In various blogs, John Holbo, Julian Sanchez, and Matthew Yglesias comment on Hayek. In commenting on Jesse Larner's views on Hayek, I have already mentioned my opinion that The Road to Serfdom can be read more as a jeopardy argument than a slippery slope argument. I've also noted Hayek's difficulties in analyzing mixed, mainly capitalist economies.
Update: Brad DeLong says that The Road to Serfdom was too a slippery slope argument, and Matthew Yglesias reacts.
Friday, October 31, 2008
Thursday, October 30, 2008
Read Colander and Klamer Before Applying to Graduate School
I am amused by the thread created by this polemic, titled "What I thought a PhD was about":
When I first envitioned the dream of having a PhD one day, I had really wrong ideas about it. At first, I thought a PhD was a synonimous of erudition in economics. I believed that someone who had a PhD would have run trhough all the economic theory. But I was mistaken.
It really amaze me that it exists some people who have a PhD in economics and who have never read the wealth of Nations. Right now, a PhD in Economics looks more like an Applied Math PhD. Which is something that really annoys me.
Today, a PhD in economics is not about mastery of economic science but about mastery of statistics and mathematics, in respect to their applications to economic theory.
If I were a graduate dean, I wouldn't admit anyone without undergrad training in economics to persuit graduate studies. In my opinion the profession is too much full with frustrated mathematician and physist who, after they realized they wouldn't do anything worth in their field turned to economics to corrupt that beautiful science with their arcane mathematics.
I hate that. And I hate people who allows that..."
Monday, October 27, 2008
A Characteristic In Common Between the New Palgrave and Wikipedia
Mark Blaug reviewed the 1987 edition of the New Palgrave, apparently for some right-wing outfit. I find much in his review to disagree with. But I think he has a point here:
Wikipedia also has closely related articles with different names. Here are some examples in economics:
The Law of Value/Labor Theory of Value and Marginalism/Neoclassical economics pairs closely follow Blaug's complaint. Each member of a pair are written from very different perspectives. (I've been in edit wars with the crank maintaining the marginalism entry.)
By the way, both the comparative advantage and the Heckscher-Ohlin entry, including related entries on HO theorems, contain the usual errors about capital. That is, these entries are simply incorrect.
"The Eatwell-Milgate-Newman policy of publishing multiple entries with slightly different titles for identical subjects constantly produces curious results... On balance, a policy of presenting competing opinions under the same title would have been vastly preferable to the Eatwell-Milgate-Newman policy of several entries under different titles on what is in fact one and the same topic." -- Mark Blaug, Economics Through the Looking Glass: The Distorted Perspective of the New Palgrave Dictionary of Economics, Institute of Economic Affairs, 1988.An example I found would be Walter Eltis' article "Falling Rate of Profit" and N. Okishio on "Choice of Technique and Rate of Profit". Neither references the other. Sometimes the Eatwell-Milgate-Newman policy makes no difference, e.g. in successive articles on "Competition," "Competition: Austrian Conceptions," "Competition: Classical Conceptions," and "Competition: Marxian Conceptions".
Wikipedia also has closely related articles with different names. Here are some examples in economics:
- Arrow-Debreu Model and General Equilibrium
- Comparative Advantage and Heckscher-Ohlin Model (Only the former is part of the International Trade template)
- Labor Theory of Value and Law of Value (Only the latter appears in the Marxist Theory template)
- Marginalism and Neoclassical Economics
The Law of Value/Labor Theory of Value and Marginalism/Neoclassical economics pairs closely follow Blaug's complaint. Each member of a pair are written from very different perspectives. (I've been in edit wars with the crank maintaining the marginalism entry.)
By the way, both the comparative advantage and the Heckscher-Ohlin entry, including related entries on HO theorems, contain the usual errors about capital. That is, these entries are simply incorrect.
Friday, October 24, 2008
Edward, You Ignorant Arse
In an email exchange with a graduate student, Edward Prescott proves himself to be an impolite, ignorant, arrogant fool. Prescott's correspondent, Leonid Teytelman, doubted this must be Prescott in full possession of his faculties - maybe an adolescent niece or nephew had somehow gotten ahold of Prescott's account. He could not be drunk, since the interchange took place over several days. Myself, I have no problem in believing that Prescott understands neither the science of economics nor basic facts about the United States economy.
