Thursday, June 12, 2014

Colin Rogers’ Money, Interest and Capital, Chapter 2

Chapter 2 of Colin Rogers’ Money, Interest and Capital deals with Wicksell’s monetary theory.

Wicksellian monetary theory was widely accepted in the period before Keynes’ General Theory, and indeed Keynes himself accepted the natural rate of interest in the Treatise on Money.

The real natural rate of interest lies at the heart of Wicksell’s version of loanable funds theory, and links Wicksell’s capital theory with his monetary theory (Rogers 1989: 22). Wicksell’s monetary theory was an attempt to extend the quantity theory to an economy with credit money and loans (Rogers 1989: 23).

Wicksell’s theory of capital was in turn developed from the work of Jevons and Böhm-Bawerk (Rogers 1989: 27).

The concept of capital can be divided into two ideas:
(1) real capital, or the physical goods themselves, e.g., machines, tools, or raw materials, or

(2) capital defined in terms of a sum of exchange value (or in monetary terms). (Rogers 1989: 27).
Real capital in sense (1) can be measured in technical units, but that would mean that there would be as many technical units as there are types of capital goods (Rogers 1989: 28).

But in order to calculate the rate of interest (the return on capital), capital has to be measured in monetary terms.

Rogers continues:
“Apart from pointing out the technical necessity of defining capital in value terms, Wicksell also suggests that it is necessary for theoretical reasons; namely, that in equilibrium the rate of interest must be the same on all capital. This condition is, of course, the classical condition of long-period equilibrium defined in terms of a uniform rate of return on all assets. It is the notion of equilibrium employed by Wicksell to define the natural rate of interest. To define such an equilibrium, however, capital must be treated as a mobile homogeneous entity so that it may move between sectors to equalize the rate of interest/profit. Capital defined as value capital (financial capital) can fulfil this role but capital defined in technical or quantity terms cannot.” (Rogers 1989: 28).
Wicksell consequently argued that all capital goods can be regarded as “saved up labour and land” (Rogers 1989: 29).

When the money rate of interest at which demand for investment credit and the monetary supply of savings is equal, there is a monetary equilibrium rate. And, when this monetary equilibrium rate is also equivalent to the expected yield on new capital, then the money rate of interest and the real Wicksellian natural rate of interest are equal (Rogers 1989: 39).

Rogers argues that the Cambridge capital critique applies to Wicksell’s theory of capital, and that it has proven that Wicksell’s natural rate of interest is untenable outside a purely abstract one-commodity world (Rogers 1989: 22).

Rogers reviews the Cambridge capital controversy (Rogers 1989: 30–39), and notes the problems with the aggregative (Wicksellian) neoclassical production function (Rogers 1989: 30–32).

In essence, the major issues raised by the Cambridge Capital controversy relevant here are as follows:
(1) the problems with the treatment of capital in the neoclassical production function Q = f(K,L), and the circularity involved in defining the quantity of capital K, when to determine K one needs to know the rate of interest, but to determine the rate of interest one needs to know the value of capital K (Rogers 1989: 31). The upshot is that K cannot be an exogenous variable in the production function.

(2) it is not possible, as noted above, to define the Wicksellian natural rate outside of a one commodity world (Rogers 1989: 32);

(3) the issue of reverse capital deepening, and

(4) capital reswitching (Rogers 1989: 32).
Rogers points to three modern neoclassical responses to the Cambridge capital controversy, as follows:
(1) those neoclassical economists who accept the critique and use an alternative neo-Walrasian analysis for general equilibrium theory that is not subject to the Cambridge capital critique, but that nevertheless has insolvable problems of its own (Rogers 1989: 34–35);

(2) those neoclassical economists who use a methodological defence of the neoclassical production function and Wicksellian general equilibrium theory applied to a one commodity world, which is supposed to be a useful pedagogical tool or “parable” teaching fundamental ideas of neoclassical interest theory, although it is untrue that such an unrealistic and empirically irrelevant model has any great lessons to teach (Rogers 1989: 34).

