The natural rate in pure exchange, intertemporal models

One more clarification on the previous discussion about the natural rate in Austrian models. In his reply,  Mr. Rallo suggests (in Spanish) that I confused the natural rate that can be derived from a barter economy with the one derived from intertemporal equilibrium model. So let's start by clarifying that barter refers to whether there is money or not, while the notion of intertemporal equilibrium is associated to the nature of equilibrium, whether it is short-term or long-term.  You can have an intertemporal model of equilibrium with barter as several Arrow-Debreu models actually are.

Traditional notions of equilibrium, like the classical authors had, are not intertemporal, but several of those were based on barter ideas. Equilibrium in classical economics is a tendency associated to the process of competition that leads to a uniform rate of profit. Some authors had the real (meaning non-monetary) rate of profit govern the system and also the rate of interest, like Ricardo, while others like Tooke suggested that the rate of interest governed the rate of profit, and arguably there are elements in Marx analysis that suggest the possibility of an independent rate of interest.*

The notion of intertemporal equilibrium is relatively new and was developed by Hayek, Hicks, Lindahl, and Myrdal (see Milgate here; subscription required)  in the 1920s and 1930s, before it become common after the capital debates on the basis of the Arrow-Debreu model. Intertemporal models do not require the notion of a uniform rate of profit, and some authors have suggested that as such they are not open to the capital critique. Because they do not require a uniform rate of profit these models are short-term.

So the relevant point is the notion of equilibrium and not whether it is a barter or credit system [additionally that would bring about the way money is introduced in the economy, as mere toke for exchange, or as a unit of account in which agents want to accumulate, but that is a different issue]. Mind you, one might think that Mr. Rallo is suggesting that in a short-term model (with no tendency ot a uniform rate of profit) there is no need in marginalist models for a natural rate of interest (although we'll see that's not his point).

Yet, the point made by Garegnani and Petri is that in an intertemporal model with disaggregated means of production (capital goods), it is still necessary for the equilibration of aggregate investment to full employment savings, and that requires a measure of the quantity of capital, and that means, and by necessity a rate of interest. That rate of interest that equilibrates savings and investment is a natural rate.

Mr. Rallo seems to believe that there is a difference between a situation in which there are "lenders (savers) lending at 5% for a year, and investors that demand 5% for 30 years" (or in Spanish "ahorradores que prestan al 5% a 1 año e inversores que piden prestado al 5% a 30 años"), which would be different if both lenders and borrowers had the same time period in mind, but different rates.
Again, this involves not the intertemporal nature of the model, but the term structure of interest rates.

So taking away the adjustment for risk associated to the longer-term that financial capital would be tied to investment, in the neoclassical theory arbitrage should still work. So presumably the rate would be more than 5% for the 30 year loan. This has nothing to do with the necessity in Austrian theory, as in any type of marginalist model, of a quantity of capital and a natural rate of interest. Neither barter nor the term structure of the rate of interest (or the more relevant discussion of the short-term nature of intertemporal models) relieves the marginalist (and Austrian) theories from a need for a natural rate of interest.

The only consistent way to get rid of the notion, is to abandon the marginalist approach, and like Sraffa assume that one distributive variable, in his case the monetary rate of interest, is given exogenously. Savings then is adjusted to investment by the multiplier process (i.e. Keynes and Kalecki's Principle of Effective Demand).

* Panico (1980, p. 269 here; subscription required) argues that: "Marx's analysis of the factors determining the rate of interest, he rejected any attempt to explain the determination of the average rate of interest on the basis of'laws of necessity'. He proposed instead, to investigate it by means of qualitative description, of those economic, conventional and institutional factors that, from time to time, affect this variable." So while its clear that Marx thought that the rate of profit determined the rate of interest, it is also reasonable to argue that there are contradictory propositions that suggest a determination of the normal rate of interest that is independent from the rate of profit.

PS: Thanks to Franklin Serrano for pointing my mistake on Quesnay (deleted; yes there is money in the Tableau as there is in Marx's simple reproduction system, derived from Quesnay) and the causality in Marx. Also, forgot the link to Milgate's paper, which is now in place.

Sraffa and the Marshallian system

(Sraffa circa 1976)

G. L. S. Shackle argues in The Years of High Theory that ‘there began in the mid-1920s an immense creative spasm, lasting for fourteen years until the Second World War, and yielding six or seven major innovations of theory, which together have completely altered the orientation and character of economics’ (Shackle, 1967, p. 5). However, by 1967, the two most important developments of this period—Keynes’s principle of effective demand and Sraffa’s criticism of the marginalist theory of value—were rapidly fading from the main corpus of mainstream theory.

The relative ease with which neoclassical economics reasserted its main conclusions is, in fact, explained by Shackle’s account of those years. First, Sraffa’s critique of the Marshallian theory of value is seen only as a step in the development of the theories of imperfect competition by Joan Robinson and Edward Chamberlin. Second, Keynes’s General Theory is seen as stating that unemployment results from the existence of uncertainty and irrational expectations (Shackle, 1967, p. 129). Both developments can be interpreted as asserting that market imperfections render neoclassical theory, although internally coherent, irrelevant for the analysis of the real world.

