The American Mathematical Society catalogs resources for increasing diversity in mathematics. The Association for Women in Mathematics is concerned with female mathematicians. The Association for Computing Machinery (ACM) Committee on Women in Computing is for computer science. The American Statistical Society (ASA) Committee on Women in Statistics and the ASA Caucus for Women in Statistics focus on statistics.
Since this is an economics blog, I'll mention the International Association for Feminist Economics (IAFEE).
Note To Myself: Read Luigi Guiso, Ferdinando Monte, Paola Sapienza, and Luigi Zingales (2008) "Culture, Gender and Math", Science, 320, 1164 (30 May)
Thursday, July 31, 2008
Sunday, July 27, 2008
Two Roads Diverged In A Yellow Wood, And Sorry I Could Not Travel Both And Be One Traveler
1.0 Introduction
Brian Arthur and Paul David, two teachers at Stanford about a decade ago, have attracted a certain amount of popular attention with the concept of path dependence. Arthur, for example, has had a certain amount of influence on policy. This post is an attempt to explain the concept, primarily as it applies to stochastic processes. Path dependence is one way of formalizing the idea that history matters.
2.0 A Stochastic Process
Path dependence relates to events economists choose to model as random. This modeling choice does not imply that economists think such events are necessarily the result of the modeled agents acting capriciously, irrationally, or mistakenly. Consider such childhood games as Odds and Evens or Paper-Rock-Scissors. The optimal strategy for each player is to choose their move randomly. The winner of such games will vary randomly. Notice that apart from the players' choices, these games are deterministic. No dice are being rolled or cards shuffled.
A stochastic process is merely an indexed set of random variables:
I consider an example of a path-dependent stochastic process that does not exhibit certain other properties. This stochastic process can be in one of eight states, {Start, B, C, D, E, F, G, H}. It begins in the Start state. State transition probabilities are indicated by
the fractions in Figure 1. For example, consider the probability distribution for the state of the process at the second time step, X( 2 ). Figure 1 shows that if the process is in the Start state, the probability that it will transition to state B is 1/2. Likewise, given that it is in the Start state, the probability that it will transition to state C is 1/2. Hence the probability distribution of X( 2 ) is:
Notice that the probabilities leading out from each state total unity. It is left as an exercise for the reader to confirm that the proability distribution of X( 3 ) is as follows:
This process exhibits certain properties that are particularly simple, as well as some properties that complicate analysis. Notice that the state transition properties are invariant across time. Given that the process is in the Start state, the probability that it will transition to state B is 1/2, no matter at what time the process may be in the Start state. It does not matter whether we are considering the initial time step or some later time when the process happens to have returned to the Start state.
Furthermore, the process is memoryless. State transition probabilities depend only on the current state, not the history with which the process reached the current state. This property of memorylessness is known as the Markov property. This example is a Markov process.
The Markov property and the assumption of time-inavariant state transition probabilities are simplifying assumptions. One might think relaxation of these assumptions might be one way of showing that "history matters." Since, as will be explained, this example exhibits path dependence, violations of these assumptions are clearly not necessary for path dependence. And Margolis and Liebowitz are incorrect:
An interesting classification of sets of states is available for Markov processes, that of transient and absorbing states. Consider the states {Start, B, C}. By assumption, the process starts in a state within this set. But eventually the process will lie in a state outside this set. Once this happens, the process will never return to this set. States Start, B, and C are known as transient states. On the other hand, consider the states {D, E, F}. Once the process is in a state in this set, the process will never depart from a state in the set. Furthermore, if the process is in a state in this set, it will eventually visit all other states in the set. {D, E, F} is a set of asorbing states. This is not the unique set of absorbing states for this process. {G, H} is also a set of absorbing states.
Consider the problem of estimating the probability distribution over the states at some large number of time step, say X(10,000), after the start. The probability that the process is in a transient state is negligible. One might be tempted to estimate X(10,000) by the proportion of time steps that a single realization of the process spends in each state. A realization might be:
If the process were ergodic, the limiting distribution in the first column in Table 1 would be a good estimate of the probability distribution for the state of the process at some time after transient behavior was likely to be completed. In this case, though, another realization might yield the limiting distribution shown for the second realization in Table 1. The probability distribution, in fact, at a given time, as that time increases without bound would have positive probabilities for all non-transient states. The last column in Table 1 shows this limiting probability distribution.
In general, estimates of parameters of the underlying probability distributions can be made across multiple realizations of the process or from a single realization. In a nonergodic process, such estimates will not converge as the number of realizations or the length of the single realization increases.
Another definition of ergodicity involves what states can be eventually reached from each state. In an ergodic process, each state can be eventually reached, with positive probability. In the example, all states can be reached from the transient states Start, B, and C. But states Start, B, C, G and H cannot be reached from states D, E, and F. Suppose an external occurrence changes the state transition probabilities. If the process were previously ergodic, this change could not possibly result in states arising that were previously unobserved.
To re-iterate, a nonergodic process does not have an unique limiting probability distribution. The applicable limiting distribution of any realization of the process depends on the history of that particular realization. Thus, the process exhibits path dependence.
Another branch of mathematics deals with deterministic dynamical systems. Such systems are typically defined by systems of differential or difference equations. Sometimes the solutions of such systems can be such that trajectories in phase space diverge, no matter how close they start. This is known as sensitive dependence on initial conditions, popularly known as the "butterfly effect." (The irritating mathematican character in Jurassic Park mumbles about this stuff.) Notice that path dependence is defined above without drawing on this branch of mathematics. Here, too, Margolis and Liebowitz are mistaken:
3.0 Conclusion
Why should economists care about the mathematics of path dependence? First, models of path dependence suggest how to construct economic models that overcome frequently criticized characteristics of neoclassical economics. Neoclassical models often depict equilibria. These equilibria are end states of path independent processes. Ever since Veblen, some economists have objected to such models as being teleological and acausal. Models in which path dependence can arise are causal and show neoclassical economics to be a special case.
This claim that neoclassical economics is merely a special case, dependent on a special case assumption of ergodicity, may lead one to wonder about connections with a theory claimed to be the "General Theory." As a matter of fact, Paul Davidson claims that a consideration of nonergodicity is useful in explicating the economics of Keynes. So a second reason economists should be concerned with nonergodicity and path dependence is to further understand possible approaches to macroeconomics.
