Debunking Economics, Part V: The Holy War Over Capital

There are probably few criticisms of neoclassical economics that have been both so universally acknowledged to be valid, and yet so completely ignored, as the Cambridge Capital Controversy (CCC). Chapter 7 of Steve Keen’s Debunking Economics provides an overview of this debate about the nature of capital.

Basic economic analysis teaches that capital, like other factors of production, is paid in proportion to its productivity – the so called ‘Marginal Product of Capital (MPC),’ which is presumed to be equal to the rate of profit. Keen gives two good criticisms before he delves fully into the CCC:

First, the MPC assumes that other factor inputs are fixed when capital is employed, which leads to our first problem: since capital is (rightly) assumed to be the least variable input, any time period in which you can employ more capital is surely one in which you can employ more labour, too? Once again we are forced to face the reality that firms tend to vary all inputs employed at once.

Second, in an industry as broadly defined as ‘the capital market’ we run into familiar Ceteris Paribus problems, where varying inputs will create effects on wages and the existing capital stock that alter the rate of profit. For small and medium sized firms these effects will be negligible, but when analysing the biggest firms and entire industries the feedback between them will create collateral effects that undermine partial equilibrium methodology.

However, even ignoring these criticisms, there are serious issues with the neoclassical treatment of capital.

Capital is often measured in units. There are obvious problems with this: capital includes brooms, blast furnaces, buckets, string and potentially any commodity you care to think of, so a single unit of measurement is difficult to justify. Generally economists either leave capital in undefined units or measure it by price. The former treatment does not deserve to be criticised formally – something that poorly defined is, like utility, Not Even Wrong. As for the latter, Keen notes that there is an “obvious circularity” to the definition. The value of capital is based on the expected profit from it, which is partly based on the price of capital. Thus the use of price as a unit of measurement is not particularly enlightening.

Piero Sraffa’s Devastating Critique of the Neoclassical Treatment of Capital

As always, Piero Sraffa offered the most fully fleshed out and devastating critique of the neoclassical theory.

Sraffa proposed that, instead of treating one factor of production as a mysterious substance called ‘capital,’ we instead supposed that goods produce other goods, when combined with labour (hence the title of his Magnum Opus, Production of Commodities by Means of Commodities). He rigorously derived an internally consistent model with the sole aim of invalidating neoclassical economics on its own terms. There is some debate about the empirical applicability of his conclusions, but logic is sufficient to invalidate the neoclassical theories, which are based on the same premises.

Sraffa builds up a complex model step by step, starting simple. In the first statement of the model, there are a few firms, whose only inputs are the goods produced by other firms and themselves.  So firm A needs a certain amount of commodities x, y and z to produce commodity x, whilst firm B needs a different combination to produce commodity y, and firm C a different combination to produce commodity z. Each firm produces just enough of their respective commodities for economy-wide production to continue at the same level in the next period. Sraffa’s next step is to alter the model so that each firm produces more than they need to in order to continue production – a profit.

The first conclusion he comes to is that the relative production of factor inputs,and the rate of profit, is not based on supply and demand, but on ‘the conditions of production’ – the amount of inputs required to keep a firm or industry going.

Sraffa then explicitly incorporates labour into his model. He notes that wages are obviously an inverse function of profit: the higher they are, the lower profit will have to be, and vice versa. He then proposes a new method of measuring capital: treat it as the dated value of the labour required to produce it (wages), plus the profit made from it since it was produced, plus the value of the commodity that was combined with the labour to produce it. This ‘residual commodity’ can then be further reduced to labour times profit, plus another commodity, and so forth:

commodity a = ((labour input at time x)*((1+rate of profit)^(time periods since time x))) + commodity b

As Sraffa himself points out, there will always be residual commodity left out if you break down a commodity into the labour and commodity required to create it. However, as you do this again and again, the resultant term becomes smaller and smaller until it can be negated. This type of reasoning is far more scientific than the neoclassical approach and actually closely resembles the perturbation methods used by mathematicians and engineers, where a function is split into an infinite amount of terms of decreasing value, but only the first few are used in calculations.

