Fabio Petri on non-substitution theorems

Sometimes there is simple and right

New paper by Professor Petri, which is always worth reading, titled "Nonsubstitution Theorem, Leontief Model, Netputs: Some Clarifications." From the abstract:

The nonsubstitution theorem concerns long-period technical choice and relative prices, and was so understood in its first (1951) formulations, but the modern advanced micro textbooks that present it do not make this clear, rendering the theorem impossible to understand for students. These modern presentations derive from a reinterpretation of the Leontief model as a ‘timeless’ economy in Walrasian equilibrium, capable of positive production in spite of zero initial endowments of all inputs except labour: an unacceptable interpretation, made possible by a use of netputs, to describe the economy’s production possibilities, that is illegitimate in this case even from a strictly neoclassical perspective. The notion of a ‘timeless’ economy disappears from the textbook presentations of the Leontief model and of the nonsubstitution theorem, but the result is that the nature of the model and of the prices to which the theorem refers is not clarified, inevitably leaving students utterly confused. This note remembers the true nonsubstitution theorem, points out that it had been correctly enunciated by Samuelson (1961), and suggests that the current inability to present it in a correct way is due to the absence of the notion of long-period prices from the theoretical horizon of contemporary neoclassical value theory. The paper opens with clarifications on the meaning of the Leontief model which prepare the ground for the discussion of the problem with netputs.

 Read full paper here.

A Brief Sketch of the Classical-Keynesian Perspective

By David Fields

From a Classical-Keynesian perspective (Bortis, 1997, 2003), rates of interest regulate rates of profits (Panico, 1980, 1985), and, thus, real wages are endogenously determined. The presence of financial instruments, which represent titles to future flows of income, makes it so that the actual center of distributive conflict in capitalism lies not in the technical conditions of production, but is rather governed by the real rate of interest, which is a conventionally-determined exogenous variable that reflects the relative powers of finance capitalists vis-à-vis industrial capitalists & labour (Pivetti, 1985, 1991, 2001).

The rate of profit, as a ratio, has a significance, which is independent of any prices, and can well be ‘given’ before the prices are fixed. It is accordingly susceptible of being determined from outside the system of production, in particular by the level of money rates of interest. (Sraffa, 1960: 33)

In this sense, high real rates of interests induce industrial capitalists to prefer short-term speculative financial investment, instead of long-term productive real investment, since access to credit is expensive. Consequentially, industrial capitalists center attention on the pursuit of immediate surplus value realization, via speculation, in order to handle the burden of costly interest payments—the social cost being nominal wage suppression, which, by implication, exhibits an enlargement of the reserve army of labour.

[…] the credit system, which has its focus in the so-called national banks and the big money-lenders and usurers surrounding them, constitutes enormous centralisation, and gives this class of parasites the fabulous power, not only to periodically despoil industrial capitalists, but also to interfere in actual production in a most dangerous manner— and this gang knows nothing about production and has nothing to do with it. (Marx 1894: 544-45)

Along these lines, heterodox growth and distribution models have been put forward (cf. Hein, 2008), highlighting the need for a redistribution of income from finance/industrial capitalists to labour (Lavoie and Seccareccia, 1999) and making unemployment the primary policy target (Smithin, 2004). Underpinning these models are works that incorporate Keynes’ principle of effective demand and Sraffian price theory in a long-period analysis of capital accumulation (Park, n.d.; Cesaratto et al. 2003). These studies pay considerable attention to the extent to which the Hicksian supermultiplier concept effectively explicates the degree to which induced consumption and investment, via the accelerator, determine average levels of total output (Serrano, 1995) and, thus, normal capacity utilization (Amadeo, 1986; Trezzini, 1998), with the richness of a framework inspired by Kaldor and Pasinetti (Docherty, 2012) that meticulously constitutes the palpability of Kalecki’s famous aphorism that ‘capitalists get what they spend…workers spend what they get’.

Originally published in the URPE blog.

References:

Amadeo, Edward J. 1986. “Notes on Capacity Utilisation, Distribution and Accumulation.” Contributions to Political Economy 5(1):83–94.