Third, some economists, e.g. Brian Arthur, have developed specific models of technological change that exhibit nonergodicity. These models, including those of a Polya urns, show how increasing returns can act as positive feedback and lead to path dependence. Inasmuch as these models cast light on economic history, path dependence can be useful for empirical work.
The theory of path dependence raises an empirical question. Are nonergodic stochastic processes useful for modeling any, or any important, economic time series? The evolution of the QWERTY keyboard seems to be an example of a path dependent process. Apparently there were several 19th century typewriter keyboard layouts. QWERTY became the dominant one, seemingly even after the jamming problem that was the rationale for its introduction had been overcome. The historical evidence suggests that with different early choices, one of the other arrangements could have become dominant. The chances that some one or other of these early arrangements can now become dominant seems quite negligible.
This discussion has been carried out without mentioning efficiency.
References
Brian Arthur and Paul David, two teachers at Stanford about a decade ago, have attracted a certain amount of popular attention with the concept of path dependence. Arthur, for example, has had a certain amount of influence on policy. This post is an attempt to explain the concept, primarily as it applies to stochastic processes. Path dependence is one way of formalizing the idea that history matters.
2.0 A Stochastic Process
Path dependence relates to events economists choose to model as random. This modeling choice does not imply that economists think such events are necessarily the result of the modeled agents acting capriciously, irrationally, or mistakenly. Consider such childhood games as Odds and Evens or Paper-Rock-Scissors. The optimal strategy for each player is to choose their move randomly. The winner of such games will vary randomly. Notice that apart from the players' choices, these games are deterministic. No dice are being rolled or cards shuffled.
A stochastic process is merely an indexed set of random variables:
{ X( 1 ), X( 2 ), X( 3 ), ... }The index often represents time. The value of a given one of these random variables is frequently referred to as the state of the process at that time.
I consider an example of a path-dependent stochastic process that does not exhibit certain other properties. This stochastic process can be in one of eight states, {Start, B, C, D, E, F, G, H}. It begins in the Start state. State transition probabilities are indicated by
the fractions in Figure 1. For example, consider the probability distribution for the state of the process at the second time step, X( 2 ). Figure 1 shows that if the process is in the Start state, the probability that it will transition to state B is 1/2. Likewise, given that it is in the Start state, the probability that it will transition to state C is 1/2. Hence the probability distribution of X( 2 ) is:
Pr[ X( 2 ) = B ] = 1/2
Pr[ X( 2 ) = C ] = 1/2
Notice that the probabilities leading out from each state total unity. It is left as an exercise for the reader to confirm that the proability distribution of X( 3 ) is as follows:
Pr[ X( 3 ) = Start ] = 1/3
Pr[ X( 3 ) = B ] = 1/6
Pr[ X( 3 ) = C ] = 1/6
Pr[ X( 3 ) = D ] = 1/6
Pr[ X( 3 ) = G ] = 1/6I deliberately created this example to exhibit a certain symmetry for the transient states (defined below).
 |
| Figure 1: Markov Process State Space |
This process exhibits certain properties that are particularly simple, as well as some properties that complicate analysis. Notice that the state transition properties are invariant across time. Given that the process is in the Start state, the probability that it will transition to state B is 1/2, no matter at what time the process may be in the Start state. It does not matter whether we are considering the initial time step or some later time when the process happens to have returned to the Start state.
Furthermore, the process is memoryless. State transition probabilities depend only on the current state, not the history with which the process reached the current state. This property of memorylessness is known as the Markov property. This example is a Markov process.
The Markov property and the assumption of time-inavariant state transition probabilities are simplifying assumptions. One might think relaxation of these assumptions might be one way of showing that "history matters." Since, as will be explained, this example exhibits path dependence, violations of these assumptions are clearly not necessary for path dependence. And Margolis and Liebowitz are incorrect:
"In probability theory, a stochastic process is path dependent if the probability distribution for period t+1 is conditioned on more than the value of the system in period t. ... path independence means that it doesn't matter how you get to a particular point, only that you got there." -- Stephen E. Margolis and S. J. Liebowitz (1988)
An interesting classification of sets of states is available for Markov processes, that of transient and absorbing states. Consider the states {Start, B, C}. By assumption, the process starts in a state within this set. But eventually the process will lie in a state outside this set. Once this happens, the process will never return to this set. States Start, B, and C are known as transient states. On the other hand, consider the states {D, E, F}. Once the process is in a state in this set, the process will never depart from a state in the set. Furthermore, if the process is in a state in this set, it will eventually visit all other states in the set. {D, E, F} is a set of asorbing states. This is not the unique set of absorbing states for this process. {G, H} is also a set of absorbing states.
Consider the problem of estimating the probability distribution over the states at some large number of time step, say X(10,000), after the start. The probability that the process is in a transient state is negligible. One might be tempted to estimate X(10,000) by the proportion of time steps that a single realization of the process spends in each state. A realization might be:
Start, B, D, E, F, D, E, F, E, F, DThe column for the first realization in Table 1 shows the proportion of time spent in each state in this realization as the number of time steps in the realization increases without bound. (Although transient states are observed in a realization, the proportion of time spent in transient states in such an infinite sequence is zero.)
| State | From One Realization | From Another Realization | Over All Realizations |
| Start | 0 | 0 | 0 |
| B | 0 | 0 | 0 |
| C | 0 | 0 | 0 |
| D | 1/3 | 0 | 1/6 |
| E | 1/3 | 0 | 1/6 |
| F | 1/3 | 0 | 1/6 |
| G | 0 | 1/2 | 1/4 |
| H | 0 | 1/2 | 1/4 |
If the process were ergodic, the limiting distribution in the first column in Table 1 would be a good estimate of the probability distribution for the state of the process at some time after transient behavior was likely to be completed. In this case, though, another realization might yield the limiting distribution shown for the second realization in Table 1. The probability distribution, in fact, at a given time, as that time increases without bound would have positive probabilities for all non-transient states. The last column in Table 1 shows this limiting probability distribution.
In general, estimates of parameters of the underlying probability distributions can be made across multiple realizations of the process or from a single realization. In a nonergodic process, such estimates will not converge as the number of realizations or the length of the single realization increases.