Apparently Prescott, in his professional work with Kyland, is equally incoherent. Jim Hartley documents that
Apparently Prescott, in his professional work with Kyland, is equally incoherent. Jim Hartley documents that
"In five different programmatic manifestos over a span of 15 years, Kydland and Prescott have offered five different—and in many ways mutually incompatible—justifications for the models they were advocating." -- James E. Hartley (2006) "Kyland and Prescott's Nobel Prize: the Methodology of Time Consistency and Real Business Cycle Models", Review of Political Economy, V. 18, N. 1 (January): 1-28At one point, business cycles are caused by the time-to-build capital equipment. No, they are caused by technology shocks in a growth model. You should believe this because "the smoothed series and the derivations from the smoothed series are quantitatively consistent with the observed behavior". No, only because the model explains co-movements of the deviations. No, because the newly interpreted model follows from "standard" theory (Solow-Swan growth modeling). And deviations from the model are because the measurements are bad. No, the model was built to explain previously observed facts, which are observed not by looking at deviations from the Solow-Swan growth model, but from deviations from the output of the Hodrick-Prescott filter. In particular, the model explains the observed acyclical nature of movements in real wages. That is, the model explains the observed strong procyclical nature of movements in real wages. And the model is merely an application of Computable General Equilibrium modeling. The parameters of the model are based on observed values. No, they are chosen so the model outputs "mimic the world".
Wednesday, October 22, 2008
A SF Fraction Or Faction
I sometimes wonder if Ken MacLeod writes science fiction novels just for me. What other novelist has characters refer to Leontief matrices?
Anyway, he has a blogroll I find quite interesting to explore. I here skip over commentators on science and on current events. The suggested reading off Kevin Carson's mutualist site makes available all sorts of old works. I trust William Godwin's Enquiry Concerning the Principles of Political Justice is the pamphlet Malthus reacted to. I am interested in how the Ricardian socialists argued, on the basis of classical political economy, that the source of returns to capital is the exploitation of labor. I expect to find that that is an aspect of Thomas Hodgskin's Labour Defended against the Claims of Capital Or the Unproductiveness of Capital proved with Reference to the Present Combinations amongst Journeymen.
Another site on MacLeod's blogroll that will take me years to explore gathers essays refuting myths & legends about Marx. I suspect I will be more open to some of these arguments than others.
I have read compliments on David Schweickart. I want to recall to look up his "Economic Democracy: A Worthy Socialism that Would Really Work" (Science & Society, V. 56, N. 1, Spring 1992: 9-38) next time I am in a university library, also available at SolidarityEconomy.net, which seems defunct.
Anyway, he has a blogroll I find quite interesting to explore. I here skip over commentators on science and on current events. The suggested reading off Kevin Carson's mutualist site makes available all sorts of old works. I trust William Godwin's Enquiry Concerning the Principles of Political Justice is the pamphlet Malthus reacted to. I am interested in how the Ricardian socialists argued, on the basis of classical political economy, that the source of returns to capital is the exploitation of labor. I expect to find that that is an aspect of Thomas Hodgskin's Labour Defended against the Claims of Capital Or the Unproductiveness of Capital proved with Reference to the Present Combinations amongst Journeymen.
Another site on MacLeod's blogroll that will take me years to explore gathers essays refuting myths & legends about Marx. I suspect I will be more open to some of these arguments than others.
I have read compliments on David Schweickart. I want to recall to look up his "Economic Democracy: A Worthy Socialism that Would Really Work" (Science & Society, V. 56, N. 1, Spring 1992: 9-38) next time I am in a university library, also available at SolidarityEconomy.net, which seems defunct.
Monday, October 20, 2008
Kaldor's Contributions: An Impressionistic Survey
Introduction
This post gives a quick overview of my impressions of the contributions to economics of Nicholas Kaldor. In writing this post, I deliberately did not review the entries on him at Gonçalo Fonseca's site on the history of economic thought, in the New Palgrave, or at Wikipedia. I did use Turner (1993) for the biographical details.
Biography
I will be brief on the biography of Lord Nicholas Kaldor (12 May 1908 - 1986). Born in Budapest, he later studied at Berlin. He transferred to the London School of Economics (LSE) as an undergraduate in the Fall of 1927. Kaldor visited the United States, including Harvard and Princeton, in 1935. He moved to Cambridge in 1939, with the evacuation of the LSE to Cambridge, and stayed on at Cambridge (King's College) after the war. He joined the United States Strategic Bombing Survey under the direction of John Kenneth Galbraith. He became a Baron in 1974 and was the president of the Royal Economic Society in 1976. Kaldor's wife was named Clarissa, and they had four daughters. Anthony P. Thirwall was named his literary executor.
