buy stock with borrowed money. By buying stock on the margin, individuals can raise the leverage ratio from whatever corporations have decided on to whatever they like.

The M&M theorem serves as a baseline in corporate finance. One considers the implications of existing deviations from the theorem assumptions. Apparently the treatment for corporate taxes in the United States of dividends and interest is one such deviation. Interest on bonds can be deducted as expenses on corporate taxes; stock dividends cannot. Therefore financing by issuing bonds is to be preferred.

"This [proposition] carried not very flattering implications for the top managements of companies with low levels of debt. It suggested that the high bond ratings of such companies in which the management took so much pride, may actually have been a sign of their incompetence; that the managers were leaving too much of their stockholders' money on the table in the form of unnecessary corporate income tax payments [of] many millions of dollars." -- Merton Miller (1988), quoted in Bernstein (2005)

The implication is that corporations should increase their leverage.

3.0 Michael Jensen and Executive Compensation

Most owners (that is, holders of stock) of modern corporations are absentee owners. They would like corporate executives to act in a non self-dealing manner, against their own interests. This is a principal agent problem. The stock holder is the principal, the Chief Executive Officer (CEO), for instance, is an agent. In theory, the problem is how to structure executive pay and corporate incentives such that in value of stock is maximized. (I gather that in this theory, social norms about how stockholders, traders, and executives should behave doesn't come into it.) A supposed answer to the principal agent problem is to pay executives partly with stock options. They will then be encouraged to do their utmost to ensure the market price of the stock exceeds the price specified in their options.

References

• Peter L. Bernstein (2005) Capital Ideas: The Improbable Origins of Modern Wall Street, John Wiley & Sons.
• John Cassidy (2002) "The Greed Cycle: How the Financial System Encouraged Corporations to go Crazy", The New Yorker (Sept. 23): pp. 64-
• Michael C. Jensen and William H. Meckling (1976) "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure", Journal of Financial Economics, V. 3, N. 4
• Meron H. Miller (1988) "The Modigliani-Miller Propositions After Thirty Years", Journal of Economic Perspectives, V. 2, N. 4 (Fall): pp. 99-120.
• Franco Modigliani and Merton H. Miller (1958) "The Cost of Capital, Corporation Finance, and the Theory of Investment", American Economic Review, V. 48, N. 3 (June): pp. 655-669

We Have Ideas Yet...

...That we haven't tried.

Ian Parker has an article, "The Poverty Lab", in this week's(May 17, 2010) issue of The New Yorker. This article is a profile of Esther Duflo, this year's winner of the John Bates Clark award and a co-founder of the Abdul Latif Jameel Poverty Action Lab (J-PAL). J-PAL conducts controlled experiments in the field in developing countries.

This is neat work. As I understand it, it can be extended. Does J-PAL conduct experiments designed to implement more than one treatment at once? In such experiments, one would analyze the results with Analysis Of Variance (ANOVA), instead of a T test (or the Mann-Whitney-Wilcoxon test, which is the corresponding nonparametric test). This would probably be challenging on the scale of their experiments, but part of the point of the design of experiments is to allocate resources efficiently.

Field experiments, in some sense, are an extension of the methodology of laboratory experiments, seen in the work of, for example, Daniel Kahneman and Amos Tversky. The design of experiments could also be extended back into theory by applying it to simulations and computer programs implementing theoretical models. Duflo's work tells us about the world, while this would tell us more about economic theory. I'm thinking of Stefano Zambelli's work on aggregate production functions.

A Nonergodic, Stationary Random Process

1.0 Introduction
Joan Robinson famously distinguished between economic models set in logical and historical time. According to Robinson, the distinguishing feature of Keynes’ General Theory is its setting in historical time. Building on Paul Davidson, one might say that one sign that a model is set in historical time is that it generates nonergodic stochastic processes.

This post explains that claim somewhat by presenting a simple example of a stationary nonergodic stochastic processes, namely a Spherically Invariant Random Process (SIRP).

2.0 Spherically Invariant Random Processes (SIRPs)
A stochastic process, {X(i), i = 0, 1, ..., n - 1}, is an indexed set of random variables. Typically, the index is taken to be time. Each random variable X(i) has an associated probability distribution, which can be specified by a Cumulative Distribution Function (CDF):

F_i(x) = Prob( X(i) ≤ x),

where F_i is the CDF. The derivative of the CDF is the Probability Density Function (PDF). (I guess differentiation, in this sense, is the inverse operation of Lebesque-Stieltjes integration.)

If the stochastic process {X(i), i = 0, 1, ..., n - 1} is a SIRP, it can be represented as the product

X(i) = Y Z(i), i = 0, 1, ..., n - 1,

where Y is a random variable not indexed on time and Z(i) is from a Gaussian distribution with a mean of zero.

