More on Murphy, and Rowe on the Natural Rate of Interest

My post on Robert Murphy's critique of Piketty generated a few comments, and a good debate (see the comments section here). But there are a few things worth clarifying, and also Robert pointed out a post by Nick Rowe, which is also worth discussing in more detail.

As I noted before there seems to be a confusion among Austrians, which think that their notion of the rate of interest is purely based on intertemporal consumption (savings) preferences, and is not open to the problems of the capital debates (this is as old as Austrian economics, by the way; for more below). It would not be, in their view, equivalent to the natural rate of interest of Wicksell and the Loanable Funds Theory of the rate of interest.

First, let me get back to Robert Murphy's original post, which led to my previous post. Just to remind you his argument was that the non-Austrian mainstream (and Piketty, as a result) confused financial or monetary measures of capital with purely physical ones. It's worth quoting extensively from his post. He says:

"If a firm hires a specific capital good for a unit of time, the payment is the rental price of the capital good. For example, suppose that a warehouse pays $100,000 per year to an independent company that maintains fleets of forklifts. These annual payments are clearly due to the "marginal product" of the forklifts; the warehouse can sell more of its own services to its customers when it has use of the forklifts. 

However, these technological facts tell us nothing about the rate of interest enjoyed by the owners of the forklifts. In order to determine that, we would have to know the market price of the forklifts. For example, if the forklifts that the independent company rents out to the warehouse could be sold on the open market for $1 million, then their owners would enjoy a 10-percent return each year on their invested capital. But if the forklifts could be sold for $2 million, then the $100,000 payments—due to the "marginal product" of the forklifts—would correspond to only a 5-percent interest rate. As this simple example illustrates, knowledge of the marginal product of capital, per se, does not allow us to pin down the rate of interest."

Note that this is a triviality, and by no means contradictory with the conventional neoclassical analysis. It only says that the rate of interest specific to a particular capital good (forklifts) and its price are inversely related. That per se, certainly does NOT mean that "the relationship between the productivity of capital and the interest rate is not [direct]." The point is that, in marginalist economics, the entrepreneur would 'hire' more capital to the point were the additional (marginal) cost would equalize the additional (marginal) revenue that can be obtained from using one more unit of capital, and the latter would depend on how much more output the additional capital (forklift in this case) unit would bring. So according to changes in prices of the capital good, and, as a result, of its rate of return, the capital good would be used if it provides a gain over the interest rate. If there is an advantage in using the capital good (forklift), then more will be used, pushing its price up, and bringing its remuneration down into equilibrium with the rate of interest (the natural one).

The point of the capital debates (go here) is that there is no reason to believe that a certain technology (forklifts) would be more profitable at low rates of interest, while at higher rates of interest firms would switch to manually powered hoists (more labor intensive, arguably), for example, to lift the cargo. It would be even impossible to define clearly that one technology (forklifts) is more capital intensive than another (manual hoists). The point is that there is no relation between intensity (relative scarcity) of the use of a capital good and its remuneration.

For example, in the conventional story if the price of the forklift goes down, more capitalists would be willing to buy it, supposedly substituting other technologies (which are now relatively more expensive for the cheaper one). Yet, the fall in the price of the forklift might reduce the remuneration of the producer of forklifts, even if demand increased, since the increase in the quantity sold might very well be trumped by the effect of a lower price. Also, and more importantly for us, the decrease in the price of forklifts might lead to a reduction in the demand for forklifts. This could be the case, for instance, if the decrease in the price of forklifts and lower remuneration reduces the forklift producers' demand for other goods, which are produced, in turn, using forklifts, leading to a lower demand for forklifts. The changes in the price of the forklift, and its remuneration, are not directly correlated to its relative use (how many forklifts are bought and used in production).

Note that the fact that forklifts are produced by means of forklifts, is central to this perverse effect (the absence of any discussion of re-switching in Robert's discussion of the capital debates is telling). Here it is also worth understanding why Sraffa used the old classical and Marxist terminology of means of production rather than factors of production. A means of production is produced (like the forklift) by using means of production (including forklifts). Robert is actually utilizing the notion of a factor of production, even though he uses emptily the same terminology as Sraffians (means of production), which means that the impact of the production on capital goods (forklifts) on the production of capital goods is actually ignored.

