Monday, February 21, 2022

A Theorem For The Reverse Substitution Of Labor

Figure 1: The Wage Frontier for a Numeric Example

Theorem: Consider a model of an economy in which n commodities are produced by means of commodities. Let Alpha be a technique in which each of the n commodities is produced by a fixed-coefficients, constant-returns-to-scale process. Suppose the Beta technique differs from Alpha only in the process operated in the nth industry. For simplicity, assume all n commodities are Sraffian basics in both techniques. Let both techniques undergo technical change, with only labor coefficients varying through time. The labor coefficient for the nth industry declines at the rate ρ for the Alpha technique:

aα0, n(t) = aα0, n(0) et

The corresponding labor coefficient for the Beta technique declines at the rate σ:

aβ0, n(t) = aβ0, n(0) et

Then the wage curves for the Alpha and Beta techniques intersect at time t0 at a rate of profits of -100 percent if the following condition holds:

σ t0 = ρ t0 - ln[ aα0, n(0)/aβ0, n (0)]

Proof: Left as an exercise for the reader.

I arrived at this theorem from a somewhat more general setting. Assume that in each industry, M processes are available to produce the corresponding commodity, at each instant in time, and that each of these processes has constant returns to scale. Each of these processes requires a positive input of labor. Consider the M techniques (out of Mn techniques) in which each commodity is produced, and the mth process in each industry is operated for the mth technique. Suppose Harrod-neutral technical change occurs for each one of these techniques, with the rate of increase of labor productivity varying among the techniques.

The theorem gives an explicit condition for the wage curves for the Alpha and Beta techniques to intersect at a rate of profits of -100 percent at time t0. Suppose a switch point also exists at this time at a positive rate of profits that is less than the minimum of the maximum rate of profits for the Alpha and Beta techniques. At that time, one has:

aα0, n(t0) = aβ0, n(t0)

Around the switch point, a variation in the rate of profits or the wage is associated with no change in the quantity of labor hired per unit of gross output in the nth industry.

The wage frontier illustrates for a numeric example with three produced commodities and two processes available in each industry. The techniques mentioned in the theorem are labeled "Gamma" and "Delta" in this example. Before the illustrated time in the example, this switch point is associated with a forward substitution of labor, in which less labor is employed in the nth industry per unit output of gross product of that industry. After this time, it is associated with a negative substitution of labor, in which increased employment per unit of gross product is associated with an increased wage around the switch point.

The ability to explicitly state mathematical theorems is a step forward for my approach of using fluke cases to partition parameter spaces associated with models of prices of production.

Saturday, February 19, 2022

New York City Subway: A Parable

A number of years ago, I was in the subway station under Times Square in New York City. I must have looked lost, because this fellow came up to me and asked me where I was going.

I said, "A bookstore, The Strand. I like to see what they have in their economics section. I am trying to decide if I should take the cross-town shuttle and go south from Grand Central."

He said, "I am an economist myself. You can have this subway map." And he handed me a map of the tube in London.

"This map is inaccurate."

"Of course. A map on a one-to-one scale would not be useful."

"I don't mean that. Here in New York, there is no circle line."

"It's called 'abstraction'. We don't care about curves between stations that do not matter."

"But this is just wrong for here."

"All models are wrong. Some are useful."

I finally saw I should just thank him, take the map, and back away. As I did, I heard him mutter to himself, "That guy does not understand scientific methodology."

I trust mainstream economists to help gather data for, for example, Simon Kuznets' National Income and Product Accounts and, for some, to provide guidance among data sources.

Tuesday, February 15, 2022

What Paul Krugman Could Learn From The Post Keynesian Roots Of MMT

To the common reader, the distinctions among old Keynesianism, new Keynesian, and Post Keynesianism might seem confusing. You might find these are political doctrines, with broad agreement among their followers. Governments should run deficits in periods of sustained unemployment. Maybe sometimes fiscal policy should be more emphasized over monetary policy. After all central banks cannot stimulate the economy by lowering interest rate when it is zero. In an inflationary period, central banks can fight it by raising interest rates, although this is a blunt, crude tool. What is there to argue about?