(3) those neoclassical economists who simply accept the neoclassical production function “on faith” (Rogers 1989: 33, n. 7).
Now the Classical loanable funds model of interest is supposed to relate how interest in a monetary economy still reflects the real forces of productivity and thrift (Rogers 1989: 40).

But in a monetary economy the act of saving money does not necessarily reflect real saving (Rogers 1989: 42).

The only viable model in which the Wicksellian neoclassical interest theory is possible is one which assumes a one commodity world where that single commodity can function either a capital good or a consumption good (Rogers 1989: 32, n. 6).

The natural rate can only be defined in a one commodity world, but not in a world with heterogeneous capital goods (Rogers 1989: 32, 43). The consequence is that only the monetary rate of interest in the loanable funds model is left after the untenable natural rate is cut out, and that the money rate of interest is cut free of the real forces of productivity and thrift (Rogers 1989: 43).

BIBLIOGRAPHY
Rogers, C. 1989. Money, Interest and Capital: A Study in the Foundations of Monetary Theory. Cambridge University Press, Cambridge.

29 comments:

  1. "and the circularity involved in defining the quantity of capital K, when to determine K one needs to know the rate of interest, but to determine the rate of interest one needs to know the value of capital K"

    I really, really hate the terms "rate of interest" and "rate of profit" because they are so badly defined.

    You forgot a third option. (there's always a third option) namely to define capital K (in the aggregate) as the sum total of nominal spending or NGDP, versus a one capital good model of marginal productivity. What exactly is the problem here? |;-) |-O

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    1. "
      You forgot a third option. (there's always a third option) namely to define capital K (in the aggregate) as the sum total of nominal spending or NGDP, versus a one capital good model of marginal productivity. What exactly is the problem here?"

      HAHAHAHAHAHAHAHAHAHA!

      No, I'm sorry... I shouldn't...

      HAHAHAHAHAHAHAHAHAHA!

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  2. One could also take "the rate of interest" to be the exogenous central bank driven rate, and measure capital that way

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    1. Oh... good GOD... OH GOOD GOD!

      Where are you getting these commenters, LK? Because they don't strike me as Austrians but my Lord are they as poorly informed and theoretically inept as Austrians.

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    2. I believe "Edward" is some type of market monetarist advocate.

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    3. Oh yeah, those guys are theoretically inept.

      He also thinks that you can solve the Cambridge controversies by using NGDP measures and the overnight rate of interest.

      Ten years. Two Nobel Prizewinners. At least a handful of the most prominent economists of the mid-century. And none of them ever said to themselves: "Jeez guys, couldn't we just use NGDP and the Fed funds rate?"

      Really? REALLY? Does he really believe this? Because if I were him I would probably say: "Hmm... it looks like some prominent figures were involved in this debate and it had controversial results. I should probably assume that they considered using NGDP and the Fed funds rate as measures and shut my trap on this issue."

      But that's just me...

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  3. From the previous post:

    "since stock and options as % of CEO compensation were minor, the low tax rate on capital gains hardly refutes anything I said. "

    The booming u.s. stock market in the 1960's means a high rate of return on stock options for ceos even though total initial percentage compensation (in the form of stock options was low. . Besides like I said before there were other schemes available for the rich in the U.S. to lower their total tax burdens

    ""they illustrate an important point, namely, that the power of the rich is not absolute. "

    And since nobody said they have "absolute" powers, yet another straw man.

    Sigh. I acknowledged these were two ANECDOTES. I could probably find more evidence if I searched harder but I'm too lazy. :-) Besides, leftists complain about the rich so much they MIGHT AS WELL be saying that the rich control everything.

    "no, edward, spending of the rich on secondary financial asset markets has very different effects from spending on final goods and services."

    No LK, :-) the secondary market is an important source of funds (401K's retirement accounts) for many people. Even people who aren't directly invested are INDIRECTLY exposed (since pension funds look for returns) Unlike cash its possible to make a nominal profit by investing in stocks. And with the push of a button, funds can be liquidated and placed into checking accounts available to spend for consumption.
    So, wrong again.