Another definition of ergodicity involves what states can be eventually reached from each state. In an ergodic process, each state can be eventually reached, with positive probability. In the example, all states can be reached from the transient states Start, B, and C. But states Start, B, C, G and H cannot be reached from states D, E, and F. Suppose an external occurrence changes the state transition probabilities. If the process were previously ergodic, this change could not possibly result in states arising that were previously unobserved.
To re-iterate, a nonergodic process does not have an unique limiting probability distribution. The applicable limiting distribution of any realization of the process depends on the history of that particular realization. Thus, the process exhibits path dependence.
Another branch of mathematics deals with deterministic dynamical systems. Such systems are typically defined by systems of differential or difference equations. Sometimes the solutions of such systems can be such that trajectories in phase space diverge, no matter how close they start. This is known as sensitive dependence on initial conditions, popularly known as the "butterfly effect." (The irritating mathematican character in Jurassic Park mumbles about this stuff.) Notice that path dependence is defined above without drawing on this branch of mathematics. Here, too, Margolis and Liebowitz are mistaken:
”Path dependence is an idea that spilled over to economics from intellectual movements that arose elsewhere. In physics and mathematics the related ideas come from chaos theory. One potential of the non-linear models of chaos theory is sensitive dependence on initial conditions: Determination, and perhaps lock-in, by small, insignificant events." -- Stephen E. Margolis and S. J. Liebowitz (1988)
3.0 Conclusion
Why should economists care about the mathematics of path dependence? First, models of path dependence suggest how to construct economic models that overcome frequently criticized characteristics of neoclassical economics. Neoclassical models often depict equilibria. These equilibria are end states of path independent processes. Ever since Veblen, some economists have objected to such models as being teleological and acausal. Models in which path dependence can arise are causal and show neoclassical economics to be a special case.
This claim that neoclassical economics is merely a special case, dependent on a special case assumption of ergodicity, may lead one to wonder about connections with a theory claimed to be the "General Theory." As a matter of fact, Paul Davidson claims that a consideration of nonergodicity is useful in explicating the economics of Keynes. So a second reason economists should be concerned with nonergodicity and path dependence is to further understand possible approaches to macroeconomics.
Third, some economists, e.g. Brian Arthur, have developed specific models of technological change that exhibit nonergodicity. These models, including those of a Polya urns, show how increasing returns can act as positive feedback and lead to path dependence. Inasmuch as these models cast light on economic history, path dependence can be useful for empirical work.
The theory of path dependence raises an empirical question. Are nonergodic stochastic processes useful for modeling any, or any important, economic time series? The evolution of the QWERTY keyboard seems to be an example of a path dependent process. Apparently there were several 19th century typewriter keyboard layouts. QWERTY became the dominant one, seemingly even after the jamming problem that was the rationale for its introduction had been overcome. The historical evidence suggests that with different early choices, one of the other arrangements could have become dominant. The chances that some one or other of these early arrangements can now become dominant seems quite negligible.
This discussion has been carried out without mentioning efficiency.
References
- W. Brian Arthur (1989) "Competing Technologies, Increasing Returns, and Lock-In by Historical Events", Economic Journal, V. 99: 116-131.
- W. Brian Arthur (1990) "Positive Feedbacks in the Economy", Scientific American, 262 (February): 92-99.
- W. Brian Arthur (1996) "Increasing Returns and the New World of Business", Harvard Business Review.
- Paul A. David (1985) "Clio and the Economics of QWERTY", American Economic Review 75, 2 (May)
- Paul A. David "Path Dependence, Its Critics and the Quest for 'Historical Economics'"
- Paul Davidson (1982-1983) "Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes", Journal of Post Keynesian Economics, V. 5 (Winter): 182-197.
- Stephen E. Margolis and S. J. Liebowitz (1988) "Path Dependence", The New Palgrave Dictionary of Economics and Law, MacMillan.
The Map Is Not The Territory
Suppose an orthodox economist hands you a map and says, "This is a map of New York City." You look at it and say, "It is not. It is a map of the London tube system."
Or suppose an orthodox economist hands you a map. And you look at it and say, "This cannot be right. Here are two interesecting contour lines supposedly of different elevations."
Suppose the orthodox economist responds, "Assumptions do not need to be realistic."
I have encountered several economists who distract from those pointing out the logical inconsistencies and factual errors in their theories. They make dismissive non sequiturs about methodology, as illustrated in the parables above.
Or suppose an orthodox economist hands you a map. And you look at it and say, "This cannot be right. Here are two interesecting contour lines supposedly of different elevations."
Suppose the orthodox economist responds, "Assumptions do not need to be realistic."
I have encountered several economists who distract from those pointing out the logical inconsistencies and factual errors in their theories. They make dismissive non sequiturs about methodology, as illustrated in the parables above.
Thursday, July 24, 2008
Davidson And Eatwell On Current Events
This post points out some recent interventions by two leading economists in schools of thought in which I am interested.
Paul Davidson is the leader of American Post Keynesians and the editor of the Journal of Post Keynesian Economics. He argues that Sraffa's economics is not compatible with Keynes insofar as it is not set in historical time. And he advocates for the economics of Keynes over Sraffa.
His recent article "Crude Oil Prices: 'Market Fundamentals' or Speculation?" is available in the Heterodox Economics Newsletter (Issue 63, 12 June 2008). Davidson argues that "the absence of any excess supply adjustment is not ... evidence of the lack of a speculative force" driving current high oil prices.
John Eatwell, or Lord Eatwell, has contributed to attempting to synthesize the ideas of Keynes and Sraffa. I am thinking the 1983 book, Keynes's Economics and the Theory of Value and Distribution, which Eatwell co-edited with Murray Milgate. He also wrote, with Carlo Panico, the New Palgrave entry on Sraffa and has influenced my understanding on how Sraffa's standard commodity can be used to understand Marx.
In a 3 July letter in the Financial Times, Eatwell argues that regulators of financial institutions should monitor the details of the systematic risks which firms are taking on. In a 17 July comment, also in the Financial Times, Eatwell and Avinash Persaud comment on Fannie Mae and Freddie Mac and argue that markets with diverse players are thicker and more liquid.
Paul Davidson is the leader of American Post Keynesians and the editor of the Journal of Post Keynesian Economics. He argues that Sraffa's economics is not compatible with Keynes insofar as it is not set in historical time. And he advocates for the economics of Keynes over Sraffa.