1930s
Economists in the 1930s had, once again, a controversy on the theory of capital, with Frank Knight on one side and Friedrich A. Hayek and Fritz Machlup on the other. Early in his career, Kaldor (1937) surveyed that dispute. He followed up with investigations (1939a, 1942) of Hayek's capital theory and exposition of the Austrian Business Cycle Theory. Although Kaldor's judgments are sharp, I think these articles might have been more convincing if the standard of the time allowed for more mathematics.
I don't recall ever reading Kaldor's original contributions to welfare economics. Apparently, he had an article in the 1939 volume of the Economic Journal. This article and one by J. R. Hicks are the primary source of the famous Hicks-Kaldor compensation principle.
Apparently the younger economists at Cambridge and LSE, such as Robinson and Kaldor, respectively, met once a month to debate macroeconomics even before the publication of Keynes' General Theory. Kaldor became a convert to Keynes, as can be seen in Kaldor (1939b). Barkley Rosser, Jr., tends to cite Goodwin and Kaldor as early explorations of non-linear dynamics in economic models. Maybe Kaldor (1940) is important here, which I have not read in at least a decade, if ever.
Later Work on Growth and Distribution Theory
Kaldor's later work on growth and distribution is more clearly Post Keynesian, in my opinion. His 1956 paper compares and contrast three theories of distribution: a neoclassical theory which makes most sense with a now exploded scarcity theory of value, a classical theory in which wages are exogeneous in the theory of value and distribution, and a Post Keynesian theory in which the distribution of income depends on macroeconomic savings propensities. I think this paper led to the souring of his relationship with Joan Robinson; she was, I guess, worried about priority in publication. Luigi Pasinetti disputed the logical consistency of Kaldor's presentation, in which workers obtain income from capital but save that portion of their income at the higher rate characteristic in Kaldor's model of savings out of profits. In a later seminar with Pasinetti, Robinson, and Samuelson & Modigliani, Kaldor (1966) clarified that he thought of the savings rate as pertaining to the source of income, not the individual savers. This ties into the idea that savings out of retained earnings is not transparent to those holding stock in corporations. Kaldor suggested these ideas can explain how the market value of corporate stock relates to the book value of the assets owned by corporations. Later work by others demonstrate that for two classes to persist in Kaldor's model, the rate of profits must exceed the rate of interest (i.e., the return to capital obtainable by workers in the financial markets they have access to). This may not be a good idea, but perhaps it would be an interesting idea to synthesize this literature with literature related to De Long et al (1990) - and I would prefer not to reference Shleifer.
Kaldor developed a related series of growth models. He presented one at the famous August 1958 Corfu conference. I guess it was in this paper he presented his "stylized facts". He presented another model in this series (Kaldor and Mirrlees 1962) in the same issue of the Review of Economic Studies in which he welcomed (1962) Arrow to the band of heretics for his "Learning by Doing" paper. Kaldor's models use a technical progress function, which, I gather, is empirically indistinguishable from a Cobb-Douglas production function with technical progress.
Kaldor emphasized increasing returns in manufacturing in these models, and he championed Verdoon's law. Thirwall (e.g., 1986) applies these ideas to developing economics. I gather a policy recommendation in this literature is for export-led growth. An emphasis on increasing returns underlies Kaldor's (1972, 1975, and 1985) mature criticisms of neoclassical economics.
Finally, I want to mention Kaldor's theory of endogenous money. Kaldor described both the inability of monetary authorities to control the supply of money under some given definition and the ability of financial institutions to continually evolve new instruments to serve as money. He used these ideas to refute monetarism (1986, first edition 1982).
References
This post gives a quick overview of my impressions of the contributions to economics of Nicholas Kaldor. In writing this post, I deliberately did not review the entries on him at Gonçalo Fonseca's site on the history of economic thought, in the New Palgrave, or at Wikipedia. I did use Turner (1993) for the biographical details.
Biography
I will be brief on the biography of Lord Nicholas Kaldor (12 May 1908 - 1986). Born in Budapest, he later studied at Berlin. He transferred to the London School of Economics (LSE) as an undergraduate in the Fall of 1927. Kaldor visited the United States, including Harvard and Princeton, in 1935. He moved to Cambridge in 1939, with the evacuation of the LSE to Cambridge, and stayed on at Cambridge (King's College) after the war. He joined the United States Strategic Bombing Survey under the direction of John Kenneth Galbraith. He became a Baron in 1974 and was the president of the Royal Economic Society in 1976. Kaldor's wife was named Clarissa, and they had four daughters. Anthony P. Thirwall was named his literary executor.