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  4. Philip Pilkington:
    Laugh it up, Mr. Condescending, you really have nothing to say
    :-)

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  5. http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/05/mrscc1r1mpkmrtcidmrtcidt.html
    From a fellow market monetarist:
    "Or, we could even say that the central bank determines r, which in turn determines both the expected growth rate of consumption and the prices of capital goods."

    Philip you are arguing from authority. I COULDN'T CARE LESS ABOUT AUTHORITY. (In itself) The rightness or wrongness of an argument doesn't depend on where it comes from

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    1. You are one of those "economists" who proudly parades your lack of understanding of economic theory. You are an embarrassment to a profession that is not difficult to embarrass.

      You intervene in debates that you have not studied and do not understand. That makes you a charlatan. And you must know it at some level. Because you do know that you have not read up on this debate. So, you must know at some level that you're faking it. Admit it to yourself. Please. Spare the rest of us the energy of responding to you. Thanks.

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  6. Besides, its likely that Sraffa and Robinson were so ideological and single minded and trying to dismiss the MPC as determining the economy wide "interest rate" that they never even considered neoclassical "tweaks" to the model.

    And Philip, why shouldn't we use the overnight rate to to measure the sum monetary total. It completely evades the circularity problem

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    1. "And Philip, why shouldn't we use the overnight rate to to measure the sum monetary total. It completely evades the circularity problem."

      There is no point in even responding to this. It indicates that you are so ignorant of the discussion taking place that giving you a response would be pointless. It would be like trying to teach differential calculus to a five year old still unable to do addition.

      I'll chalk this one up under the "not even wrong" heading.

      http://en.wikipedia.org/wiki/Not_even_wrong

      Delete
  7. "You are one of those "economists" who proudly parades your lack of understanding of economic theory. You are an embarrassment to a profession that is not difficult to embarrass.

    You intervene in debates that you have not studied and do not understand. That makes you a charlatan. And you must know it at some level. Because you do know that you have not read up on this debate. So, you must know at some level that you're faking it. Admit it to yourself. Please. Spare the rest of us the energy of responding to you. Thanks."

    "There is no point in even responding to this. It indicates that you are so ignorant of the discussion taking place that giving you a response would be pointless. It would be like trying to teach differential calculus to a five year old still unable to do addition.

    I'll chalk this one up under the "not even wrong" heading."

    Ad hominems are a sign of someone who's lost the debate.. Pray tell, what books should i read that are so informative? I'm always open to learning more.

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    1. First, read up on the difference between the natural and the money rate of interest. This short FRBSF article will clear up the errors that you have already made:

      http://www.frbsf.org/economic-research/publications/economic-letter/2003/october/the-natural-rate-of-interest/

      That will explain the difference between the natural and the money rate. To understand how the two rates function in economic theory you can read either Wicksell's "Interest and Prices" or Keynes' "Treatise on Money". (They are both tough reads though...).

      As far as capital aggregation goes there is so much literature on this that I don't know where to start. Maybe the paper that started the debate?

      http://theme.univ-paris1.fr/M1/hpe/HPEM1-TD4.pdf

      That will at least give you an idea of the technical versus financial measures (hint: the national account measures are financial and NGDP doesn't measure capital it measures income. The NIPA financial measure of capital is 'Gross Capital Formation'.)

      Also, stay away from Nick Rowe on these issues. He's incoherent like he is on most issues that are not included in macro textbooks.

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    2. I should add that the FRBSF letter is not actually a good theoretical definition of the natural rate. Rather it is a definition that is used to calculate the estimates of this natural rate. However, it will at least show you why you cannot use the Fed funds rate.

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  8. Could you expand about what would be the problem with disaggregated general equilibrium models?

    Because while it's true that in Arrow-Debreu GE model with multiple capital goods one could have different interest rates for each good, expressed in its own units (e.g. rate between tractors now and next year in terms of tractors), all these interest rates expressed in common numeraire (e.g. in terms of consumption good) would have to be equal in order to prevent arbitrage. To define "natural" rate one would still need to choose the numeraire, but that's seems to me a different problem than the one alluded in your post.