Further, Robert does NOT deny that supply and demand determine prices and by substitution lead to allocation of resources (which makes him, and all Austrians, marginalist).* He seems just to be suggesting that a monetary rate of interest might be at some point different than the rate of remuneration of forklifts.** And it sure can. However, there must be some reason, for an agent not to invest in forklifts if the remuneration is higher than the monetary rate of interest. With free entry, and using Robert's conventional (Austrian) supply and demand logic, the entry should bring prices down, univocally lead to more demand for forklifts and equalize the marginal productivity of the forklifts and remuneration to the natural rate of interest.

Note that this opens up the question of the time preference, the other leg in Loanable Funds Theory of the rate of interest. Assume that you start from a situation in which the rate of return on forklifts is the same as the monetary rate of interest. Now assume that for some reason (Robert would say a change in intertemporal consumer preferences) the monetary rate of interest changed. Then, all of a sudden the demand for forklifts should increase, and the prices of forklifts go up, reducing its remuneration to the new equilibrium. This is when Nick's post comes in handy (again, link here).

Nick shows a very conventional story of the Loanable Funds Theory. On the one hand, we have the conventional Production Possibilities Frontier (PPF, in red), which shows how much more consumption in the future can be obtained by using less resources to produce consumption goods in the present. That is basically the marginal productivity story, in this case with the traditional neoclassical assumption of marginal diminishing returns, since the technology only allows for more consumption tomorrow at a decreasing rate (graph from Nick's post).

On the other hand, you have the indifference curve (in blue) and its slope represents the marginal intertemporal rate of substitution, which gives you how much economic agents are willing to part with consumption today in order to obtain more consumption tomorrow. When the two curves are tangential, and the marginal productivity of capital equals the marginal rate of substitution you are in equilibrium. Two things are important to note here. The intertemporal notion used in this discussion, is not exactly the same as the intertemporal notion of equilibrium used in General Equilibrium models. Not only the notion of capital above is aggregative, but more relevantly, the individual capital goods, when they are considered, would have to obtain a long-term uniform rate of profit. In fact, Bhöm-Bawerk used this notion, which was then lifted by Wicksell and Fisher (cited by Nick).***

In addition, Nick suggests that the marginal productivity of capital is NOT necessary to determine the rate of interest, but the marginal rate of transformation at which we transform less consumption goods today into more tomorrow does. Actually this is an empty distinction, since the rate at which one investment good allows you to produce (transform) more consumption goods in the future is, essentially, its marginal productivity.

This is an old and well-known confusion by Bhöm-Böhm-Bawerk, who wanted to suggest that interest rates were not the remuneration of marginal productivity of capital. His solution revolved about the notion of roundaboutness of productive process, and it does not scape the notion that marginal productivity is still relevant in the Austrian framework, and Wicksell, as well as Fisher (and if I recall correctly even J.B. Clark was too) seemed to be aware of the limitations of Böhm-Bawerk's analysis (a full explanation would require another post).

In sum, this is another case of a mainstream author that does think that markets (supply and demand) determine prices efficiently, producing the correct allocation of resources (in this case capital) confused with his own theory (for a similar lack of understanding of his own neoclassical theory by Noah Smith go here). There is the added perversity of trying to use a critique of his own theory (the capital debates) to show that the theoretically challenged but politically progressive Piketty is wrong (he is, but that idea of wealth taxes is NOT the problem).

The lack of understanding of neoclassical economics by neoclassical economists is, not surprisingly, a result of their defeat in the capital debates, and the fragmentation of teaching thereafter, something that I referred to as the return of vulgar economics. It could be said that the mainstream graduate programs are now basically the production of confused economists by means of confused economists.

* Actually his argument against Piketty's tax is that it would distort prices, and hence the incentives for entrepreneurs to invest, being detrimental to growth. So there is a lot of faith in the powers of supply and demand to allocate resources efficiently.

** One wonders if Robert read the Hayek-Sraffa debate on own rates of interest, in which Hayek committed a similar mistake.

*** Again here there is a terrible confusion in Robert's understanding of the meaning of the intertemporal models, since the latter presume, inconsistently, that the notion of a uniform rate of profit can be abandoned. That's why the intertemporal General Equilibrium models remain short-term models. By the way, as shown in the graph above the determination of the rate of interest (1+r), which is the slope at the tangential point of the PPF and the indifference curve, is the natural rate and is open to the capital debates critique.

Nick Rowe's misconceptions about Sraffians II

As promised here are my additional responses to Nick Rowe’s assumptions (here) on the Sraffian or Cambridge UK side of the capital debates. I had agreed to comment also on assumptions 3 and 4, which stated that:

3. But they still couldn't explain the rate of interest. Because it's hard to explain the rate of interest if you don't want to talk about time preferences. And all the other prices depend on the rate of interest, as well as on technology. So they assumed the rate of interest was exogenous;

4. Some economists in Cambridge US made a very special assumption that let them explain the rate of interest without talking about time preferences. They assumed that there was only one good, and it could be converted back and forth between the consumption good and the capital good by waving a wand.