2.1 A Single Realization
To consider an example, I picked a distribution for Y, namely the Chi distribution. (A random variable is from a Chi distribution if it is the square root of a random variable from a Chi Squared distribution.) Arbitrarily, I set the degrees of freedom of the corresponding Chi Squared distribution to be 2. For simplicity, let the variance of the normally distributed random variables {Z(i), i = 0, 1, ..., n - 1} be unity.

Figure 1 shows 100 time samples generated from this stochastic process. A single realization y of the Chi distribution is generated for each realization of the SIRP. The time samples consist of the product of this value and 100 realizations generated from a standard normal distribution. Figure 2 is a histogram formed from these 100 time samples. Does the histogram look bell-shaped?

Figure 1: A Realization of a Random Process

Figure 2: Distribution Over Time

2.2 Many Realizations
I generated 100 realizations of this SIRP, each consisting of 100 time samples. Consider a fixed time sample, say i = 4. The 100 realizations of the SIRP allow one to create a sample of the value of the SIRP at this time sample. Figure 3 shows the resulting distribution. The distribution shown reflects variation resulting from the Chi distribution, as well as the variation in the Gaussian distribution. I don’t find it obvious to the eye that this distribution is peaked differently (has a different kurtosis) than a Gaussian distribution.

Figure 3: Distribution Across Realizations

2.3 Nonergodic Stochastic Processes
Figures 2 and 3 are constructed from two random samples, each of 100 points. These samples can each be used to estimate parameters of the stochastic process – for example, the CDF at specified values. If the stochastic process were ergodic such estimates would converge as the sample sizes increased. That is, an estimator based on a large enough number of time samples from a single realization would be equally as good, in some sense, as an estimator based on data across a large enough number of realization at a specified time sample.

But this SIRP is nonergodic. Figure 4 shows the CDFs estimated from the two random samples. The Kolmogorov-Smirnov statistic provides a formal statistical test for deciding whether the difference between these two estimates of the CDF can be explained by random variation. And that test rejects the null hypothesis at a 5% level of statistical significance. To summarize – this post has presented a Monte Carlo demonstration that a SIRP can be nonergodic. The question raised for the economist is whether their theories apply if stochastic processes observed in actual economies (for example, the prices of stocks) are nonergodic.

Figure 4: Empirical Cumulative Distribution Functions (CDF)

References

• Paul Davidson, "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. V, N. 2 (Winter 1982-83): 182-198.
• Joan Robinson, "History versus Equilibrium", in Contributions to Modern Economics, Blackwell (1978)

My Fame

A couple of weeks back, some silly anonymous commentators on Tyler Cowen's blog wrote:

"Who gives two [esses] what Robert Vienneau thinks about anything?"

and

"...and Robert Vienneau is a self-published hack."

And last week, Econ Job Market Rumors witnessed this typically enlightening exchange:

"Robert Vienneau is a [effing] retard."

"Why?"

"Still complaining that GE theory doesn't deal with reswitching and other sraffian critiques when it clearly does."

I don't know what that response is about. I follow Barkley Rosser, Jr., in thinking that reswitching points to the possibility of some interesting dynamics in General Equilibrium models. And I know of no adequate response to Fabio Petri's critique of General Equilibrium theory, particularly what he calls the impermance problem.

This has nothing to do with me. But I thought I'd quote it for an illustration of a completely wrong opinion:

"A related paper of interest is Mas-Collel (1989), 'Capital Theory Paradoxes: Anything Goes,' which notes that the 'problems' coming from aggregating capital are very much related to the Anything Goes theory of Sonnenschein-Mantel-Debreu, and about as problematic to neoclassical theory (meaning, not very problematic)."

Empirical Results in a Whig History of Mainstream Economics

A comprehensive history of physics would not be only about changing ideas and the social setting in which they evolved. It would include stories of many experiments. One might talk about Galileo, the moons of Jupiter, inclined planes, and pendulums. One would have experiments that demonstrate a result long after physicists became convinced of it for other reasons. I think Foucault'a pendulum and the rotation of the earth falls into this category. And one would have empirical results that were cited at times of paradigm shifts - for example, the Michelson Morley experiment and precession of Mercury's orbit for Einstein's theory of special and general relativity, respectively.

What would go into a corresponding history of economics? I suppose one would mention unemployment in the Great Depression and stagflation during the 1970s. Notice these phenomena are not controlled experiments. Vernon Smith's experiments would enter into such a history. I'm not sure where Kahneman and Tversky's prospect theory would go. I suppose it is a triumph for neoclassical economics that it can be formulated sufficiently rigorously that it can be shown experimentally to be false. I suppose natural and field experiments are too recent to get a good historical perspective on. Looking back, one might mention Wesley Clair Mitchell and the National Bureau of Economic Research. I like Wassily Leontief's work. One might mention Richard Stone and work on setting up the system of national accounts. But, as far as I am aware, this gathering of a body of empirical data is not tightly linked to changes in economic theory. What am I missing?