In the equation above, there are two competing effects: profits and wages. As one rises, the other must decrease. It is easy to see in this in equation that there is a peak value for capital somewhere in the middle; either side of this the reduction in one term will overwhelm the other and the measured value of capital will decrease.

This creates an interesting phenomenon known as capital reswitching. Consider two production techniques, A and B, which involve inputting different amounts of labour at different times – a common example is creating wine through ageing it (A) or through a chemical process (B). A requires more labour input in the distant past; B requires more labour input in the near past. At a zero rate of profit, both techniques are identical. As the rate of profit rises, technique A, which relies on more distant, fewer labour inputs, will remain cheaper and therefore more viable. However, as the effect of the rising rate of profit compounds due to the time delay, technique A will become more and more expensive, and technique B will take over.*

The point of this approach is to show a few things:

(1) The value of capital varies depending on the rate of profit, as the rate of profit is a variable in the equation for measuring capital. Since the measured amount of capital depends on the rate of profit, profit cannot simply be said to be the ‘Marginal Product of Capital.’

(2) There is no easy to discern relationship between profitability and the amount of capital employed. Generally, neoclassical economics teaches that output is simply a concave but increasing function of the amount of capital employed, much like any other demand/utility curve. Capital reswitching destroys this idea.

(3) We cannot calculate prices without first knowing the distribution between wages and profits. The measured price of inputs depends on income distribution, not the other way round.

Many might be struck by the sheer level of abstraction in Sraffa’s approach. It’s worth noting that in Commodities, he adds many more levels of realism past those that Keen explores. But, as I said before, the basic point was taking on neoclassicism with its own logic, rather than presenting an alternative. By the end of the debate, Samuelson and Solow had both conceded that the criticisms were valid, and their models were wrong or incomplete.

Discussions of the CCC since then have tended to assume the standard neoclassical tactic of asserting the objections have been incorporated. But this stuff was 50 years ago. Why do undergraduate and postgraduate programs still teach concepts like the MPC? The Solow-Swan growth model, which depends on an aggregated capital stock K, subject to diminishing returns? As Robert Vienneau says, if neoclassicism were really revising itself to the extent that’s needed, we’d expect some of the modifications to filter down over time. But the fact is that they haven’t.

In fact, what seems to have happened is that economists have done a fairly typical dance – weaving between ‘that is unimportant’ and ‘that has been incorporated:’

Aggregative models were deployed for the purposes of teaching and policymaking, while the Arrow-Debreu model became the retreat of neoclassical authors when questioned about the logical consistency of their models. In this response, a harsh tradeoff between logical consistency and relevance was cultivated in the very core of mainstream economics.

This sort of evasiveness is common – there will always be a paper written recently that attempts to shoehorn any objection one cares to think of into the neoclassical paradigm. But these objections are incorporated one at a time, rarely find their way into the core teachings, and never involve questioning the foundations of neoclassicism on any substantive level. The reality is that, when the problems are as deep as the ones highlighted in the CCC, we need a meaningful overhaul rather than mere ad-hoc modifications.

*For those interested, the linked Wikipedia article has a fairly simple numerical example where the most effective method goes from A to B and back to A again.

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  1. #1 by ivansml on July 26, 2012 - 4:36 pm

    Neoclassical paradigm can work with heterogeneous capital just as well – simply measure each good in its own physical units, with its own price and with separate argument in the production function. It’s true that some results from single-capital models may not hold generally with multiple capitals goods (in fact, my copy of Mas-Colell says so in section 20.E) – so what? Consumer theory cannot rule out Giffen goods either – does that constitute “devastating critique” of downward-sloping demand curves?