1930s
Economists in the 1930s had, once again, a controversy on the theory of capital, with Frank Knight on one side and Friedrich A. Hayek and Fritz Machlup on the other. Early in his career, Kaldor (1937) surveyed that dispute. He followed up with investigations (1939a, 1942) of Hayek's capital theory and exposition of the Austrian Business Cycle Theory. Although Kaldor's judgments are sharp, I think these articles might have been more convincing if the standard of the time allowed for more mathematics.
I don't recall ever reading Kaldor's original contributions to welfare economics. Apparently, he had an article in the 1939 volume of the Economic Journal. This article and one by J. R. Hicks are the primary source of the famous Hicks-Kaldor compensation principle.
Apparently the younger economists at Cambridge and LSE, such as Robinson and Kaldor, respectively, met once a month to debate macroeconomics even before the publication of Keynes' General Theory. Kaldor became a convert to Keynes, as can be seen in Kaldor (1939b). Barkley Rosser, Jr., tends to cite Goodwin and Kaldor as early explorations of non-linear dynamics in economic models. Maybe Kaldor (1940) is important here, which I have not read in at least a decade, if ever.
Later Work on Growth and Distribution Theory
Kaldor's later work on growth and distribution is more clearly Post Keynesian, in my opinion. His 1956 paper compares and contrast three theories of distribution: a neoclassical theory which makes most sense with a now exploded scarcity theory of value, a classical theory in which wages are exogeneous in the theory of value and distribution, and a Post Keynesian theory in which the distribution of income depends on macroeconomic savings propensities. I think this paper led to the souring of his relationship with Joan Robinson; she was, I guess, worried about priority in publication. Luigi Pasinetti disputed the logical consistency of Kaldor's presentation, in which workers obtain income from capital but save that portion of their income at the higher rate characteristic in Kaldor's model of savings out of profits. In a later seminar with Pasinetti, Robinson, and Samuelson & Modigliani, Kaldor (1966) clarified that he thought of the savings rate as pertaining to the source of income, not the individual savers. This ties into the idea that savings out of retained earnings is not transparent to those holding stock in corporations. Kaldor suggested these ideas can explain how the market value of corporate stock relates to the book value of the assets owned by corporations. Later work by others demonstrate that for two classes to persist in Kaldor's model, the rate of profits must exceed the rate of interest (i.e., the return to capital obtainable by workers in the financial markets they have access to). This may not be a good idea, but perhaps it would be an interesting idea to synthesize this literature with literature related to De Long et al (1990) - and I would prefer not to reference Shleifer.
Kaldor developed a related series of growth models. He presented one at the famous August 1958 Corfu conference. I guess it was in this paper he presented his "stylized facts". He presented another model in this series (Kaldor and Mirrlees 1962) in the same issue of the Review of Economic Studies in which he welcomed (1962) Arrow to the band of heretics for his "Learning by Doing" paper. Kaldor's models use a technical progress function, which, I gather, is empirically indistinguishable from a Cobb-Douglas production function with technical progress.
Kaldor emphasized increasing returns in manufacturing in these models, and he championed Verdoon's law. Thirwall (e.g., 1986) applies these ideas to developing economics. I gather a policy recommendation in this literature is for export-led growth. An emphasis on increasing returns underlies Kaldor's (1972, 1975, and 1985) mature criticisms of neoclassical economics.
Finally, I want to mention Kaldor's theory of endogenous money. Kaldor described both the inability of monetary authorities to control the supply of money under some given definition and the ability of financial institutions to continually evolve new instruments to serve as money. He used these ideas to refute monetarism (1986, first edition 1982).
