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).

Nick Rowe's misconceptions about Sraffians I

Nick Rowe continues his very welcome discussion of the issues related to the capital debates in a recent post (see also the reply by Unlearning Economics). However, there are several misconceptions in his post that are worth clarifying. I'm going to deal with his first four assumptions (1 and 2 in this post, and 3 and 4 in a subsequent one), which are the more substantial from a theoretical point of view, namely:

1. Some economists in Cambridge UK wanted to explain prices without talking about preferences. I don't know why they didn't want to talk about preferences;

2. They made some special assumptions that helped them explain prices from technology alone, without talking about preferences. Like: all labour is identical; all technology is linear; prices never change over time;

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.

The Cambridge economists are, of course, Sraffa and his followers. First, one of the most frequent confusions about Sraffa was that he assumed that demand, and, as a result, preferences were irrelevant. Before I tackle the issue per se, it is worth quoting this phrase, brought to my attention in Robert Vienneau’s blog:

"I am sorry to have kept your MS so long - and with so little result. The fact is that your opening sentence is for me an obstacle which I am unable to get over. You write: 'It is a basic proposition of the Sraffa theory that prices are determined exclusively by the physical requirements of production and the social wage-profit division with consumers demand playing a purely passive role.' Never have I said this: certainly not in the two places to which you refer in your note 2. Nothing, in my view, could be more suicidal than to make such a statement. You are asking me to put my head on the block so that the first fool who comes along can cut it off neatly. Whatever you do, please do not represent me as saying such a thing." -- Piero Sraffa (1964). Letter to Arun Bose (italics added).

Clearly Sraffa says that demand plays a role. However, the role is not the same as in marginalist theory. One has to understand what role demand played in the surplus approach in the determination of relative prices to get what Sraffa is saying.

Classical authors, in particular Adam Smith and David Ricardo (and certainly not Marx), did not think in terms of individual utility. When they talk about utility they are referring to social utility. Hence, commodities to be produced must be socially useful, otherwise they would not be produced, since nobody would buy them, but their price, their exchange value, is not based or connected with their use value. For example, Smith in his discussion of the diamond/water paradox (Wealth of Nations, Book I, ch. IV) argues that things with a high use value often have little or no exchange value, since things that are not costly to produce will command no price, even if they are useful. It is only with Thomas De Quincey, after Ricardo and the demise of classical economics, that the notion that utility (and use value) had a functional relation to exchange value becomes entrenched in economics, an idea that was picked up by Stuart Mill, and through him by Marshall (marginalism or neoclassical economics), as it is well documented by Krishna Bharadwaj (subscription required).

As Bharadwaj says of the Quincey/Mill/Marshall notion:

"This was a different notion of use-value than that accepted by Smith and Ricardo, for whom use-value was a necessary condition for a commodity to possess in order to be an object of exchange, but referred to the physical properties socially known to belong to a commodity, and not dependent upon the individual's estimation of its capacity to gratify subjective inclinations, measured in quantitative terms. In fact, use-value and exchange-value were incomparable in so far as the former covered the qualitative aspect and the latter was a quantitative notion. In De Quincey and Mill, the two notions had become quantitatively comparable (one acting as an extreme limit upon another) and this was only a step towards the later resolution of the paradox in terms of 'total' and 'marginal' utility."

In other words, social utility not individual estimation is behind the classical notion of preferences. The point then is that social utility and, as a result, demand considerations are essential for the determination of long term prices. However, these preferences are not the subjective preferences of individuals, about which nothing scientific can be said, since there are no regularities and they can change for irrational and circumstantial reasons.

The utility that society attaches to a particular good, say a car, however, can be taken as given at a particular point in time. The reasons are not only directly connected to objective characteristics, like the fact that a car is a means of transportation or negatively that they worsen environmental conditions, but also that cars socially may be a source of status, as Veblen later suggested. In other words, preferences (and demand) are socially determined and taken as given for the determination of relative prices, but there is a role for historical and institutional analysis in understanding why and how demand and preferences change over time. The idea was, also, that social preferences are relatively slow to change, and for that reason one can take them as given.

Thus, in the surplus approach there is a role for historical/institutional analysis (not just social preferences, but income distribution too, e.g. the discussion of the determination of the exogenous real wage), and a different role for theoretical analysis (the determination of exchange value). Note that the assumption of given social preferences, as correctly noted by Unlearning Economics, can be seen as a ceteris paribus clause. So Nick is right that there is no reason not to talk about preferences. However, it is far from clear that knowledge has been advanced by the marginalist treatment of individual subjective preferences. As I noted in my comments to his post, the reasons for convex, homothetic preferences is not dictated by knowledge about a regularity about people’s behavior, but simply by the teleological need of finding a solution to the maximization problem. I would say rather that there is no reason to talk about individual preferences. Social utility is fine.