    Of course not. We still consider downward-sloping demand as a reasonable assumption in most situations. Maybe it’s the case that reswitching does happen in reality, in which case we should spend more time building models with heterogeneous capital, thinking about functional forms of production functions, estimating their parameters etc. But that is an empirical question and should be argued as such.

    PS: I’m not familiar with Sraffa’s critique, but what you describe sounds simply as a sum of geometric series, not perturbation. Actual perturbation methods are sometimes used in economics, e.g. for solving functional equations arising from DSGE models. But of course, just because a method is “used by mathematicans and engineers” doesn’t make its application in economics any more or less “scientific”.

    • #2 by Unlearningecon on July 26, 2012 - 10:33 pm

      Neoclassical paradigm can work with heterogeneous capital just as well – simply measure each good in its own physical units

      What is the usefulness of this approach? Strikes me that it faces immediate consistency problems: one apple is bigger than another, different blast furnaces work differently, etc.

      It’s true that some results from single-capital models may not hold generally with multiple capitals goods (in fact, my copy of Mas-Colell says so in section 20.E) – so what?

      That’s not the point of the critique at all! Even in a single capital model the criticisms about measurement will still apply. Neoclassical economists generally interpret the problem as just to do with aggregation, but it isn’t. And ‘so what?’ So half the models taught in economics are incoherent!

      Consumer theory cannot rule out Giffen goods either – does that constitute “devastating critique” of downward-sloping demand curves?

      Giffen goods are an issue, but no, they are not in the same category as showing the fundamental treatment of capital is incoherent.

      Maybe it’s the case that reswitching does happen in reality, in which case we should spend more time building models with heterogeneous capital, thinking about functional forms of production functions, estimating their parameters etc. But that is an empirical question and should be argued as such.

      As I said, the whole point of Sraffa’s approach was to take neoclassicism on by its own logic. That it is a theoretical possibility is sufficient to invalidate the core tenets of neoclassical capital theory – Samuelson himself admitted as much.

      But of course, just because a method is “used by mathematicans and engineers” doesn’t make its application in economics any more or less “scientific”.

      Well mathematicians and engineers have a far better record than economists. And the point was more that negating a small term is a more scientific assumption than, say, homogeneity or perfect knowledge.

  2. #3 by Ben Brennan on July 26, 2012 - 8:15 pm

    @ivansml But you’re missing the key point – which is that one firm’s capital input is another firm’s commodity they sell in the market place. This has constantly destabilizing effects on the system.

  3. #4 by ivansml on July 26, 2012 - 10:51 pm

    @Ben Brennan:
    Which is exactly why Arrow, Debreu and others gave us general equilibrium theory. Whether there are some destabilizing effects (how would they look like, exactly?) will depend on details of particular model (technologies, preferences, endowments).

    @Unlearningecon
    In a model with single capital, there is just that – a single capital good that can be measured in its own units. I don’t see what the problem is. Yeah, in applied work we often pretend that this single good can be replaced by value of all capital goods in the economy, which leads to aggregation issues that you mentioned. But that doesn’t mean that the original single-good model was incoherent.

    I think that Giffen good is a relevant analogy – if you insist that CCC somehow proves _logical_ flaws and incoherencies in neoclassical theory, then same argument must hold for consumer theory. I mean, pretty much every supply-and-demand picture shown to undergrads has downward-sloping demand curve, which is invalidated (is it?) by logical possibility of Giffen good.

    • #5 by Robert on July 27, 2012 - 1:40 am

      I have run into many economists online who are clearly ignorant of the arguments put forth in the CCC, price theory, the literature in capital theory, etc., who yet think they have a response. In some sense, this is not puzzling – many people clearly have no interest in whether their statements are true or false. In another sense, it is a problem for the sociology of “knowledge”, the history of economics, and related fields.

    • #6 by Unlearningecon on July 27, 2012 - 5:37 am

      Ivan I appreciate your comments but you really need to read this more carefully. E.g.:

      Which is exactly why Arrow, Debreu and others gave us general equilibrium theory. Whether there are some destabilizing effects (how would they look like, exactly?) will depend on details of particular model (technologies, preferences, endowments).