Also Shackle’s failure in 1967 — well after the publication of Production of Commodities — to acknowledge the importance of the revival of classical political economy to the debates of the 1930s represents a serious inadequacy of his interpretation of ‘the years of high theory’.

Before getting into Sraffa's critique of Marshall, it is worth noticing that Sraffa came to economics via monetary economics, like Ricardo and Keynes. His dissertation for the Law Degree, L’Inflazione Monetaria in Italia Durante e Dopo la Guerra (subscription required), dealt with postwar inflation and the return to the Gold Standard, the same topic of Keynes’s Tract on Monetary Reform. According to Eatwell and Panico (subscription required), in the analysis of the asymmetric effects of inflation and deflation Sraffa reveals the heterodox character of his position, more akin with the works of the classical authors and Marx than the conventional marginalist analysis. The notion that social conflicts and monetary factors determine the normal real wage was part of Sraffa’s analysis, although several elements of his analysis were still conventional, e.g. the acceptance of the Quantity Theory and of the Purchasing Power Parity theory.

Sraffa’s criticism of the Marshallian theory of supply represents an analogous situation, in the sense that some elements of the conventional marginalist views were still present. Marshall’s or Sraffa’s dilemma (which appears in Sraffa's 1926 paper) refers to the incompatibility between increasing returns and perfect competition. It is a long period problem. Sraffa’s critique can be summarized in the following way. First, rising costs derive from diminishing returns to substitution, and, therefore, in the general case where there are no fixed factors, increasing costs do not seem to exist. Secondly, increasing returns are incompatible with perfect competition. In the long period, when the firm cannot experience marginal costs arising from the existence of some fixed input, there can be no diminishing returns. Replication is always possible, except for the case of indivisibilities. In addition, Sraffa showed that increasing returns to scale are inconsistent with the notion of perfect competition.

In the case of increasing returns, the average cost is decreasing, implying that the marginal cost is below average variable cost, and, hence, there is no infinite, non-zero solution for the profit maximization problem. In other words, there is a tendency for the firm to expand to infinite size. Sraffa’s argument proves the failure of perfectly competitive assumptions to determine any equilibrium of the individual firm. Two alternatives are opened by Sraffa’s critique of Marshallian theory. If it is not legitimate to treat average cost as either increasing or decreasing within the framework of perfect competition, we are left with the result that the only satisfactory assumption is that of constant returns. On the other hand, ‘everyday experience shows that a very large number of undertakings work under conditions of individual diminishing costs’ (Sraffa, 1926, p. 543), which suggests that we should instead abandon the notion of perfect competition.

Sraffa considered the imperfect competition approach to be the only logical way to develop the theory of value along Marshallian lines. However, he showed no inclination to pursue this solution, and he appears to have already been working toward the revival of the classical approach. The origins of this project can be traced back to his early draft of the opening propositions of the Production of Commodities, which he asked Keynes to read in 1928 (Sraffa, 1960, p. vi). The reasons for not pursuing imperfect competition were never quite explained by Sraffa, but are fairly reasonable to infer (note that in Cambridge it was two of his students, Richard Kahn and Joan Robinson, that developed the imperfect competition theory).

Note that in order to obtain partial equilibrium, which is what the Marshallian model presumes, one must assume that prices in a particular industry are not affected by and do not affect the prices in other industries. Hence, externalities have to be internal to the industry, since otherwise production in one sector would affect the prices in other industries [perfect competition in partial equilibrium, the U-shaped cost curves and the equilibrium at the minimum with marginal cost equal marginal revenue, require also that externalities are external to the firm, since if they weren't the firm would became a monopolist; of course externalities that are internal to an industry and external to firms are an empty set]. That seems to be a dead end. Sraffa was already interested in the determination of long term prices. By this time, the summer of 1927 when he was preparing his ‘Lectures on Advanced Value Theory’ that he gave from 1928 until 1930, it was already clear to him that he needed to start from classical preocupation of determining relative prices and one of the distributive variables (the rate of profits or wages) strictly in material terms, that is, the quantities of labor and commodities needed to produce commodities.

For further on Sraffa's critique of Marshall see Gary Mongiovi's paper here (subscription required). For a general critique of Shackle's stance in the history of 'the years of high theory' read this one. For the implications of Sraffa's 1960 book for economics go to this old post (yes on the capital debates!).

Investigación Económica at 70

Investigación Económica, a journal that has become the most important in México, is turning 70, and Ignacio Perrotini, the editor, is organizing a very interesting conference (disclosure, I'm in the board, and will be at the conference). Jesús Silva Herzog was the founder, and while he cannot be considered a structuralist, it is clear that he was very open to publish the authors that would become central for that school of thought in Latin America, like Juan Noyola Vázquez, the father of the structuralist theory of inflation, Hans Singer, of Prebisch-Singer fame, and Celso Furtado, a central figure in early structuralism and the Economic Commission for Latin America (ECLA) when Prebisch was the Executive Secretary. IE published original and translated articles of the main heterodox economists over the years, and now that it is bilingual it has become a central outlet for high quality heterodox research.  So if you cannot go to the conference, you can check the various issues in the link above.

PS: A partial list of the conference participants includes Amitava Dutt, Anthony Thirlwall, Carlo Panico, Guadalupe Mántey, Tom Palley and Jaime Ros among others.