References
- J. Bradford De Long, Andrei Shleifer, Lawrence H. Summers, and Robert J. Waldmann (1990) "Noise Trader Risk in Financial Markets", Journal of Political Economy, V. 98, N. 4 (August): 703-738
- Nicholas Kaldor (1937) "Annual Survey of Economic Theory: The Recent Controversy on the Theory of Capital", Econometrica, V. 5, N. 3 (July): 201-233
- -- (1939a) "Capital Intensity and the Trade Cycle", Economica, New Series, V. 6, N. 21 (February): 40-66
- -- (1939b) "Speculation and Economic Stability", Review of Economic Studies, V. 7, N. 1 (October): 1-27
- -- (1940) "A Model of the Trade Cycle", Economic Journal, V. 50, N. 197 (March): 78-92
- -- (1942) "Professor Hayek and the Concertina-Effect", Economica, New Series, V. 9, N. 36 (November): 359-382
- -- (1956) "Alternative Theories of Distribution", Review of Economic Studies, V. 23: 83-100
- -- (1962) "Comment", Review of Economic Studies V. 29, N. 3 (June): 246-250
- -- (1966) "Marginal Productivity and Macro-Economic Theories of Distribution: Comment on Samuelson and Modigliani", Review of Economic Studies, V. 33, N. 4 (October): 309-319
- -- (1985) Economics without Equilibrium, M. E. Sharpe
- -- (1972) "The Irrelevance of Equilibrium Economics", Economic Journal, V. 82, N. 328 (December): 1237-1255
- -- (1975) "What is Wrong with Economic Theory", Quarterly Journal of Economics, V. 89, N. 3 (August): 347-357
- -- (1986) The Scourge of Monetarism, Second Edition, Oxford University Press
- Nicholas Kaldor and James A. Mirrlees (1962) "A New Model of Economic Growth", Review of Economic Studies V. 29, N. 3 (June): 174-192
- A. P. Thirwall (1986) "A General Model of Growth and Development on Kaldorian Lines", Oxford Economic Papers (July)
- Marjorie S. Turner (1993) Nicholas Kaldor and the Real World, M. E. Sharpe
"Macroeconomics as an Autonomous Discipline"
"Paradoxically, the main result obtained by the new classical economists is the demonstration - against their wishes and expectations - that a satisfactory synthesis of macroeconomics and microeconomics is not yet mature. As a matter of fact, the micro-foundations of macroeconomics which they suggest are by now far from satisfactory. They rely on the heroic assumption that the decision-makers of the models are representative agents, whose behavior fairly well approximates the aggregate behavior of the economy. Unfortunately this assumption surreptitiously eliminates the main object that should be studied by macroeconomics: aggregation problems and failures of coordination between the behavior of individuals. Even so, the suggested micro-foundations work only under very special assumptions which actually deny any importance to the main problems considered by Keynes's macroeconomics: uncertainty, disequilibrium, instability, structural change, etc. As we have seen, disequilibria are assumed to be non-intelligible and are therefore ignored; uncertainty is emasculated by the 'certainty equivalence' hypothesis; instability is defined away by arbitrarily restricting the analysis to stationary and ergodic processes and taking account only of the subset of stable solutions...
The failure of this reductionist research programme may be due to the immaturity of current macroeconomics, but it may also be due to weaknesses in existing microeconomic theory. Notwithstanding the widespread belief in its intrinsic solidity, the micro theory currently accepted by the new classical economists may prove on closer examination to be insufficiently powerful to provide solid foundations for a satisfactory macroeconomics. To take the preliminary steps towards a real synthesis between macro and micro theories, it is necessary to consider not only the micro-foundations of macroeconomics but also the macro-foundations of microeconomics (Hicks 1983).
The history of scientific thought shows that whenever a synthesis between different disciplines has been successfully accomplished, the result has been a new discipline with features not reducible to those of the original disciplines. Such a synthesis between micro and macroeconomics, if it is possible, is still far away. In the meantime the reciprocal autonomy of disciplines should be carefully safeguarded. It is particularly important to defend the autonomy of macroeconomics, as today this is greatly jeopardized by views like those mentioned above. Therefore we should revert to the original Keynesian concept of macroeconomics as an autonomous discipline. This does not imply that we should give up making serious efforts to provide rigorous micro-foundations for our macroeconomic statements, if that means searching for greater consistency between the two disciplines. In other words we should continue to pursue a full synthesis between microeconomics and macroeconomics. Many things have been learned from past attempts, unsuccessful as they were, and many others may be learned through future efforts.
But in the meantime one should not reject as non-scientific any contribution that lacks proper 'micro-foundations,' particularly in the restricted sense of a 'reduction to current Walrasian microeconomics.' As a matter of fact, though it may be found impossible to provide proper micro-foundations to a given macroeconomic statement, this might become possible in the future. Such developments have occurred many times in the past and it could happen again, especially if microeconomics extends its range well beyond its Walrasian bounds. To reject this view would be as irrational as to reject as non-scientific any biological statement not yet reducible to chemical statements. Unfortunately, as has been wisely remarked, the only known way to reduce biology to chemistry is murder." -- Alessandro Vercelli, Methodological Foundations of Macroeconomics: Keynes & Lucas, Cambridge University Press, 1991.
Thursday, October 16, 2008
You Got Me Babe
Here are two books one can read on-line and that I may read:
The second book is Nicholas Kaldor's demonstration that monetarism does not work. On this blog, Kaldor should need no introduction.