      From the post, quoted from this Naked Keynes article:

      Aggregative models were deployed for the purposes of teaching and policymaking, while the Arrow-Debreu model became the retreat of neoclassical authors when questioned about the logical consistency of their models. In this response, a harsh tradeoff between logical consistency and relevance was cultivated in the very core of mainstream economics.

      Arrow-Debreu obviously has its own problems. But you can’t cling to an internally inconsistent set of models in any case.

      In a model with single capital, there is just that – a single capital good that can be measured in its own units. I don’t see what the problem is.

      First, you have to assume homogeneity among particular types of capital, to make it consistent. But more importantly this definition doesn’t tell us anything about the real conditions of production, unlike Sraffa’s approach which uses wages, profits and time. It’s not really a measure of ‘capital’ in any meaningful sense as we don’t know what the capital units can produce, what they are worth etc.

      I think that Giffen good is a relevant analogy – if you insist that CCC somehow proves _logical_ flaws and incoherencies in neoclassical theory, then same argument must hold for consumer theory.

      The logical flaws – which extend beyond reswitching – apply under all conditions. Giffen goods, on the other hand, are not really a logical flaw but a possible exception to the standard story.

  4. #7 by srini on July 27, 2012 - 12:42 am

    Ivasmi has had these same arguments over and over and again and has not bothered to read the relevant mainstream literature. This is not an empirical question. The conditions under which you can aggregate capital are extremely stringent and in practice unobtainable–read Franklin Fisher. The idea of an aggregate production function is just bunk. So, all we have left with is disaggregated GE, where DMS states that aggregate excess demand functions can be any which way even if the underlying functions are well-behaved. So, you really can’t do comparative statics with the aggregates. BTW, Mascollel had a paper in 1980s which essentially extended DMS to capital and admitted that Joan Robinson was right. That is, there is no well-defined relationship between interest rates and capital (by extension consumption). The burden of proof is with those who use GE and DSGE not the other way. You need to come up with reasons why your restrictive assumptions are reasonable.

    GE has is own host of problems. You need to assume gross substitution, which is problematic, especially in a monetary economy–money simply does not have gross substitution property–at least that much should be clear to anyone with even a tenuous link to the real world.

    The macroeconomy is an emergent phenomenon–studying it on the basis of individual decisions is like building up biology on the basis of quantum mechanics, which makes no sense. At any rate, even the foundations of micro are not solid–they are basically based on 19th century folk psychology when 21st fMRI is revolutionizing our ideas about cognitive psychology.

    • #8 by Unlearningecon on July 28, 2012 - 5:13 pm

      Good comment – do you have links to/names of the papers you reference?

      • #9 by srini on July 29, 2012 - 1:54 pm

        Here is the link to the Mascollel paper:

        http://www.econ.upf.edu/~mcolell/research/art_065.pdf

        If you google Franklin Fisher and Jesus Felipe, you should be able to get their papers on capital aggregation. Lots of it. The issues in capital aggregation go beyond reswitching. When neoclassical apologists bring up reswitching they are either disingenuous or ignorant.

        On GE, especially the gross substitution property for global uniqueness should be there in any standard grad school book such as Mascollel Green and Winston. Again this is all standard neoclassical stuff that they themselves conveniently forget.

        On new studies in neuroscience–Subliminal by Mlodinow is an easy book for complete layman like me. Obviously, I am not qualified to refer to actual academic studies on the subject–they are beyond my paygrade. BTW, reading these should make it clear that the idea of behavioral economists that agents are more or less rational itself is sketchy. I think utility maximization needs to be junked, period. Of course, Herbert Simon said that long ago, but he was ignored.