His recent article "Crude Oil Prices: 'Market Fundamentals' or Speculation?" is available in the Heterodox Economics Newsletter (Issue 63, 12 June 2008). Davidson argues that "the absence of any excess supply adjustment is not ... evidence of the lack of a speculative force" driving current high oil prices.
John Eatwell, or Lord Eatwell, has contributed to attempting to synthesize the ideas of Keynes and Sraffa. I am thinking the 1983 book, Keynes's Economics and the Theory of Value and Distribution, which Eatwell co-edited with Murray Milgate. He also wrote, with Carlo Panico, the New Palgrave entry on Sraffa and has influenced my understanding on how Sraffa's standard commodity can be used to understand Marx.
In a 3 July letter in the Financial Times, Eatwell argues that regulators of financial institutions should monitor the details of the systematic risks which firms are taking on. In a 17 July comment, also in the Financial Times, Eatwell and Avinash Persaud comment on Fannie Mae and Freddie Mac and argue that markets with diverse players are thicker and more liquid.
Tuesday, July 22, 2008
Sunday, July 20, 2008
In Economics Departments, Marx's Days Are Like Grass, Like A Flower Of The Field He Bloomed
Russell Jacoby asks, in the 25 July 2008 issues of The Chronicle of Higher Education, "How is it that Freud is not taught in psychology departments, Marx is not taught in economics, and Hegel is hardly taught in philosophy?"
I occasionally point out treatments of Marx using the techniques of modern mathematical economics. Lots of work has been done in this vein. I might as well mention analytical Marxism, as developed by, for example, John Roemer; Morishima's 1970s work drawing on Johnny Von Neumann; and, of course, Sraffians, such as John Eatwell or Ian Steedman. In regard to the latter, some economists have disputed Steedman's interpretation of Marx's work. I here have in mind Dumenil, Lipietz, and Foley's "New interpretation" and the Temporal Single System approach associated with such economists as Alan Freeman and Andrew Kliman. Perhaps Jacoby is aware that if economists chose to teach Marx, they have much work to draw on. After all, Jacoby notes that Wassily Leontief taught a 1936 seminar on Marx at Harvard. Duncan Foley's testimony (I believe in Colander, Holt and Rosser (204)) is just one demonstration that the ignorance of Marx among orthodox economists cannot be justified on normal scholarly or scientific norms.
I don't expect vulgar political economic monopolists to even acknowledge the existence of their suppressed competition. Orthodox economists just refuse to reference lots of literature, for example, in heterodox journals.
Reminder to myself: Read Andras Bródy's Proportions, Prices, and Planning: A Mathematical Restatement of the Labor Theory of Value (Akadémiai Kiadó, 1970) for an early analytical examination of Marx. Read Victor S. Venida's "Marxian Categories Empirically Estimated: The Philippines, 1961-1994" (Review of Radical Political Economics, V. 39, N. 1 (2007): 58-579) for recent econometric work.
I occasionally point out treatments of Marx using the techniques of modern mathematical economics. Lots of work has been done in this vein. I might as well mention analytical Marxism, as developed by, for example, John Roemer; Morishima's 1970s work drawing on Johnny Von Neumann; and, of course, Sraffians, such as John Eatwell or Ian Steedman. In regard to the latter, some economists have disputed Steedman's interpretation of Marx's work. I here have in mind Dumenil, Lipietz, and Foley's "New interpretation" and the Temporal Single System approach associated with such economists as Alan Freeman and Andrew Kliman. Perhaps Jacoby is aware that if economists chose to teach Marx, they have much work to draw on. After all, Jacoby notes that Wassily Leontief taught a 1936 seminar on Marx at Harvard. Duncan Foley's testimony (I believe in Colander, Holt and Rosser (204)) is just one demonstration that the ignorance of Marx among orthodox economists cannot be justified on normal scholarly or scientific norms.
I don't expect vulgar political economic monopolists to even acknowledge the existence of their suppressed competition. Orthodox economists just refuse to reference lots of literature, for example, in heterodox journals.
Reminder to myself: Read Andras Bródy's Proportions, Prices, and Planning: A Mathematical Restatement of the Labor Theory of Value (Akadémiai Kiadó, 1970) for an early analytical examination of Marx. Read Victor S. Venida's "Marxian Categories Empirically Estimated: The Philippines, 1961-1994" (Review of Radical Political Economics, V. 39, N. 1 (2007): 58-579) for recent econometric work.
Thursday, July 17, 2008
Tuesday, July 15, 2008
Greg Mankiw Still A Fool
Greg Mankiw presents a non-argument from authority to the readers of The New York Times.
Is what a majority of members of the American Association of Economists believe of any interest? How abut a majority of the Association For Evolutionary Economics (AFEE), the International Association For Feminist Economics (IAFFE), or the Union for Radical Political Economics (URPE)?
I care about the beliefs of the majority of AEA members as data for the sociology of economics. (I deliberately don't write here of the sociology of knowledge.) As guidance for deciding on public policy - not so much.
Insofar as Mankiw claims to believe in the distinction between positive and normative economics, he should even agree.
Better public intellectuals, please.
Is what a majority of members of the American Association of Economists believe of any interest? How abut a majority of the Association For Evolutionary Economics (AFEE), the International Association For Feminist Economics (IAFFE), or the Union for Radical Political Economics (URPE)?
I care about the beliefs of the majority of AEA members as data for the sociology of economics. (I deliberately don't write here of the sociology of knowledge.) As guidance for deciding on public policy - not so much.
Insofar as Mankiw claims to believe in the distinction between positive and normative economics, he should even agree.
Better public intellectuals, please.
Sunday, July 13, 2008
Ricardo And The Iron Law Of Wages
1.0 Introduction
The interpretation of classical economists by historians of economic thought is an area of intense debate that Sraffians have contributed to. Sraffians claim that Classical economics has a distinct and coherent approach to economics. And that the theory of value and distribution within this theory has a different structure and role than within so-called neoclassical theory. I want to focus here particularly on the interaction of the Classical theory of wages and the theory of value. I think Ricardo's treatment of wages is a particularly controversial topic in this interpretation. This post notes a couple of difficulties for understanding Ricardo on wages. I developed it in response to an essay on the iron law of wages that the author e-mailed me.
