Saturday, August 10, 2013

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.


  1. Wildly off-topic:

    Taylor and Francis website made available a series of papers on Joan Robinson and F.A. von Hayek:

    Included a FREE Vernengo and Rochon paper:

    Kaldor and Robinson on money and growth
    Matias Vernengo, Louis-Philippe Rochon
    The European Journal of the History of Economic Thought
    Vol. 8, Iss. 1, 2001

  2. With respect to Marx and the rate of interest variable, he is an oldey, but goodey: (subscription required)

  3. Thanks, David, for the link.

    If you guys haven't seen it yet, you must read the Harcourt-King paper (Talking About Joan Robinson: Geoff Harcourt in Conversation with John King):

    Harcourt: "And Joan, partly in retrospect, saw that the thrust of the attack of Imperfect Competition on laissez faire, and capitalism generally, was showing that it was a system of exploitation, because it discredited marginal productivity. As soon as you had imperfect competition, workers got paid less than the value of their marginal product." (page 34)

    The only difference with what He-Who-Must-Not-Be-Named said is that the much maligned and ridiculed German Bearded One extended this conclusion to perfectly competitive markets.

  4. By my reading Marx was pretty confused on the question of the rate of interest. In Volume I everything is determined by the extraction of surplus value. But by Volume III, when he examines, the financial system he finds it impossible to deny that the rate of interest is an exogenous variable. Here is the relevant passage:

    "[A]ssuming the average profit to be given, the rate of the profit of enterprise is not determined by wages, but by the rate of interest. It is high or low in inverse proportion to it." (Marx, K. 1894. Chap. 23)

    This seems to me to cause immeasurable difficulties for Marx's earlier idea that everything relevant to the study of political economy can be derived by studying the production process from the ground up, as it were.

  5. Philip is to humble to promote his own blog post on the topic natural rate etc. that i find very interesting so i put up the links to this posts instead if anyone missed it.I find well worth reading for all interested the subject.

  6. Congratulations for your blog an for this lively debate. I´m not an economist yet reading Mr Rallo criticism of what he calls "neoricardian theory of value" I found this comment of him quite remarkable (sorry if my translation is somewhat poor, English is not my native language):

    "It´s true any Price theory has to be able to explain the tendency of convergence of prices towards fragile market equilibriums, but the theory can not pass over the fact that those equilibriums, as the forces that are dragging prices towards them, are fragile because of the subjectivity of economics agents.

    That will be tantamount to say Jack the Ripper did not kill his victims: it was the victims were ripped as a consequence of the relative spatial position of his necks and abdomens with the murdering knives.

    It is the subjectivity of consumer preferences what determines the relative proportions of the goods to be provided, and it´s the subjectivity of the entrepreneurial expectations and calculus what set up productive plans directed to met the consumer preferences.

    This does not mean, by the way, that objective circumstances do not play a role in individual subjectivity (human beings prefer to eat by physiological reasons; and the entrepreneurs can not implement physically impossible business plans) but that objective circumstances does not determine individual subjectivity in a way anybody can know."

    So I am amazed. From a myriad of "individual degrees of utility" and time preferences for consumption or abstention thereof, there are relatively stable prices along significant periods of time.

    And secondly, he seems to me to be claiming that if "objective circumstances" does not determine "individual subjectivity" in a way anybody can know (not even approximately) certainly apart from entrepreneurs having magical qualities, I fail to see how can not you take into account that your workers have to eat, that a certain amount of nutritive substances is unfortunately indispensable and that you may know it. Or it is not the point; precisely that "objective circumstances" have a decisive role in "subjectivity"?


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