  5. #10 by Min on July 27, 2012 - 2:27 am

    “First, the MPC assumes that other factor inputs are fixed when capital is employed, which leads to our first problem: since capital is (rightly) assumed to be the least variable input, any time period in which you can employ more capital is surely one in which you can employ more labour, too? Once again we are forced to face the reality that firms tend to vary all inputs employed at once.”

    Well, if MPC is a partial derivative, that’s what you would expect, no?

    “As for the latter, Keen notes that there is an “obvious circularity” to the definition.”

    Circularity is not necessarily a big deal. After all, Eddington reworded Newton’s First Law as, “A body will remain in a state of rest or uniform motion, except inasmuch as it doesn’t.” ;) Now, you can operationalize the concept of force, and operational definitions are a good idea, but careful analysis indicates that in reality you only approximate force. A precise operational definition depends upon idealized procedures and instruments.

    • #11 by Unlearningecon on July 27, 2012 - 6:42 pm

      I made that point poorly and I clarified it in another comment.

      I think that is a funny but not altogether fair characterisation of Newton’s Law, which if anything is more of a tautology than circular. In this case, the amount of capital employed depends on profit but the amount of capital employed also depend son the rate of profit. So where do we start?

      • #12 by Loren on July 31, 2012 - 4:15 am

        When excess credit money (created by the banks loans) flood the economy they produce an asset bubble. When this asset bubble bursts, the banks balance sheets are in trouble and all their claims against their debtors are transformed in base money (by FED direct printing) in order to repair their balance sheets. In this way what once has been considered households’ wealth (houses, savings, superannuation investments etc. household assets) depreciates or disappear, because of the bubble burst and value assets collapse. But by printing money and giving them to the banks, the households’ lost wealth is resurrected again, but this time it is reallocated in a few hands – those of the bankers, not the households. With
        repeating money printing, this wealth is not only resurrected and “reallocated” to the banks, but it start its own growth by sucking the household wealth remains Left savings) and incomes through hidden inflation.

  6. #13 by Blue Aurora on July 27, 2012 - 3:17 am

    Capital theory aside…I have a question for Unlearningecon.

    What is your opinion of Modern Monetary Theory?

    • #14 by Unlearningecon on July 28, 2012 - 5:49 pm

      I’m not that well versed in it but I’m not sure about their use of taxes to manage inflation, as taxes tend to increase the cost of production and so the price level. I could get on board with many of their policy prescriptions, though.

      I also get an unfortunate cult-like feeling from them.

      • #15 by Blue Aurora on July 29, 2012 - 3:04 am

        Same, I also get that cult feeling about them too. Do you know what does Steve Keen make of MMT?

      • #16 by Unlearningecon on July 29, 2012 - 10:44 am

        They disagree on the role of government spending and taxation, but here Keen works with an accounting expert to try and reconcile the two somewhat.

  7. #17 by ivansml on July 27, 2012 - 11:43 am

    @Unlearningecon
    The point of GE is that it allows you to build logically consistent models with heterogeneous capital if you want to. Apparently, most economists don’t want to, which means one of two things: 1) either capital heterogeneity is not that important in real world and we can build useful models even when abstracting from it, or 2) they are all wrong and introducing capital heterogeneity will make our models significantly more consistent with empirical reality. In case of 2), there should be plenty of evidence and opportunities for writing papers proving this, so where are they?

    And, sticking to my question, why exactly mere logical possibility of reswitching and aggregation issues is understood as logical flaw of neoclassical theory, while mere logical possibility of Giffen good is an exception to standard story?

    @srini
    In that paper, Mas-Colell also writes:
    “The interpretation of the negative results is rather that comparative statics is not an area for armchair thinking but for empirical assesment of parameters. [...] What the ‘paradoxical’ comparative statics has taught us is simply that modelling the world as having a simple capital good is not a priori justified. So be it.”
    Well said. As an economist, I don’t care that much about general comparative statics results in abstract GE models. Instead, I’m interested in specific models that illustrate particular economic ideas. Often those models will use single capital good, or even abstract from capital alltogether, but they can still be useful.