Yet economists argue. Kelton (2020) has a popular book emphasizing that, given how money and banks work, governments need not be concerned with balancing their budgets because of a fear that the money to pay for it will not be there. And then Clinton's Secretary of the Treasury and Obama's director of the National Economic Council responds to Kelton getting publicity:

"I am sorry to see the [New York Times] taking MMT serious as an intellectual movement. It is the equivalent of publicizing fad diets, quack cancer cures or creationist theories" -- Larry Summers

Those who follow MMT have seen the claim that it is revolutionary and that mainstream economists do not understand money. Paul Krugman, a leading mainstream economist, reacts:

"...And I will say that I am, to use the technical term, pissed at this kind of thing. I spent years after the 2008 financial crisis arguing against austerity and the obsession with debt, taking a lot of abuse in the process.." -- Paul Krugman

What is going on here? Is this just pettiness about who should have more influence in the public square?

I have said before that what is being argued is not the desirability of certain policies. Keynes stated that his book was about something else:

"This book is chiefly addressed to my fellow economists. I hope that it will be intelligible to others. But its main purpose is to deal with difficult questions of theory, and only in the second place with the application of this theory to practice." -- Keynes (1936) [first three sentences]

Keynes' attempt at revolution failed. Mainstream economists, after Keynes and maybe before, argued that sometimes governments should spend more and tax less in a recession to prod the economy toward a long run equilibrium.

The background theory is that of an economy that is always approaching an equilibrium, in the long-run. The current "saltwater" school, also known as new Keynesianism, argues that this approach is too slow to be relied on for policy. Monopolies and limitations to competition, information asymmetries, sticky wages and prices are just too large. Government policy should focus on removing these limitations or somehow getting the economy to simulate a desired equilibrium path. I do not know that Joseph Stiglitz, for example, would argue that some these hindrances to equilibrium could ever be removed.

The "freshwater" school, once known as new classical economics, argues that, empirically, modern economies function close enough to the ideal competitive model that any such government policies should be looked on with great suspicion. Their simple macroeconomic models are the baseline with which both schools operate.

The names come from historical associations. Freshwater economists came out of the University of Chicago, the University of Minnesota, and the University of Rochester, all near one of the Great Lakes. Saltwater economists tend to be nearer ocean coasts, such as at Harvard and the Massachusetts Institute of Technology.

New classical economists, such as Robert Lucas and Thomas Sargeant, overthrew, in the 1970s, the Neokeynesianism or Old Keynesian of Alvin Hansen, Paul Samuelson, and Robert Solow. In the 1960s, Old Keynesian was known as the "New Economics" and the neoclassic synthesis. There is good reason for the common reader to be confused.

MMT builds on Post Keynesianism, and I am going to take it for granted that their proponents accept a Post Keynesian take on the above. (Which is not to say that Post Keynesians do not argue, sometimes vehemently, among themselves.) Joan Robinson called the neoclassical synthesis "bastard Keynesianism". Both freshwater and saltwater economists are pre-Keynesian. Carter (2020) provides an interestingly structured popular presentation of the unjustified rejection of the economics of Keynes

I find it hard to locate the logic in arguments that labor markets, good markets, and money markets tend to clear in any run. Some, such as Davidson (2007) emphasize money and uncertainty. Minsky (2008) and Marglin (2021) note the dynamic setting of Keynes' theory. In a model of the United States economy, it should not matter whether one calculates prices in dimes or dollars. This is a far cry from arguing that money is neutral, that the same real equilibrium would be approached if prices fell to 10 percent of their current nominal values.

I tend to emphasize microeconomics, following Sraffa. The theory of prices of production does not provide a logical foundation for the substitution mechanisms marginalists require for their ideas to make sense. Well-defined supply and demand functions do not exist in the long run.

Mainstream economists are apparently not taught any of this:

"...This article aroused the anger of just about every macroeconomist on Twitter..."

"...The brief description of freshwater and saltwater economics is fine, but to describe MMT as being 'brackish' — i.e., some sort of fusion of freshwater and saltwater, or a middle ground between the two — is absurd..."

-- Noah Smith The NYT article on MMT is really bad

I suspect many economists on twitter were not angered by this article. As far as I know, James Galbraith came up with the metaphor of brackwater economics. As seen above, it is not intended to be a fusion or middle ground. Rather it is a matter of rejecting both freshwater and saltwater economics. The nonexistence of an intertemporal budget constraint is another aspect of macroeconomics that Noah Smith seems to be confused about. Mainstream macroeconomists absurdly postulate that governments must always pay off their debts as time approaches infinity.