Point 2 is just a poorly built straw man of the Sraffian/surplus approach model. There is no assumption of a linear technology. In fact, that’s typical of the neoclassical aggregative models. The only situation in which a linear relation between wages and profits in the Sraffian model is in the case of the standard commodity [I still owe you all a post on that topic; didn't forget], if this is what Nick means by linearity, which would be the only relevant case (unless he is against input-output models). The input-output framework of any system in which production is done by using commodities to produce commodities (a feature of the real world, by the way), does not imply that there is no technical change either. Technical input-output coefficients can change.

Note that any theory has to say something about the determination of relative prices for a given technology anyway. By the way, in this case Sraffa assumes, like the classical authors, a given level of output (again is a ceteris paribus condition, and a different theory of the determination of output is needed; we know through Garegnani, Sraffa’s disciple, that effective demand is what Sraffa had in mind, and not some version of Say’s Law). That does not imply, hence, constant returns to scale, since that would require an increase in output proportional to the increase in inputs, something that cannot happen when output is given. Remember that output is given for the theory of long term prices only.

Finally, there is enough literature showing that one can reduce, theoretically speaking, labor of different qualities to a uniform type. It is ironic that a neoclassical author would complain about this, since the production function, which is beset with unfathomable problems, also assumes identical labor, and in fact it also assumes a unique capital good (not many means of production) and is fundamentally a world of only one commodity (on this and point 4 by Nick, more on the following post).

TO BE CONTINUED

Nick Rowe on Reswitching and the Capital Debates

Nick Rowe gives a shot to the capital debates, which is a nice development indeed. [Robert Vienneau has a lenghty reply here.] In spite of the importance of the topic, and the previous engaging of mainstream economists like Samuelson, Solow – to cite two prominent ones – the topic has all but vanished from modern mainstream economics, with a consequent loss of understanding.

Let me clarify a few things before we get to Nick’s post. As I argued in a previous post, classical authors (e.g. Smith, Ricardo and Marx) understood that they needed to determine the rate of profit independently from relative prices to avoid circular reasoning. The Labor Theory of Value (LTV) provided a solution. Prices were determined by labor incorporated (or commanded for Smith) and profits, and the surplus, were determined on that basis [Sraffa’s solution to the problems with the LTV build on Ricardo’s use of a commodity, corn, to measure the profit rate as a ratio of two physical quantities]. However, most neoclassical/marginalist authors today are completely oblivious to the fact that their theory too must deal with the independent determination of the rate of profit and relative prices, and that this is problematic if you also accept the notion of a uniform rate of profit (a natural rate of interest).

Also, and before I show why the problem is a general one, that any theory has to deal with it is essential to note that the rate of profit and the rate of interest must be in the proverbial long run (when everything is flexible and there is no ceteris paribus) in equilibrium. That is, either the rate of interest adjusts to the rate of profit (the position taken by Ricardo and Wicksell, which called the real variable the natural rate of interest), or vice versa (as Tooke and Sraffa believed; Marx and Keynes pose more problems to be clearly defined, but I would put them in this camp too).

In the case of neoclassical economics, if you want to determine the natural rate of interest by the interaction of the discounted profitability of investment and the intertemporal savings (i.e. consumption) decisions of agents, you must be able to bring the gains to present value (as in the examples provided by Nick). That means that the discount rate (to bring the investment schedule to present value) must be known, while the rate of interest you want to determine requires knowing the value of investment (the demand for capital goods). Thus, we encounter the circularity of the determination of the natural rate of interest in the Loanable Funds Theory, noted by Joan Robinson long ago.

Note also that the process implies that the rate of interest (which in equilibrium is equal to the rate of profit) is a variable that is determined by intertemporal decisions, which must equalize the rate of profit associated with the production of capital goods (i.e. produced means of production). What happens if, as Nick suggests, “There isn’t just one future period; there are many future periods.” Nothing much really happens, since for all those possible future periods, there must be a uniform rate of profit. For several different capital endowments, or several different sets of preferences (which seems to be what Nick has in mind), the interaction of investment and savings will solve for the rate of interest. But the inconsistency is still there.

But really what Nick is suggesting is that one might have a multitude of interest rates (which he refers to as the term structure, but think more of a term structure of interest rates associated with different capital goods, rather than financial ones, even if you do have monetary rates too). In fact, that is exactly what the mainstream did, when they changed the notion of equilibrium, as noted by Garegnani in his 1976 paper. It was only then, after the capital debates, that the Arrow-Debreu (AD; not Anno Domini) intertemporal general equilibrium notion became dominant. In that case you must give up the notion of a uniform rate of profit. Note that you cannot have both (in his replies to my comments Nick seems to believe that you can have it both ways; scroll down for the various comments which are worth reading I might add).