    • #18 by Unlearningecon on July 27, 2012 - 4:28 pm

      2) they are all wrong and introducing capital heterogeneity will make our models significantly more consistent with empirical reality. In case of 2), there should be plenty of evidence and opportunities for writing papers proving this, so where are they?

      The first part of your statement is correct. The second part is based on the premise that economics is a progressive research program, or possibly even more strongly that economists are always going in the right direction. I believe these to be false.

      And, sticking to my question, why exactly mere logical possibility of reswitching and aggregation issues is understood as logical flaw of neoclassical theory, while mere logical possibility of Giffen good is an exception to standard story?

      Because every single capital good exhibits the a hyperbolic function for value as the rate of profit increases. This means reswitching is highly likely with any two techniques for producing the same substance (though not certain). On the other hand, in my experience giffen goods are just thought as a possibility with no real justification.

      Re: your comments to srini. Can you provide a brief example of a single or zero capital good model that has proven useful?

      • #19 by ivansml on July 28, 2012 - 12:16 pm

        “Because every single capital good exhibits the a hyperbolic function for value as the rate of profit increases. This means reswitching is highly likely with any two techniques for producing the same substance (though not certain).”

        Sraffa uses linear activity models, which do not allow for any substitution between inputs. This is obviously an extreme case. Allowing for smoothness and substitution in production function may rule out reswitching (e.g. Stiglitz, 1973). Regarding empirical relevance, Han & Schefold (2006) analyze OECD input-output tables and find that “Reverse substitution of labour or reverse capital deepening are observed in about 3.65% of tested cases”. That doesn’t seem to be that much (although I’d need to read the paper more closely).

        “Can you provide a brief example of a single or zero capital good model that has proven useful?”

        Zero capital goods:
        Lucas asset pricing model – you specify preferences, exogenous process for consumption and work out implication for asset prices
        basic 3-equation New Keynesian model – widely used to analyze monetary policy

        One capital good:
        real business cycle models (to clarify – RBC models as definitive explanation of business cycles are no good, RBC models used to gain insights about responses of economy to supply-side shocks can be useful)

      • #20 by Unlearningecon on July 28, 2012 - 5:20 pm

        The Stiglitz paper looks interesting although I don’t regard the empirical evidence presented by Han & Schefold as particularly enlightening, given that reswitching is all about showing the conclusions do not follow from premises.

        Robert Vienneau’s link explains why Giffen Goods are not analogous to reswitching better than I have. It is also worth noting that reswitching is not the primary issue Sraffa raised (much more important is what determines the distribution of income).

        Lucas asset pricing, afaik, has not been a great empirical success and NK DSGE clearly has not been either. RBC is obviously not a great explanation of business cycles as you point out, but has it been good for gaining insights about supply shocks? You don’t show any empirical evidence for the usefulness of these models.

  8. #21 by pontus on July 27, 2012 - 1:33 pm

    “Once again we are forced to face the reality that firms tend to vary all inputs employed at once.”

    Oh my god. Not only are you refuting neoclassical economics, but also calculus of variation! This means that everything we know from Newtonian physics onwards is wrong. Have you notified the Fields medal committee?

    And maybe you can explain how this is a problem in a single-capital good economy? What enters the production function is of course not the value of the capital good, but the quantity. So how can prices distort anything?

    • #22 by Unlearningecon on July 27, 2012 - 4:09 pm

      Oh my god. Not only are you refuting neoclassical economics, but also calculus of variation! This means that everything we know from Newtonian physics onwards is wrong. Have you notified the Fields medal committee?

      Wow what a straw man. Either firms vary all inputs employed at once or they hold some fixed and vary others. Nothing to do with the foundations of calculus.

      What enters the production function is of course not the value of the capital good, but the quantity.

      How do you propose to measure that?

      And maybe you can explain how this is a problem in a single-capital good economy?