Both books are in a freely readable on-line format that I find annoying. I suppose the format of the free version of the first is a business decision to encourage the purchase of the PDF version. And I blame copyright law for the format of the second.
- Protecting Individual Privacy in the Struggle Against Terrorists: A Framework for Program Assessment, National Academies Press (2008)
- Nicholas Kaldor, The Scourge of Monetarism, Second Edition, Oxford University Press (1986)
The second book is Nicholas Kaldor's demonstration that monetarism does not work. On this blog, Kaldor should need no introduction.
Both books are in a freely readable on-line format that I find annoying. I suppose the format of the free version of the first is a business decision to encourage the purchase of the PDF version. And I blame copyright law for the format of the second.
Saturday, October 11, 2008
"Just Look At The Marginal Product Of Capital"
Friday's New York Times has an editorial by Casey Mulligan, a professor of economics at the University of Chicago. Mulligan says that the U.S. economy will keep on doing fine, as shown by "the profitability of non-financial capital, what economists call the marginal product of capital." Mulligan is, of course, incorrect. Economists do not call the rate of profits "the marginal product of capital". Even the proposition that, in equilibrium, the rate of profits and the marginal product of capital are equal is without any theoretical or empirical justification. Casey Mulligan is, at best, ignorant and incompetent.
Post Keynesians and others would also tend to be skeptical of other aspects of Mulligan’s editorial. It is a Post Keynesian belief that money is not a veil, neither in the long run nor the short run. Finance can cause the real economy to become discoordinated. Mulligan looks at trends in the rate of profits from before the Great Depression to now. One could assert that one aspect of such trends is a class struggle over the distribution of the surplus. Perhaps workers are sufficiently cowed today that, unlike in the 1970s, no danger exists of a profitability crisis. (Given the Okishio theorem, I do not think that a law of the tendency of the rate of profits to fall follows from Marx’s assumptions, at least in my favorite formalizations of Marx’s approach.) A realization crisis might still arise. When income distribution is so unequal, one might expect effective demand to be weak.
Post Keynesians and others would also tend to be skeptical of other aspects of Mulligan’s editorial. It is a Post Keynesian belief that money is not a veil, neither in the long run nor the short run. Finance can cause the real economy to become discoordinated. Mulligan looks at trends in the rate of profits from before the Great Depression to now. One could assert that one aspect of such trends is a class struggle over the distribution of the surplus. Perhaps workers are sufficiently cowed today that, unlike in the 1970s, no danger exists of a profitability crisis. (Given the Okishio theorem, I do not think that a law of the tendency of the rate of profits to fall follows from Marx’s assumptions, at least in my favorite formalizations of Marx’s approach.) A realization crisis might still arise. When income distribution is so unequal, one might expect effective demand to be weak.
Thursday, October 09, 2008
Who Should Win The "Nobel" Prize In Economics?
I say Paul Davidson and Luigi Pasinetti should win it.
Sunday, October 05, 2008
For Whatever Can Walk - It Must Walk Once More
1.0 Introduction
This post presents a simple macroeconomic model that combines trend and cycle. It presents some possible aspects of economic growth and business cycles. This model has some features that I find objectionable, but I find it interesting nonetheless. It is a non-linear model of dynamics presenting a formalization of some ideas to be found in Marx's Capital. And it is a model that does not impose equilibrium, but allows for the stability of equilibrium to be analyzed.
2.0 Technology
Assume a Leontief (fixed coefficients) production function:
The capital stock depreciates at a rate of 100 δ percent. That is, output can either be consumed or added to a capital stock that experiences a force of mortality of δ. Technical progress is disembodied, and labor productivity increases at a constant rate:
3.0 Wages, Profits, Investment
Let w be the wage rate. Then (w l) or (w q/a) are total wages. Define u to be the workers share of the gross product:
Finally, assume that the rate of growth of wages is a (linear) increasing function of the employment rate:
4.0 Derivation of the Model
The rate of growth of the employment rate is the difference between the rate of growth of employment and the rate of growth of the labor force:
The following pair of equations, the fundamental equations of this model, restate equations derived above:
5.0 Solution of the Model
For what its worth, a trajectory in phase space has the equation:
6.0 Discussion
I think it interesting to note that the rate of growth of wages at the limit point is positive due to growth in productivity; in fact, the rate of growth of wages at the limit point is equal to the rate of growth in productivity. If productivity did not grow, if the labor force were stationary, and if there were no depreciation, wages would consume the entire product at the limit point; the capitalists would receive no profits.