2.0 Contending Interpretations of Classical Political Economy
As usual, I deny much, if any, originality. But I am going to be vague on references. As I understand it, Sraffa and Dobb's introduction in Sraffa (1951) was not initially perceived as offering a novel interpretation of Ricardo. Bharadway (1989) and Garegnani (1984) offer other statements of the Sraffian interpretation. Stirati (1994) focuses specifically on the theory of wages.
Samuel Hollander, I think, has the highest stature of those today arguing, pace Sraffa, for the continuous evolution of Classical economics into Neoclassical economics. I take Hollander to be continuing the line of argument to be found in Appendix I of Alfred Marshall's Principles of Economics. Despite my respect for Hollander, I have yet to thoroughly read any of his massive tomes of scholarship (e.g., Hollander 1979). My acquaintance with Hollander's primary work is mainly in the journal literature, such as his tournament with Giancarlo de Vivo in the mid 1980s and later Cambridge Journal of Economics over de Vivo's discovery in Robert Torrens of something much like Sraffa's standard commodity.
Others have entered into this controversy, while taking positions that I think differ from both Sraffian positions and Hollander's. I mention Carvale and Tosato (1980), which, as I recall, contains dynamic models which formalize an interpretation of Ricardo's views on wages. I also like Peach (1993), which surveys other interpretations and offers Peach's own reading of Ricardo.
2.0 Sraffian Interpretation
The givens in Ricardo's theory of value include, the level of effective demand for the output of each industry and the technique in use. From these givens, the capital equipment that must be advanced in each industry is also known. The level of wages is also among the givens of the theory of value. The rate of profit then is roughly the ratio of the surplus to the advances, including wages.
A problem arises here. The surplus output of the economy, the commodities on which wages are spent, and the capital equipment are each heterogeneous collections. How can these quantities be treated as commensurate? Ricardo's corn-ratio model, the labor theory of value, and Sraffa's standard commodity are all approaches to address this issue.
So the Sraffians claim that the Classical theory of value makes sense, at least formally if the natural rate of wages is exogenous to the theory of value, albeit still to be explained within Political Economy. This is not a novel position:
4.0 The Natural Wage Outside The Stationary State
I have pointed to a theory of the natural level of prices above, where the natural level of prices is to be contrasted with market prices. Adam Smith uses the metaphor of centers of gravitation for the natural levels. They attract market prices. Ricardo focuses his analysis on natural levels. One might think the given wage in Ricardo's theory of value and distribution must be the natural rate of wages.
This quote seems to say that the natural rate of wages is defined to be the wage that prevails in the stationary state:
5.0 The Iron Law of Wages and Ricardo
As I understand it, the iron law of wages is that wages tend towards the natural rate of wages, defined as physiological subsistence. Outdated teaching in the history of economic thought is that Ricardo held to this iron law.
Ricardo clearly states that natural rate of wages is not defined solely by physiological requirements. It includes habits and social norms:
This raises the question of who came up with the iron law of wages, if it was not Ricardo. Apparently the "Iron Law" was named by Ferdinand Lassalle. Stirati (1994) reads Marx as here saying that Malthus was the law's creator:
As I understand it, the formal mathematics of the theory of value merely requires the wage to be given. But, as my email correspondent points out, if the wage is above subsistence, workers can save and class structure of capitalism will not be reproduced.
As I understand it, in the formal mathematics of the theory of value, the wage, for example, is taken as given. The formalism does not require the wage to be any particular value between zero and some maximum. But, as my email correspondent points out, if the wage is appreciably is above subsistence, workers can accumulate capital before retirement age and the class structure of capitalism will not be reproduced.
Updated 19 July 2008
References
The interpretation of classical economists by historians of economic thought is an area of intense debate that Sraffians have contributed to. Sraffians claim that Classical economics has a distinct and coherent approach to economics. And that the theory of value and distribution within this theory has a different structure and role than within so-called neoclassical theory. I want to focus here particularly on the interaction of the Classical theory of wages and the theory of value. I think Ricardo's treatment of wages is a particularly controversial topic in this interpretation. This post notes a couple of difficulties for understanding Ricardo on wages. I developed it in response to an essay on the iron law of wages that the author e-mailed me.
2.0 Contending Interpretations of Classical Political Economy
As usual, I deny much, if any, originality. But I am going to be vague on references. As I understand it, Sraffa and Dobb's introduction in Sraffa (1951) was not initially perceived as offering a novel interpretation of Ricardo. Bharadway (1989) and Garegnani (1984) offer other statements of the Sraffian interpretation. Stirati (1994) focuses specifically on the theory of wages.
Samuel Hollander, I think, has the highest stature of those today arguing, pace Sraffa, for the continuous evolution of Classical economics into Neoclassical economics. I take Hollander to be continuing the line of argument to be found in Appendix I of Alfred Marshall's Principles of Economics. Despite my respect for Hollander, I have yet to thoroughly read any of his massive tomes of scholarship (e.g., Hollander 1979). My acquaintance with Hollander's primary work is mainly in the journal literature, such as his tournament with Giancarlo de Vivo in the mid 1980s and later Cambridge Journal of Economics over de Vivo's discovery in Robert Torrens of something much like Sraffa's standard commodity.
Others have entered into this controversy, while taking positions that I think differ from both Sraffian positions and Hollander's. I mention Carvale and Tosato (1980), which, as I recall, contains dynamic models which formalize an interpretation of Ricardo's views on wages. I also like Peach (1993), which surveys other interpretations and offers Peach's own reading of Ricardo.
2.0 Sraffian Interpretation
The givens in Ricardo's theory of value include, the level of effective demand for the output of each industry and the technique in use. From these givens, the capital equipment that must be advanced in each industry is also known. The level of wages is also among the givens of the theory of value. The rate of profit then is roughly the ratio of the surplus to the advances, including wages.
A problem arises here. The surplus output of the economy, the commodities on which wages are spent, and the capital equipment are each heterogeneous collections. How can these quantities be treated as commensurate? Ricardo's corn-ratio model, the labor theory of value, and Sraffa's standard commodity are all approaches to address this issue.