Before we get to why Sraffa argued that the rate of interest is exogenously determined by the monetary authority, let me discuss the neoclassical assumptions behind Nick’s proposition. I would argue that point 3 is exactly in reverse, that is, it is impossible (not hard) to explain the rate of interest on the basis of subjective preferences.

Böhm-Bawerk famously argued that there are three conditions for the determination of the rate of interest, namely: (1) the differences between wants and provision in different periods of time; (2) the systematic underestimation of future wants and the means available to satisfy them; and (3) the technical superiority of present compared with future goods of the same quality and quantity. The first two are related to subjective preferences, and are behind the supply of savings or abstinence from consumption, while the third is related to productivity. With both thriftiness and productivity one gets a version of the neoclassical loanable funds theory of the natural rate of interest.*

Note that the subjective basis for the determination of the rate of interest is incredibly shaky. The marginalist approach suggests that there is a positive rate of time preference, that is people prefer to consume now rather than latter, and are willing to part with consumption now in order to get more at some future date. That is why there must be a positive rate of interest to convince consumers to postpone the immediate fruition of pleasure. Yet it is far from clear that the positive time preference precedes the positive rate of interest. It seems rather more logical to assume that given a positive rate of interest some people might be willing to postpone consumption. The neoclassical subjective analysis is no more than a tautology with very dubious assumptions about causality, to say the least. It is hard to see why one could base a theory of interest on such uncertain foundations.

Remember that classical authors were very skeptical of subjective individual behavior. They actually referred to social utility when they talked about preferences. In that sense, Sraffa, not only thought that the foundations for subjective theories were unsound, but also from a methodological point of view were not particularly relevant. Interest rates were not positive because some individual preferred things now rather than latter, but they had an institutional foundation, associated to the fact that certain social groups could extract a surplus from society as a whole.

What about the productivity part of the marginalist/neoclassical argument? That’s the part that the capital debates disqualified, as was accepted by no other than Paul Samuelson. I’m not going to discuss the whole issue again, but it suffices to say that there is no logical way to determine the quantity of capital independently of the rate of interest, which implies circular reasoning.

Sraffa had determined very early in his investigation of the determination of relative prices, as early as his first equations in 1927 (with the help of Ramsey) that he could solve the system of simultaneous equations simply with the technical coefficients of production and an exogenous rate of interest (see DeVivo, 2003; subscription required). Sraffa after several changes and developments of his basic equations eventually settled (by the 1940s) on the notion that the rate of profit was determined exogenously by the monetary rate of interest (a proposition not unlike that of certain classical authors, in particular Thomas Tooke, and similar to Keynes idea of a conventional normal rate of interest in the General Theory), in the famous paragraph 44 of PCMC.

Note that classical authors for the most part assumed that the real wage was the exogenously determined distributive variable. The reasons for why Sraffa settled with a monetary theory of distribution require a different post. However, it should be clear that the exogenous rate of interest is not an arbitrary assumption as Nick suggests, but is required for the logical solution of the system of simultaneous equations (which demand the rate of profit to be determined independently of relative prices, something that the marginalist theory is unable to do in a system with a uniform rate of profit). Finally, the important part of the exogeneity of the rate of interest, besides the fact that it fits the historical/institutional framework of the capitalist economies that we live in, where central banks actually do determine the rate of interest, is that institutions play a role in the classical-Keynesian theory of distribution. As noted above, it is class and power that are behind a positive rate of interest and not you aunt's preferences for chocolate cake tomorrow.

Regarding point 4, there is an incredible confusion in the comment by Nick. Sraffa’s system never assumes any aggregate production or a one good economy. There is a composite commodity in the construction of the standard commodity and system, but production is a circular process. Even if it has similar properties as the Ricardian corn model, it is actually composed of several commodities. It is in fact the neoclassical theory, including the disaggregate Walrasian (in its Arrow-Debreu version) model, that requires a one commodity world to bring about the equilibrium of investment (the demand for a quantity of capital) to full employment savings. It is the marginalist theory of the natural rate of interest that lacks any logical foundation.

* Irving Fisher was critical of the limitations of Böhm-Bawerk’s theory even within the neoclassical paradigm. For the debate between them see Avi Cohen (2011).