Bortis, Heinrich. 1997. Institutions, Behaviour and Economic Theory: A Contribution to Classical-Keynesian Political Economy. Cambridge: Cambridge University Press.

Bortis, Heinrich. 2003. “Keynes and the Classics: Notes on the Monetary Theory of Production.” In Modern Theories of Money: The Nature and Role of Money in Capitalist Economies, (eds.) Louis-Philippe Rochon and Sergio Rossi. Cheltenham, UK: Edward Elgar.

Cesaratto, Sergio, Franklin Serrano, and Antonella Stirati. 2003. “Technical Change, Effective Demand and Employment.” Review of Political Economy 15(1):33.

Docherty, Peter. 2012. “Long Period Interest Rate Rules in a Demand-Led Kaldor-Pasinetti-Sraffa-Keynes Growth Model.” Journal of Post Keynesian Economics 34(3):521–46.

Hein, Eckhard. 2008. Money, Distribution Conflict and Capital Accumulation: Contributions to 'Monetary Analysis'. Basingstoke: Palgrave Macmillan.

Kalecki, Michal. 1971. Selected Essays on The Dynamics of the Capitalist Economy 1933-1970. Cambridge: Cambridge University Press

Kaldor, Nicholas. 1955. “Alternative Theories of Distribution.” The Review of Economic Studies 23(2):83–100.

Kaldor, Nicholas. 1966. “Marginal Productivity and the Macro-Economic Theories of Distribution: Comment on Samuelson and Modigliani.” The Review of Economic Studies 33(4):309–19.

Lavoie, Marc, and Seccareccia, Mario. 1999. “Interest Rate—Fair.” In Encyclopedia of Political Economy, vol. 1, (ed.) Phillip Anthony O’Hara. London: Routledge.

Marx, Karl. 1894. Capital Vol. III. New York: International Publishers.

Panico, Carlo. 1980. “Marx’s Analysis of the Relationship between the Rate of Interest and the Rate of Profits.” Cambridge Journal of Economics 4(4):363–78.

Panico, Carlo. 1985. “Market Forces and the Relation between the Rates of Interest and Profits.” Contributions to Political Economy 4(1):37–60.

Park, Man-Seop. n.d. “Towards a ‘Classical-Keynesian’ analysis of Effective Demand in the Long Period.” Retrieved May 8, 2014.

Pasinetti, Luigi L. 1962. “Rate of Profit and Income Distribution in Relation to the Rate of Economic Growth.” The Review of Economic Studies 29(4):267–79.

Pasinetti, Luigi L. 1974. Income Distribution and Growth. Cambridge: Cambridge University Press

Pivetti, Massimo. 1985. “On the Monetary Explanation of Distribution.” Political Economy: Studies in the Suplus Approach 1(2):73–104.

Pivetti, Massimo. 1991. An Essay on Money and Distribution. London: Macmillan.

Pivetti, Massimo. 2001. “Money Endogeneity and Monetary Non-Neutrality: A Sraffian Perspective.” In Credit, Interest Rates and the Open Economy, (eds.) Louis-Philippe Rochon and Matias Vernengo. Cheltenham, U.K: Edward Elgar.

Serrano, Franklin. 1995. “Long Period Effective Demand and the Sraffian Supermultiplier.” Contributions to Political Economy 14(1):67–90.

Smithin, John. 2004. “Interest Rate Operating Procedures and Income Distribution.” In Central Banking and the Modern World, (eds.) Marc Lavoie and Mario Seccareccia. Cheltenham, UK: Edward Elgar.

Sraffa, Piero. 1960. Production of Commodities by Means of Commodities. Cambridge: Cambridge University Press.

Trezzini, Attilio. 1998. “Capacity Utilisation in the Long Run: Some Further Considerations.” Contributions to Political Economy 17(1):53–67.