But why should Noah Smith be any different? Larry Summers ignorantly cited James Galbraith, who is a proponent of MMT or, at least, theories of endogenous money. I doubt that Summers believes this:

"I am all for intellectual diversity and wish that the NYT would give more attention to Marxist scholars like Steve Marglin, whose book Raising Keynes deserves extensive debate, or other left scholars like Tom Palley, Dean Baker or Jamie Galbraith." -- Larry Summers

You can find a post-2008 YouTube video, where Marglin says something like that his colleages are polite to him at holiday parties, but they have nothing to say about his research. Anyways, his long tome, which I have barely started, is clear that Keynes was arguing about more than government policy. He argues that models like the Keynesian cross and IS/LM are only a first pass description of the General Theory. The dynamic setting has to be taken into account in further passes. According to one review I stumbled upon Marglin's book could be improved in its account of money. Keynes' Treatise on Money contains a theory of endogeneous money. I can see reading the General Theory as assuming the central bank can set the stock of money, as a concession to the view he was arguing against, even though others say otherwise.

One could pursue political economy because one is interested in advancing political means that improve the lives of the vast majority of the population. One might make a compromise here. One might think one's policies are more likely to be enacted if one does the least to challenge hegemonic ideas about how the world works. As I understand it, Krugman has said somewhere that his academic strategy is to think in terms of simple models, like IS/LM, and then recast the argument into a publishable model of a Representative Agent, Rational Expectations (RARE) economy, also known as Dynamic Stochastic General Equilibrium (DSGE) model. In this approach, one puts forth arguments that one correctly believes have nothing to do with how actually existing capitalist economies function. One ignores some conclusions of the model. And it is doubtful that this approach will ever approach an useful description of a capitalist economy. I think Brad DeLong has said somewhere that this approach of boring from within is wasted time. (I welcome explicit links for the above.) It would seem that however politically useful such attempts have been, maybe after a half century of scientific failure by mainstream economists, heterodox approaches should be taken more seriously.

  • Zachary D. Carter. 2020. The Price of Peace: Money, Democracy, and the Life of John Maynard Keynes. Random House.
  • Paul Davidson. 2007. John Maynard Keynes. Palgrave Macmillan
  • John Hicks. 1981. IS-LM: an explanation. Journal of Post Keynesian Economics 3(2): 139-154.
  • Stephamie Kelton. 2020. The Deficit Myth: Modern Monetary Theory and the Birth of the People's Economics. Public Affairs.
  • John Maynard Keynes. 1936. The General Theory of Employment, Interest, and Money. Harcourt-Brace.
  • Stephen A. Marglin. 2021. Raising Keynes: A Twenty-First-Century General Theory., Harvard University Press.
  • Hyman Minsky. 2008. John Maynard Keynes. McGraw-Hill.
  • Franco Modiglani. 1944. Liquidity preference and the theory of interest. Econometrica 12(1): 45-88.

Thursday, February 10, 2022

Some Twitter Feeds

Suggestions for more? There are other feeds from scholars just starting out. One can also find mainstream economists on twitter who do not know that almost everything they say was shown to be, at best, wrong more than half a century ago.

Updated 14 and 15 February 2022

Saturday, February 05, 2022

Engels To Bloch in 1890

Engels had a lot to do with formulating orthodox interpretations of Marx in the period after Marx's death. So it is interesting to see what he says. I have transcribed another letter before, about the law of value. The following is about historical materialism and the relation of the superstructure to the economic base:

According to the materialist conception of history, the ultimately determining element in history is the production and reproduction of real life. Other than this neither Marx nor I have ever asserted. Hence if somebody twists this into saying that the economic element is the only determining one, he transforms that proposition into a meaningless, abstract, senseless phrase. The economic situation is the basis, but the various elements of the superstructure - political forms of the class struggle and its results, to wit: constitutions established by the victorious class after a successful battle, etc., juridical forms, and even the reflexes of all these actual struggles in the brains of the participants, political, juristic, philosophical theories, religious views and their further development into systems of dogmas - also exercise their influence upon the course of the historical struggles and in many cases preponderate in determining their form. There is an interaction of all these elements in which, amid all the endless host of accidents (that is, of things and events whose inner interconnection is so remote or so impossible of proof that we can regard it as non-existent, as negligible), the economic movement finally asserts itself as necessary. Otherwise the application of the theory to any period of history would be easier than the solution of a simple equation of the first degree.