A single cycle can easily be described in intutitive terms. Start with low unemployment. Wages will increase as a share in output. Consequently, saving and investment will decline. The growth of output will slow. Eventually, the "reserve army of the unemployed" will be recreated. Wages will decrease as a share in output, although they may still be increasing in absolute terms. Eventually, investment will pick back up. When the growth of output exceeds the growth in productivity by more than the growth of the labor force, the employment rate will increase.
Clearly, this model can reproduce a qualitative resemblance to some empirical properties of some economic time series. If one plots empirical data in the illustrated phase space, one may see a suggestion of motion in the indicated directions, but one will not find a single cycle. Perhaps shocks change the parameters of the model on some occasions. Or perhaps important considerations are not embodied in the model. This model is Classical in important respects, where I mean by "Classical" to refer to the economics of Smith and Ricardo. Richard Goodwin, the inventor of this model, has done important work attempting to integrate this model with Keynesian and Schumpeterian themes.
References
There was a conference in Sienna a number of years back devoted to this model. There's also discussion of this model in a Festschrift volume devoted to Richard Goodwin.
Update: Serena Sordi has a recent generalization of this model to four dimensions, presented at a sort of festschrift for Barkley Rosser, Jr.
This post presents a simple macroeconomic model that combines trend and cycle. It presents some possible aspects of economic growth and business cycles. This model has some features that I find objectionable, but I find it interesting nonetheless. It is a non-linear model of dynamics presenting a formalization of some ideas to be found in Marx's Capital. And it is a model that does not impose equilibrium, but allows for the stability of equilibrium to be analyzed.
2.0 Technology
Assume a Leontief (fixed coefficients) production function:
q = min(a l, k/σ)where q is gross output, l is the labor employed, k is the value of capital, a is labor productivity, and σ is the capital-output ratio. Both constraints in the production function are always met with equality:
l = q/a
σ = k/qThe capital stock is always employed, but sometimes employment can fall short of the entire labor force, as explained below.
The capital stock depreciates at a rate of 100 δ percent. That is, output can either be consumed or added to a capital stock that experiences a force of mortality of δ. Technical progress is disembodied, and labor productivity increases at a constant rate:
a = a0 exp( α t )The labor force also grows at a constant rate:
n = n0 exp( β t)where n is the labor supply. Hence, v is the employment rate, where the employment rate is defined as follow:
v = l/nWhen v is unity, the labor force is fully employed. v ranges from (a subinterval of) zero to unity in this model.
3.0 Wages, Profits, Investment
Let w be the wage rate. Then (w l) or (w q/a) are total wages. Define u to be the workers share of the gross product:
u = w/aThen (1 - u) is the capitalists' share of the product. Assume that wages are entirely consumed and that a fixed proportion of profits are saved and invested:
dk/dt = s (1 - u) q - δ kwhere s is the savings rate out of profits.
Finally, assume that the rate of growth of wages is a (linear) increasing function of the employment rate:
(1/w) dw/dt = - γ + ρ vThe above equation could also be written as:
(1/w) dw/dt = ρ [v - (γ/ρ) ]In words, wages grow faster in a tight labor market. The marginal productivity of labor is beside the point in this model.
4.0 Derivation of the Model
The rate of growth of the employment rate is the difference between the rate of growth of employment and the rate of growth of the labor force:
(1/v) dv/dt = (1/l) dl/dt - βBy similar manipulations, one can show that the rate of growth of employment is the difference between the rate of growth of output and the rate of growth of productivity:
(1/l) dl/dt = (1/q) dq/dt - αCombining these two equations yields an equation relating the rate of growth of the employment rate to the rate of growth in output:
(1/v) dv/dt = (1/q) dq/dt - (α + β)The derivation of the following equation from the definition of the capital-output ratio and the equation for the rate of change in the value of capital is simpler:
(1/q) dq/dt = (1 - u) s/σ - δHence,
(1/v) dv/dt = (1 - u)(s/σ) - (α + β + δ)The rate of growth of workers' share in gross ouput is the difference between the rate of growth of wages and the rate of growth of productivity:
(1/u) du/dt = (1/w) dw/dt - αSubstitute from the postulated relation between the rate of growth in wages and the employment rate:
(1/u) du/dt = ρ v - (α + γ)
The following pair of equations, the fundamental equations of this model, restate equations derived above:
dv/dt = (s/σ - α - β - δ) v - (s/σ) u v
du/dt = -(α + γ) u + ρ u vHere's the cool part - this is the Lotka-Volterra predator-prey model. It is a canonical non-linear dynamical system used to model, say, lynx and rabbits.