Nick says:

“I hadn't realised, until I read your comment just now, that *maybe*, when some people talk about “uniform rate of profit”, they mean something very different to what I thought they meant. I thought they meant: A uniform rate of profit across different industries (adjusting for or ignoring risk). But you seem to mean: A uniform rate of profit across different periods of time (i.e. a flat term structure). I would say that arbitrage is what creates a uniform rate of profit across different industries (or different assets). I would say that *nothing* creates a uniform rate of profit across different periods of time. The term structure is not (in general) flat. It could slope either up or down, or wiggle around. Even if we are talking about Wicksellian “natural” rates of interest. E.g., if everyone wants to go on a big consumption binge every 7 years, and fast for the remaining 6 years, (and if everyone knows about this), we are in general going to see a big spike in the term structure at 7 year terms.”

So let me clarify what I mean. Capital goods, the produced means of production, are an heterogeneous set of goods, but if one believes in competition (in the classical sense of free entry) then one must believe that a uniform rate of profit on the supply price of those goods will be established (not as a real world phenomena, but as a tendency; the long run is a theoretical construct). So what is established by free entry (and not arbitrage, which would be associated with the equalization of prices in an exchange economy) is a uniform rate of profit across sectors.

So what does that mean about the term structure? First, the term structure of monetary rates (i.e. the Fed Funds versus the ten year Treasury bonds) depends on the actions of the central bank, among other things (and I’ll let that for another post; mind you as you see I tend to think the monetary rates rule the roost, as Tooke and Sraffa). Nick is talking about the real or natural rate, having for reasons associated with the demand (the preferences about consumption in the future) different levels. That is, there would be more than one natural rate, associated with different preferences regarding consumption [echoes of the Sraffa-Hayek debate about the existence of several own rates of interest perhaps].

Yet, the point still is whether you have competition (free entry) or not. So if more people, as in Nick’s example, want to consume more in 7 years, wouldn’t the supply of capital adjust, to provide more in that year allowing for the consumption binge, and reduce the gains associated with providing more goods in that period? After all there is no reason for profitable opportunities, unless there are imperfections (e.g. lack of capital mobility or lack of information, which does not seem to be what Nick is arguing, since he says that "everybody knows"), to be left unfulfilled. The intertemporal nature of the decisions, meaning the decisions are being made now with all the information available about the future, does not affect the equalization of the rate of profit (interest). So competition should also lead to a uniform rate of profit not across different periods of time, but now for different states of preferences and the capital endowments (and technology of course).

Hence, the existence of a myriad of capital goods, or changing preferences (or technological change, which used to be the one that the capital debates concentrated more), do not per se justify abandoning the notion of a long term uniform rate of profit. That is what the AD model does. In the process it abandons the classical notion of competition (free entry) for one that has less meaning from the point of view of understanding capitalism (atomistic agents that are price takers; both links to the New Palgrave require subscription I'm afraid).

Note that the centrality of the results of the capital debates is that one cannot say that changes in relative prices govern decisions about the allocation of resources in any clear way. Not only capital will not be used more intensively with lower rates of interest (even if lower rates of interest may stimulate other forms of demand, not capital, and eventually lead to more demand for means of production), but also lower real wages (the relative price of labor force) might not lead to higher employment. Think of the policy implications of this result for Europe now.

But let me finish saying that beyond the differences we might have, real or of interpretation (and I think both things play a role), I think it is important to thank Nick for thinking about the relevance of these issues and taking them seriously, which can only lead to clarify differences and provide a better understanding, if not of the real world, about what economists think about the real world. And that is a step in the right direction.

Who holds the American public debt?

Just a clarification following up my comments on Nick Rowe's post.  Several people are under the impression that the Fed can still monetize debt if the debt-ceiling is not raised beyond the US$ 14.3 trillion limit.  Not the case. Otherwise there would be no default by definition.  There might have been some problems associated with monetization, but not default (see more about monetization here).

Of the US$ 14 trillion of debt outstanding by December 2010, around US$ 5.6 were held by the Fed and other intra-government agencies (Fed holds around US$ 1.6; see Dean Baker's proposal and discussion here).  So if the Fed buys debt, to monetize it, it just reduces the privately held part of the debt and increases the publicly held, but it cannot increase the total amount.  The graph below shows the public, private, and the foreign (within the private) held shares of US public debt.

As you can see, since the Great Recession, the private share increased from around 50% to close to 60%, and of that the increase has been mostly associated to foreign ownership.  So apparently nobody has been worried (correctly so) about the possibility of an American default.  In fact, since the crisis Treasuries have been increasingly a demanded asset by the private sector, particularly foreign investors, as a safe heaven against the risk of default (data here).  The problem is that the debt-ceiling limit creates a situation which would otherwise be impossible, namely: the US can default on bonds issued in its own currency.

Well understood what the debt-ceiling limit implies is a fiscal restriction, and it would force drastic cuts in spending.  Consider it a very large government shutdown.  So in reply to Nick, if you are Keynesian, and believe your model, this is really bad news.