So the Sraffians claim that the Classical theory of value makes sense, at least formally if the natural rate of wages is exogenous to the theory of value, albeit still to be explained within Political Economy. This is not a novel position:
"Therefore the foundation of modern political economy, whose business is the analysis of capitalist production, is the conception of the value of labour-power as something fixed, as a given magnitude-as indeed it is practice in each particular case. The minimum of wages therefore correctly forms the pivotal point of Physiocratic theory. They were able to establish this although they had not yet recognised the nature of value itself, because this value of labour-power is manifested in the price of the necessary means of subsistence, hence in a sum of definite use-values. Consequently, without being in any way clear as to the nature of value, they could conceive the value of labour-power, so far as it was necessary to their inquiry, as a definite magnitude. If moreover they made the mistake of conceiving this minimum as an unchangeable magnitude-which in their view is determined entirely by nature, and not by the stage of historical development, which is itself a magnitude subject to fluctuations-this in no way affects the abstract correctness of their conclusions, since the difference between the value of labour-power and the value it creates does not at all depend on whether the value is assumed to be great or small." -- Karl Marx (1963) p. 45
4.0 The Natural Wage Outside The Stationary State
I have pointed to a theory of the natural level of prices above, where the natural level of prices is to be contrasted with market prices. Adam Smith uses the metaphor of centers of gravitation for the natural levels. They attract market prices. Ricardo focuses his analysis on natural levels. One might think the given wage in Ricardo's theory of value and distribution must be the natural rate of wages.
This quote seems to say that the natural rate of wages is defined to be the wage that prevails in the stationary state:
"Notwithstanding the tendency of wages to conform to their natural rate, their market rate may, in an improving society, for an indefinite period, be constantly above it; for no sooner may the impulse, which an increased capital gives to a new demand for labour be obeyed, than another increase of capital may produce the same effect; and thus, if the increase of capital be gradual and constant, the demand for labour may give a continued stimulus to an increase of people." -- David Ricardo (p. 94-95 in Sraffa 1951)And Ricardo says that the stationary state is far distant:
"But if our progress should become more slow; if we should attain the stationary state, from which I which I trust we are far distant, then will the pernicious nature of these [Poor] laws become more manifest and alarming; and then, too, will their removal be obstructed by many additional difficulties." -- David Ricardo (p. 109 in Sraffa 1951)So Ricardo seems to be inconsistent. He thinks that the system of natural prices and wages is explanatory for empirical tendencies at any moment, that the stationary state is far distant, and the natural rate of wages is defined only for the stationary state. Maybe he has different theories for the long run and the intermediate run, so to speak.
5.0 The Iron Law of Wages and Ricardo
As I understand it, the iron law of wages is that wages tend towards the natural rate of wages, defined as physiological subsistence. Outdated teaching in the history of economic thought is that Ricardo held to this iron law.
Ricardo clearly states that natural rate of wages is not defined solely by physiological requirements. It includes habits and social norms:
"It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. It varies at different times in the same country, and very materially differs in different countries. It essentially depends on the habits and customs of the people. An English labourer would consider his wages under their natural rate, and too scanty to support a family, if they enabled him to purchase no other food than potatoes, and to live in no better habitation than a mud cabin; yet these moderate demands of nature are often deemed sufficient in countries where 'man's life is cheap', and his wants are easily satisfied. Many of the conveniences now enjoyed in an English cottage, would have been thought luxuries in an earlier period of our history." -- David Ricardo (p. 96-67 in Sraffa 1951)Hystersis arises in this approach. If the market rate is above the natural wage for a long time, the norms and habits embodied in workers' consumption can change. In a sense, the natural level of wages moves towards the market wage, as well as vice-versa. Ricardo draws on this idea for some policy ideas:
"The friends of humanity cannot but wish that in all countries the labouring classes should have a taste for comforts and enjoyments, and that they should be stimulated by all legal means in their exertions to procure them. There cannot be a better security against a superabundant population. In those countries, where the labouring classes have the fewest wants, and are contented with the cheapest food, the people are exposed to the greatest vicissutudes and miseries. They have no place of refuge from calamity; they cannot seek safety in a lower station; they are already so low, that they can fall no lower..." -- David Ricardo (p. 100-101 in Sraffa 1951)You can see the same idea later in John Stuart Mill:
"It would, however, be of little avail that either or both these measures of relief [emigration for colonization and something like homesteading] should be adopted, unless on such a scale as would enable the whole body of hired labourers remaining on the soil to obtain not merely employment, but a large addition to the present wages - such an addition as would enable them to live and bring up their children in a degree of comfort and independence to which they have hitherto been strangers. When the object is to raise the permanent condition of a people, small means do not merely produce small effects, they produce no effect at all. Unless comfort can be made as habitual to a whole generation as indigence is now, nothing is accomplished..." J. S. Mill (1848, Book II, Chapter XIII)How can Ricardo's words be reconciled with the claim that Ricardo held the iron law? My preferred approach is to reject the claim. Ricardo did not endorse the iron law of wages.
This raises the question of who came up with the iron law of wages, if it was not Ricardo. Apparently the "Iron Law" was named by Ferdinand Lassalle. Stirati (1994) reads Marx as here saying that Malthus was the law's creator:
"It is well known that nothing of the 'iron law of wages' is Lassalle's except the word 'iron' borrowed from Goethe's 'great, eternal iron laws'. The word 'iron' is a label by which the true believers recognize one another. But if I take the law with Lassalle's stamp on it, and consequently in his sense, then I must also take it with his substantiation for it. And what is that? As Lange already showed, shortly after Lassalle's death, it is the Malthusian theory of population (preached by Lange himself). But if this theory is correct, then again I cannot abolish the law even if I abolish wage labor a hundred times over, because the law then governs not only the system of wage labor but every social system. Basing themselves directly on this, the economists have been proving for 50 years and more that socialism cannot abolish poverty, which has its basis in nature, but can only make it general, distribute it simultaneously over the whole surface of society!" - Karl Marx (1875)
As I understand it, in the formal mathematics of the theory of value, the wage, for example, is taken as given. The formalism does not require the wage to be any particular value between zero and some maximum. But, as my email correspondent points out, if the wage is appreciably is above subsistence, workers can accumulate capital before retirement age and the class structure of capitalism will not be reproduced.