5.0 Solution of the Model
For what its worth, a trajectory in phase space has the equation:
(uν1) exp(- θ1 u) = H(v- ν2) exp(θ2 v)where
θ1 = s/σ
θ2 = ρ
ν1 = s/σ - (α + β + δ)
ν2 = (α + γ)and H is an arbitrary integrating constant. All these trajectories consist of cycles, as illustrated in Figure 1. The limit point around which these trajectories cycle is given by:
u* = ν1/θ1
v* = ν2/θ2 = (α + γ)/ρ(The origin in phase space is also a limit point; the origin has the stability of a saddle-point.)
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| Figure 1: Phase Space |
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| Figure 2: A Trajectory |
6.0 Discussion
I think it interesting to note that the rate of growth of wages at the limit point is positive due to growth in productivity; in fact, the rate of growth of wages at the limit point is equal to the rate of growth in productivity. If productivity did not grow, if the labor force were stationary, and if there were no depreciation, wages would consume the entire product at the limit point; the capitalists would receive no profits.
A single cycle can easily be described in intutitive terms. Start with low unemployment. Wages will increase as a share in output. Consequently, saving and investment will decline. The growth of output will slow. Eventually, the "reserve army of the unemployed" will be recreated. Wages will decrease as a share in output, although they may still be increasing in absolute terms. Eventually, investment will pick back up. When the growth of output exceeds the growth in productivity by more than the growth of the labor force, the employment rate will increase.
Clearly, this model can reproduce a qualitative resemblance to some empirical properties of some economic time series. If one plots empirical data in the illustrated phase space, one may see a suggestion of motion in the indicated directions, but one will not find a single cycle. Perhaps shocks change the parameters of the model on some occasions. Or perhaps important considerations are not embodied in the model. This model is Classical in important respects, where I mean by "Classical" to refer to the economics of Smith and Ricardo. Richard Goodwin, the inventor of this model, has done important work attempting to integrate this model with Keynesian and Schumpeterian themes.
References
There was a conference in Sienna a number of years back devoted to this model. There's also discussion of this model in a Festschrift volume devoted to Richard Goodwin.
- Richard Goodwin, "A Growth Cycle," in Socialism, Capitalism, & Economic Growth: Essays Presented to Maurice Dobb, (edited by C. H. Feinstein), Cambridge University Press, 1967.
- Richard Goodwin, Chaotic Economic Dynamics, Oxford University Press, 1990.
- Paul Ormerod, The Death of Economics, St. Martins, 1994.
Update: Serena Sordi has a recent generalization of this model to four dimensions, presented at a sort of festschrift for Barkley Rosser, Jr.
Saturday, October 04, 2008
Economists as Liars
Robert Waldmann makes some strong statements:
Update: Having now read Mark Buchanan's New York Times editorial, I'm not at all sure I agree with Robert Waldmann in aspects of his post not quoted above. Buchanan is arguing for an agent-based modelling, out-of-equilibrium, econophysics approach. Buchanan maybe overstates the contrast between his approach and most mainstream economics, but Waldmann's post contains an element of boundary-patrolling anyways.
"...The conclusions of economic theory as presented by many or perhaps most economists do not follow from current economic theory, but rather from the 50 year old efforts at mathematical economic theory...Read the whole thing. (Hat tip to Ezra Klein)
The problem is, I think, that when they talk to non economists, many economists pretend that traditional economic theory is a good approximation to reality. By 'traditional' I mean 50 year old. The fact that the conclusions are the result of strong assumptions made for tractability and are known to not hold without these assumptions is irrelevant...
...Once a model has been put in textbooks, it becomes immortal invulnerable not only to the data (which can prove it is not a true statement about the world but no one ever thought it was) but also to further theoretical analysis...
...I think the worse problem is that economists who are also libertarian ideologues are lying about the current state of economic theory, not only its very weak scientific standing, but the fact that, even if it were all absolutely true, their policy recommendations do not at all follow from current economic theory..." -- Robert Waldmann
Update: Having now read Mark Buchanan's New York Times editorial, I'm not at all sure I agree with Robert Waldmann in aspects of his post not quoted above. Buchanan is arguing for an agent-based modelling, out-of-equilibrium, econophysics approach. Buchanan maybe overstates the contrast between his approach and most mainstream economics, but Waldmann's post contains an element of boundary-patrolling anyways.