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    1. Rogers presents the problem with the natural rate somewhat differently than Sraffa did, but both critiques -- Sraffa's and Roger's do -- indeed show how the natural rate is impossible to define outside a one commodity world.

      I've written a great deal on the natural rate:

      http://socialdemocracy21stcentury.blogspot.com/2013/02/the-natural-rate-of-interest-in-abct.html

      http://socialdemocracy21stcentury.blogspot.com/2011/12/hayeks-natural-rate-on-capital-goods.html

      http://socialdemocracy21stcentury.blogspot.com/2011/07/robert-p-murphy-on-sraffa-hayek-debate.html

      http://socialdemocracy21stcentury.blogspot.com/2011/06/natural-rate-of-interest-wicksellian.html

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    2. The critiques were addressed to the production functions of the 1960s. They were not addressed to the GE constructions which were, in part, taken up in response to the Capital Controversies (see: Frank Hahn etc.). Garegnani is convinced that he has found the same problems in the GE constructions but I've never been interested in the argument.

      The typical Post-Keynesian position on GE models is that they are so abstract that they don't have any meaning for the real economy (again, Hahn states this explicitly in his famous Cambridge lecture). Meanwhile, the production function is thought to be a "real world" model in that it is often applied and estimated.

      If you are interested in the GE games you might look into the literature on it. To me, and most practical economists, the GE games cannot be taken seriously on their own terms. They are mathematical games. Not economic models.

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    3. Here is a paper that seems to deal with this (rather boring, in my opinion) side of the debate:

      http://host.uniroma3.it/eventi/sraffaconference2010/abstracts/pp_gram.pdf

      It should also be said that the GE models are famously internally inconsistent because of the Sonnenschein-Mantel-Debreu theorem. Or, what might be called: income effects.

      I still feel that when we get to this level of abstraction, however, we're really going off the deep-end into la-la-land. Solow's famous quip on Napoleon seems apt here.

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    4. ivansml seems right to me.

      Let's take a standard GE model. Now assume constant returns to scale. Now assume that model is in very long run equilibrium stationary state, where all relative prices are constant over time. The economy is reproducing itself.

      How is that model any different from a Sraffian model?

      But it seems to me that that model is even more vulnerable to the charge: "To me, and most practical economists, the GE games cannot be taken seriously on their own terms. They are mathematical games. Not economic models."

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    5. Nick,

      You've just fallen into that awful trap that economists so often do. "But if the models produce the same results then surely they must be identical...".

      http://fixingtheeconomists.wordpress.com/2014/04/29/the-sraffian-versus-the-marginalist-worldview-a-strong-case-for-academic-pluralism/

      Only economists fall into this trap. And it is characteristic of the (homogenous) clone mode of thinking that the profession promotes. It really needs to be done away with.

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    6. Sraffa's model is not built to be empirically applied. It is a high-level abstraction like the GE models. If you want something approaching an applicable model that takes non-marginalist distribution seriously you look to the Cambridge models. Kalecki, Robinson, Kaldor and so on.

      These are far more realistic than there marginalist counterparts. Because in the real world distribution is set prior to the setting of prices. Distribution is fundamental. And distribution is set in line with relative social power (as EVERY social science apart from economics recognises...):

      http://s1.epi.org/m/?src=http://www.epi.org/files/2012/snapshot-unionmembership.png&w=608

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  9. LK: I disagree with Colin on this.

    "Natural rates" are a theoretical construct. Like all theoretical constructs, they only make sense within a particular class of models. In this case, the class of models where money is, in some "long run" sense, neutral and super-neutral. (If for example, a permanent increase in the growth rate of the money supply caused real variables to change permanently, it would not make sense to talk about "natural rates" in such a model.)

    Within that class of models, we can define a 'natural rate" for any real variable. We can talk about the natural rate of output, or employment, or unemployment, or real wages, or real rates of interest.