Ariel Dvoskin on the limits of Walrasian equilibrium

Here is Ariel's PhD dissertation, which is well worth reading for those interested in the evolution and limitations of the marginalist (neoclassical) models. From the abstract:

"The marginalist approach is unable to satisfactorily incorporate capital goods within the supply and demand explanation of prices and distribution, and this seems to have condemned modern general equilibrium theory to face an unpleasant dilemma: either this theory is, like Hahn, truly consistent with its own theoretical object, a notion of equilibrium that must be silent on the issue of how actual economies work; or, alternatively, the theory attempts to provide some explanation of the working of actual economies and in so doing, it must inescapably rely on traditional gravitational ways of reasoning that must presume the illegitimate notion of capital in value terms. Either way modern general equilibrium theory runs into a blind alley, with the implication that, to predict with reasonable accuracy price, quantity and distributional trends as observed in actual economies, an explanation with different theoretical foundations is necessarily called for."

The meaning of short and long-term and the natural rate

From a history of economic thought point of view the turning point in the demise of the Keynesian Consensus based on the Neoclassical Synthesis was Friedman's rediscovery of Wicksell's natural rate. It was peculiar, in a sense, that it happened in the 1960s when the capital debates demonstrated (and was accepted by Samuelson, the High Priest of the Neoclassical Synthesis) that the natural rate made no theoretical sense. That led to a more significant and insidious change in economics. The abandonment of the notion of long-term equilibrium method, as noted by Garegnani.

Briefly stated, what the process entailed is that confronted with the fact that there is no possible way to relate some measure of capital with its remuneration (the idea that abundant capital would lead to a low level of remuneration, i.e. a low rate of interest, and the analogous one that full employment of capital could be obtained with a sufficiently low rate of interest) the mainstream reverted to the Arrow-Debreu (AD) notion that different types of capital had different remunerations and there was no tendency to a uniform rate of profit (interest). That, as noted by Garegnani, was a departure from the traditional method of economics. Up to the 1930s all economists, including the marginalists (neoclassical) ones did follow it.

Note that the long-term, associated with the uniform rate of interest (or profit), is a methodological instrument, not a particular period of chronological time. The long-term is just a period in which no variables are constant or fixed, and the process of competition, that allows for new entrants in every sector (with perfect competition) to lead to a uniform rate of interest. The short-term is by symmetry a situation in which something precludes the long-term situation to be achieved. For example, a typical short-term macroeconomic assumption is to assume a given level of productive capacity. The demand effect of investment (demand for equipment and installations) is taken into account, but not the capacity effect (the increase in the number of machines and plants).

That's why this comment by Miles Kimball (a supply-side liberal, talk about oxymoron) is so revealing of the confusion that now dominates the mainstrem. He says:

"To think clearly about economic fluctations at a somewhat more advanced level, I find I need to use these four different time scales:

• The Ultra Short Run: the period of about 9 months during which investment plans adjust—primarily as existing investment projects finish and new projects are started—to gradually bring the economy to short-run equilibrium. 

• The Short Run: the period of about 3 years during which prices (and wages) adjust gradually bring the economy to medium-run equilibrium.

• The Medium Run: the period of about 12 years during which the capital stock adjusts gradually to bring the economy to long-run equilibrium. 

• The Long Run: what the economy looks like after investment, prices and wages, and capital have all adjusted. In the long run, the economy is still evolving as technology changes and the population grows or shrinks."

Yes, that now passes for clarity of thinking. Short-term is a period of chronological time, long-term is conceptual methodological position. The confusion is compounded by the fact that he is trying to clarify what he sees as "a lot of confusion about the natural interest rate ... [and] the main source of confusion is that there is both a medium-run natural interest rate and a short-run natural interest rate." The natural rate is by definition a long-term position.

Old marginalists, like Wicksell or Marshall didn't think the system was at the natural rate in the short-run. It gravitated around it in the long-term. This idea of a short-run natural rate, derives from the AD short-run notion of a system that is always in equilibrium. And then he does use an aggregative version of an ISLM model (which is a long term sort of equilibrium notion). But he has no clue about the capital debates and its consequences. Oh well.