Updated 19 July 2008
References
- Krishna Bharadwaj (1989) Themes in Value and Distribution: Classical Theory Reappraised, Unwin Hyman
- Giovanni A. Caravale and Domenico A. Tosato (1980) Ricardo and the Theory of Value, Distribution and Growth, Routledge & Kegan Paul
- P. Garegnani (1984) "Value and Distribution in the Classical Economists and Marx", Oxford Economic Papers, V. LXXIII: 291-325
- Samuel Hollander (1979) The Economics of David Ricardo, Toronto: University Press
- Karl Marx (1875) Critique of the Gotha Program
- Karl Marx (1963) Theories of Surplus Value, Part I (Trans. by E. Burns), Progress Publishers
- John Stuart Mill (1848) Principles of Political Economy
- Terry Peach (1993) Interpreting Ricardo, Cambridge University Press
- Piero Sraffa (editor) (1951) The Works and Correspondence of David Ricardo: Volume I: On the Principles of Political Economy and Taxation, Cambridge University Press
- Antonella Stirati (1994). The Theory of Wages in Classical Economics: A Study of Adam Smith, David Ricardo and Their Contemporaries (trans. by Joan Hall), Edward Elgar
Friday, July 11, 2008
A Different World
Suppose that all equipment used in production were privately owned by individuals. Being fairly well-off, I might have a house with some sort of blast furnace in the back yard. Production in this imaginary world would be performed entirely by self-employed artisans.
One can allow some people in this world to perform no work. Some of these artisans would be lending or borrowing specific equipment from others. So any specific piece of capital equipment would have a rental price. If I happened to own equipment that could command high enough rents, I would be able to lend all my equipment out and live off these rents.
It seems to me that inasmuch as a neoclassical theory of value exists that is logically consistent in its assumptions, it is a map of the above sort of society. It is not even an attempt to describe a society in which one can loan out money at interest or buy and sell shares in firms that themselves own capital equipment. Given the lack of a stock market in this imaginary world, I do not see the point of introducing wage labor into the model either. One would still not end up with a model of a capitalist economy.
References
One can allow some people in this world to perform no work. Some of these artisans would be lending or borrowing specific equipment from others. So any specific piece of capital equipment would have a rental price. If I happened to own equipment that could command high enough rents, I would be able to lend all my equipment out and live off these rents.
It seems to me that inasmuch as a neoclassical theory of value exists that is logically consistent in its assumptions, it is a map of the above sort of society. It is not even an attempt to describe a society in which one can loan out money at interest or buy and sell shares in firms that themselves own capital equipment. Given the lack of a stock market in this imaginary world, I do not see the point of introducing wage labor into the model either. One would still not end up with a model of a capitalist economy.
References
- Joan Robinson (1962) Essays in the Theory of Economic Growth, Macmillan
- Joan Robinson (1973) Economic Heresies: Some Old-Fashioned Questions in Economic Theory, Basic Books
Wednesday, July 09, 2008
What Has Been, That Will Be; What Has Been Done, That Will Be Done
Stiglitz has an editorial in "Egypt's only independent newspaper in English:
"Neo-liberal market fundamentalism was always a political doctrine serving certain interests. It was never supported by economic theory. Nor, it should now be clear, is it supported by historical experience. Learning this lesson may be the silver lining in the cloud now hanging over the global economy." -- Joseph E. Stigliz, , 7 July 2008And some bloggers are flabbergasted. Interestingly enough, Stiglitz said the same thing last October. Maybe if enough economists say the same thing over and over and over, other economists should examine their rationale. Clearly, Stiglitz is not just saying whatever momentarily passes through his mind.
Saturday, July 05, 2008
Some History of the Label 'Neoclassical"
I suppose if I want to note the origin of the term "neoclassical" in relation to economics, I should quote Aspromourgos. But I happen to have a Colander essay nearer at hand. The term grew to have a extremely general connotation:
References
"The term, neoClassical, was initially coined by Thorstein Veblen (1900) in his 'Preconceptions of Economic Science.'...By the way, shortly before World War II, Austrian economists did not see themselves as lying outside neoclassical economics or putting forth a separate doctrine:
Hicks (1932, 1934) and Stigler (1941) extended the meaning of neoClassical to encompass all marginalist writers, including Menger, Jevons, and J.B. Clark. Most writers after Hicks and Stigler used the term inclusively. Thus it lost most of its initial meaning. Instead of describing Marshallian economics, it became associated with the use of calculus, the use of marginal productivity theory, and a focus on relative prices. As has been noted by a number of authors, while the neoClassical terminology makes some sense for Marshall, who emphasized the connection of his approach with the Classical approach, it makes far less sense for the others, such as Jevons, who emphasized the difference between his views and those of the Classicals. Some have suggested that anti-Classical would have been preferable.
...In the third edition of his principles textbook Samuelson (1955) built on Keynes' classification and turned it around on Keynes by developing the neoClassical synthesis. In the neoClassical synthesis, Keynes' dispute with Classical economists was resolved. This use of the term 'neoClassical' as an alternative to Keynesian models provides another confusion because it adds another reference point that brings to mind different elements of thought than would other comparisons." -- David Colander
"Referring to the usual separation of economic theorists into three schools of thought, 'the Austrian and the Anglo-American schools and the School of Lausanne', Mises (citing Morgernstern) emphasizes that these groups 'differ only in their mode of expressing the same fundamental idea and that they are divided more by their terminology and by peculiarities of presentation than by substance of their teachings' (Mises 1960 [1933])." - Israel KirznerFor completeness, I expand the references in the above quotations.
References
- Tony Aspromourgos, "On the Origins of the Term 'Neoclassical'", Cambridge Journal of Economics, V. 10, N. 3: 265-270
- David Colander, "The Death of Neoclassical Economics"
- J. R. Hicks (1932) "Marginal Productivity and the Principle of Variation", Economica (February)
- J. R. Hicks (1934) "Leon Walras", Econometrica (October)
- Israel Kirzner (1987) "The Austrian School of Economics", The New Palgrave Dictionary of Economics
- L. von Mises (1960) Epistemological Problems of Economics, Van Nostrand (translation of Grundprobleme der Nationalökonomie, 1933)
- G. J. Sigler (1941) Production and Distribution Theories, Macmillan
Tuesday, July 01, 2008
Marx Was Skint - But He Had Sense / Engels Lent Him The Necessary Pence
Marx may or may not be correct in these passages. But these, and expansions of these passages, certainly contain claims worth thinking about:
"Let us take England. Its political economy belongs to the period in which the class-struggle was as yet undeveloped. Its last great representative, Ricardo, in the end, consciously makes the antagonism of class-interests, of wages and profits, of profits and rent, the starting point for his investigations, naively taking this antagonism for a social law of nature. But by this start the science of bourgeois economy had reached the limits beyond which it could not pass. Already in the lifetime of Ricardo, and in opposition to him, it was met by the criticism, in the person of Sismondi.