    If there are two types of labour, there will be two natural rates of real wages, one for each type of labour.

    If there are two goods (apples and bananas) there will be two natural rates of interest: the nominal rate minus the inflation rate on apples; the nominal rate minus the inflation rate on bananas. Only if apples and bananas have the same inflation rate (so the relative price of apples and bananas does not change over time) will those two natural rates be the same.

    But the fact that those two real rates of interest may be different does not mean that it is more profitable to buy forward contracts in apples than forward contracts in bananas. What you gain in a higher real interest rate you lose through a falling relative price. Similarly it does not mean it is more profitable to invest in apple trees than banana trees.

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    1. Natural rates are needed to make the theoretical case that monetary policy alone can steer the economy. And this is indeed believed today by most monetary authorities.

      http://www.frbsf.org/economic-research/publications/economic-letter/2003/october/the-natural-rate-of-interest/

      But the natural rate, for a wide variety of reasons, does not exist. You yourself seem to recognise this (utilising the very early Sraffa criticism). But there are far more cogent criticisms than the early Sraffa criticism.

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    2. Philip: suppose an (Austrian) economists said: "The central bank should set the nominal rate of interest equal to *the* natural rate of interest."

      It would be quite appropriate to say, like Sraffa, "*Which* natural rate of interest?"

      It would be like a New Keynesian economist saying that the central bank should target 2% inflation, but not say whether he is talking about the inflation rate on apples, bananas, or on a bundle of one apple + one banana.

      But New Keynesian/Neo Wicksellian economists *do* say what inflation rate they want to target. (Normally it's the CPI bundle.) So when they talk about "*the* natural rate of interest", we should interpret them as implicitly talking about the natural rate of interest on that same bundle.

      There are indeed other problems with natural rates. (And no theoretical constructs, strictly speaking, "exist".) But this one isn't a problem.

      I have read (skimmed) the FRBSF letter you linked. Simple standard NK stuff. But I don't see him saying what you say he says. Yes, they find it a useful concept for implementing monetary policy (I disagree) but he does not say that "Natural rates are needed to make the theoretical case that monetary policy alone can steer the economy."

      It is easy to build a macro model where money is not superneutral (where the money growth rate affects long run equilibrium real interest rates) so natural rates do not exist, but where monetary policy alone can steer the economy. Actually, in such a model monetary policy would have *more* power to steer the economy than in a similar model where money was neutral and superneutral. Simply because monetary policy would then have real effects, even if fully anticipated.

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    3. But of course you can construct a model where money is non-neutral in the short run but neutral in the long run, but the question is: how realistic is such a model?

      I assume you are aware of the Post Keynesian critique of such models: that money can never be neutral in either the short or long run, and that economies do not have any necessary or reliable tendency to general equilibrium.

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    4. LK: Yep, I am aware of criticisms of long run neutrality. I make them myself sometimes. If I thought that monetary policy was really neutral, in all respects, I would stop caring about monetary policy. If it doesn't affect real variables, and only nominal variables, it doesn't matter.

      Whether or not economies have any reliable tendency towards general equilibrium depends on the sort of monetary policy being followed. That's another way of saying that monetary policy matters.

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    5. But Nick, that's why I stated quite clearly:

      "...there are far more cogent criticisms than the early Sraffa criticism..."

      Sraffa's criticism was aimed at a very specific abstract model (Hayek's). When you take his criticism into account the model falls apart. That means that, even if you target CPI, you cannot logically prove that you may be able to stabilise prices through monetary policy alone.

      But, again, there are better ways to show this. At the end of the day you cannot logically prove this. And so the reliance on monetary policy by the New Consensus macro-guys (who, I believe, you are part of) is a wholly faith-based endeavour. A good, solid logically coherent story is not provided for why this should work and instead it is simply asserted that it should work. That's not Science. That is Religion.

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  10. I'm impressed you have picked up on Roger's book. I thought it had vanished into the sink of "great but sadly neglected books". I read it as an undergraduate. Helped resolve a lot of puzzles.

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