We make our history ourselves, but, in the first place, under very definite assumptions and conditions. Among these the economic ones are ultimately decisive. But the political ones, etc., and indeed even the traditions which haunt human minds also play a part, although not the decisive one. The Prussian state also arose and developed from historical, ultimately economic, causes. But it could scarcely be maintained without pedantry that among the many small states of North Germany, Brandenburg was specifically determined by economic necessity to become the great power embodying the economic, linguistic and, after the Reformation, also the religious difference between North and South, and not by other elements as well (above all by its entanglement with Poland, owing to the possession of Prussia, and hence with international political relations - which were indeed also decisive in the formation of the Austrian dynastic power). Without making oneself ridiculous it would be a difficult thing to explain in terms of economics the existence of every small state in Germany, past and present, or the origin of the High German consonant permutations, which widened the geographic partition wall formed by the mountains from the Sudetic range to the Taunus to form a regular fissure across all Germany.

In the second place, however, history is made in such a way that the final result always arises from conflicts between many individual wills, of which each in turn has been made what it is by a host of particular conditions of life. Thus there are innumerable intersecting forces, an infinite series of parallelograms of forces which give rise to one resultant - the historical event. This may again itself be viewed as the product of a power which works as a whole unconsciously and without volition. For what each individual wills is obstructed by everyone else, and what emerges is something that no one willed. Thus history has proceeded hitherto in the manner of a natural process and is essentially subject to the same laws of motion. But from the fact that the wills of individuals - each of whom desires what he is impelled to by his physical constitution and external, in the last resort economic, circumstances (either his own personal circumstances or those of society in general) - do not attain what they want, but are merged into an aggregate mean, a common resultant, it must not be concluded that they are equal to zero. On the contrary, each contributes to the resultant and is to this extent included in it.

I would furthermore ask you to study this theory from its original sources and not at second-hand; it is really much easier. Marx hardly wrote anything in which it did not play a part. But especially The Eighteenth Brumaire of Louis Bonaparte is a most excellent example of its application. There are also many allusions to it in Capital. Then may I also direct you to my writings: Herr Eugen Dühring's Revolution in Science and Ludwig Feuerbach and the End of Classical German Philosophy, in which I have given the most detailed account of historical materialism which, as far as I know, exists.

Marx and I are ourselves partly to blame for the fact that the younger people sometimes lay more stress on the economic side than is due to it. We had to emphasise the main principle vis-a-vis our adversaries, who denied it, and we had not always the time, the place or the opportunity to give their due to the other elements involved in the interaction. But when it came to presenting a section of history, that is, to making a practical application, it was a different matter and there no error was permissible. Unfortunately, however, it happens only too often that people think they have fully understood a new theory and can apply it without more ado from the moment they have assimilated its main principles, and even those not always correctly. And I cannot exempt many of the more recent "Marxists" from this reproach, for the most amazing rubbish has been produced in this quarter, too.... -- Engels to J. Bloch, 21 September 1890

I expected to see the phrase, "In the last instance" here. I guess that is how Lenin phrased the idea that the material base ultimately explains or determines the course of history. If you read Lenin as not so determinist, is Engels' letter consistent with Gramsci's ideas? One can see that Engels is almost quoting the second paragraph of The Eighteenth Brumaire of Louis Bonaparte:

"Hegel remarks somewhere that all great world-historic facts and personages appear, so to speak, twice. He forgot to add: the first time as tragedy, the second time as farce...

Men make their own history, but they do not make it as they please; they do not make it under self-selected circumstances, but under circumstances existing already, given and transmitted from the past. The tradition of all dead generations weighs like a nightmare on the brains of the living..."

As I understand it, Engels' Anti-Dhüring was easier to obtain than even most of Marx's published writings during the period of the Second International and the founding of German social democracy. Engels has something to say about the application of dialectics to natural sciences in this book, an idea I find questionable. He does say that he needs to address a broad range of topics because "Herr Dhüring ... dealt with all things under the sun and then a few more." What should one make of Engels' mechanical analogy about about a parallelogram of forces? I like the idea that the result is not something anybody is necessary conscious of willing.

I also like the first three chapters of the last part of Anti-Dhüring, in which Engels (I gather with Marx's help) writes about the distinction between utopian and scientific socialism. These chapters were published as a stand-alone pamphlet. My take is that the experience of the Soviet Union, of no-longer-actually existing socialism, cannot discredit Marx's plans for a post-capitalist society, not because it was not "true communism", but because he refused on principle to draw up such plans. I suppose I ought to have a caveat about The Civil War in France and Critique of the Gotha Program. You might think those who want to abolish or transcend capitalism should draw up such plans, especially after these terrible experiences. And Marx and Engels do have somewhere, I guess, some naive comments about all that is needed for successful economic planning is widespread knowledge among the workers of arithmetic and accounting, and these comments should be criticized. I do not necessarily take issue with some criticisms. But, still, the position of Marx and Engels was not to draw up such plans.