The succeeding period, from 1820 to 1830, was notable in England for scientific activity in the domain of Political Economy. It was the time as well of the vulgarizing and extending of Ricardo's theory, as of the contest of that theory with the old school. Splendid tournaments were held... The literature of Political Economy in England at this time calls to mind the stormy forward movement in France after Dr. Quesnay's death, but only as a Saint Martin's summer reminds us of spring. With the year 1830 came the decisive crisis.
In France and in England the bourgeoise had conquered political power. Thenceforth, the class-struggle, practically as well as theoretically, took on more and more outspoken and threatening forms. It sounded the death knell of scientific bourgeois economy. It was no longer a question, whether this theorem or that was true, but whether it was useful to capital or harmful, expedient or inexpedient, politically dangerous or not. In place of disinterested enquirers, there were hired prize-fighters; in place of genuine scientific research, the bad consequence and the evil intent of apologetic..." -- K. Marx, Capital, Volume 1, Author's Preface to the Second Edition
"A commodity is therefore a mysterious thing, simply because in it the social character of men's labour appears to them as an objective character stamped upon the product of that labour; because the relation of the producers to the sum total of their own labour is presented to them as a social relation, existing not between themselves, but between the products of their labour. This is the reason why the products of labour become commodities, social things whose qualities are at the same time perceptible and imperceptible by the senses... With commodities... the existence of the things qua commodities, and the value relation between products of labour which stamps them as commodities, have absolutely no connection with their physical properties and with the material relations arising therefrom. There it is a definite social relation between men, that assumes, in their eyes, the fantastic form of a relation between things. In order, therefore, to find an analogy, we must have recourse to the mist-enveloped regions of the religious world. In that world the productions of the human brain appear as independent beings endowed with life, and entering into relation both with one another and the human race. So it is in the world of commodities with products of men's hands. This I call the Fetishism which attaches itself to the products of labour, so soon as they are produced as commodities, and which is therefore inseperable from the production of commodities." -- K. Marx, Capital, Volume 1, Chapter 1, Section 4: The Fetishism of Commodities and the Secret Thereof
"Capital - profit (profit of enterprise plus interest), land - ground-rent, labour - wages, this is the trinity formula which comprises all the secrets of the social production process.
Furthermore, since as previously demonstrated interest appears as the specific characteristic product of capital and profit of enterprise on the contrary appears as wages independent of capital, the above trinity formula reduces itself more specifically to the following: Capital - interest, land - ground-rent, labour - wages, where profit, the specific characteristic form of surplus-value belonging to the capitalist mode of production, is fortunately eliminated.
On closer examination of this economic trinity, we find the following: First, the alleged sources of the annually available wealth belong to widely dissimilar spheres and are not at all analogous with one another. They have about the same relation to each other as lawyer's fees, red beets and music.
Capital, land, labour! However, capital is not a thing, but rather a definite social production relation, belonging to a definite historical formation of society, which is manifested in a thing and lends this thing a specific social character. Capital is not the sum of the material and produced means of production. Capital is rather the means of production transformed into capital, which in themselves are no more capital than gold or silver in itself is money. It is the means of production monopolised by a certain section of society, confronting living labour-power as products and working conditions rendered independent of this very labour-power, which are personified through this antithesis in capital. It is not merely the products of labourers turned into independent powers, products as rulers and buyers of their producers, but rather also the social forces and the future [? illegible] [A later collation with the manuscript showed that the text reads as follows: "die Gesellschaftlichen Kräfte und Zusammenhängende Form dieser Arbeit" (the social forces of their labour and socialised form of this labour). - Ed.] form of this labour, which confront the labourers as properties of their products. Here, then, we have a definite and, at first glance, very mystical, social form, of one of the factors in a historically produced social production process.
And now alongside of this we have the land, inorganic nature as such, rudis indigestaque moles, [Ovid, Metamorphoses, Book I, 7. - Ed] in all its primeval wildness. Value is labour. Therefore surplus-value cannot be earth. Absolute fertility of the soil effects nothing more than the following: a certain quantity of labour produces a certain product - in accordance with the natural fertility of the soil. The difference in soil fertility causes the same quantities of labour and capital, hence the same value, to be manifested in different quantities of agricultural products; that is, causes these products to have different individual values. The equalisation of these individual values into market-values is responsible for the fact that the 'advantages of fertile over inferior soil ... are transferred from the cultivator or consumer to the landlord'. (Ricardo, Principles, London, 1821, p.62.)
And finally, as third party in this union, a mere ghost - 'the' Labour, which is no more than an abstraction and taken by itself does not exist at all, or, if we take... [illegible], the productive activity of human beings in general, by which they promote the interchange with Nature, divested not only of every social form and well-defined character, but even in its bare natural existence, independent of society, removed from all societies, and as an expression and confirmation of life which the still non-social man in general has in common with the one who is in any way social." -- K. Marx, Capital, Volume 3, Part Seven, "Revenue and Theirs Sources", Chapter 48: The Trinity Formula
"The form of revenue and the sources of revenue are the most fetishistic expression of the relations of capitalist production. It is their form of existence as it appears on the surface, divorced from the hidden connections and the intermediate connecting links. Thus the land becomes the source of rent, capital is the source of profit, and labour the source of wages. The distorted form in which the real inversion is expressed is naturally reproduced in the views of the agents of this mode of production. It is a kind of fiction without fantasy, a religion of the vulgar. In fact, the vulgar economists - by no means to be confused with the economic investigators we have been criticizing - translate the concepts, motives, etc., of the representatives of the capitalist mode of production who are held in thrall to this mode of production and in whose consciousness only its superficial appearance is reflected. They translate them into a doctrinaire language, but they do so from the standpoint of the ruling section, i.e., the capitalists, and their treatment is therefore not naive and objective, but apologetic. The narrow and pedantic expression of vulgar conceptions which are bound to arise among those who are the representatives of this mode of production is very different from the urge of political economists like the Physiocrats, Adam Smith and Ricardo to grasp the inner connection of the phenomena." -- K. Marx, Theories of Surplus Value, Part III, Addenda, "Revenue and Its Sources. Vulgar Political Economy", 1.