      The distribution between wages and profits must be known before we calculate the value of capital, so supply-demand as an explanation for prices of factor inputs does not work. The MPC is also false.

      Of course we don’t live in anything close to a single capital good economy anyway.

      • #23 by Philip Walker on July 27, 2012 - 5:16 pm

        “Either firms vary all inputs employed at once or they hold some fixed and vary others. Nothing to do with calculus.”

        Quite right. This fact is nothing to do with calculus: but you were critiquing the assumption that mixed partial derivatives commute in the problem under discussion. *That* is exactly to do with calculus.

        If well-behavedness were to hold, it would be quite legitimate to consider any path which takes a firm from state 1 to state 2. That would then mean that we can legitimately consider varying capital independently of labour or other factors, even if in the real world we don’t see it. So the fact that we don’t see it is irrelevant to your critique, whereas well-behavedness is crucial.

      • #24 by Unlearningecon on July 27, 2012 - 6:27 pm

        Ah, I see your point. I do gloss over this a bit but it is actually explored far more in Keen’s book – there’s only so much I can put in a blog post. The problems become clear with simple differentiation.

        The point is:

        MPC = Change in income due to change in capital

        = change in wages due to change in capital + change in profit due to change in capital

        = change in wages due to change in capital + profit*change in capital due to change in capital (one) + capital*change in profit due to change in capital

        = change in wages + rate of profit + capital*change in rate of profit due to change in capital

        The MPC only holds as long as the first and last are zero, which doesn’t apply when industries are broadly defined.

  9. #25 by john77 on July 27, 2012 - 3:25 pm

    I may have missed something in your precis but as I read it Sraffa is pulling a sleight of hand – profit and return on capital are fundamentally different. Profit is revenue minus material, labour and operating costs and interest on borrowings; return on capital is revenue minus material labour and operating costs minus a fair wage for the proprietor/partners divided by the amount of capital employed (equity plus borrowings). NOT the same thing so treating them as such leads to gross fallacies.
    Secondly it IS possible to add capital without adding labour – there is a process known as “de-bottlenecking” (if you’ve never worked in a process industry you may not know that the optimal scale of plants undetaking different stages of a multi-stage process are often different so the company will build a plant that optimises roce on a cautious prediction of future demand and later add capacity by adding modules in the stages that can cope with the lowest level of throughput). This does not require additional labour on a continuous basis (just to build and install the extra module). So your third paragraph belongs in an alternate universe.

    • #26 by Unlearningecon on July 27, 2012 - 4:34 pm

      minus a fair wage for the proprietor/partners

      This is just wages?

      divided by the amount of capital employed

      Measured in?

      Secondly it IS possible to add capital without adding labour – there is a process known as “de-bottlenecking”

      I’m sure it’s possible; what I’m saying is that it’s not a good general rule.

      So your third paragraph belongs in an alternate universe.

      89% of firms disagree.

      • #27 by john77 on July 27, 2012 - 6:08 pm

        You are normally better than this but it was too hot until sundown yesterday so mebbe you are in the sun.
        I was quite explicit that net revenue needs to be divided economically although not by HMRC between partners’/proprietors wages and business profit. The latter includes the value of the brand name – 40 years ago we knew that we could trust Caz so we didn’t to spend so much time checking the small print compared to certain firms that I might name if the late Lord Goodman volunteered to act for me pro bono.

      • #28 by john77 on July 29, 2012 - 3:35 pm

        It’s cooler today so I’ve looked at your reference which is totally irrelevant. It is a survey of opinions, not an analysis of hard facts.
        I have given you an example (not unusual in practice as compared to economic theory) of adding capital without adding labour where the increased production and net revenue can be clearly identified as arising solely from the additional capital. Usually such examples give a very high rate of return on capital which should not be extrapolated to the general case,
        Other examples could include buying a machine tool that reduces the number of widgets that have to be scrapped because they do not meet specification.
        It is possible in the real world to add capital without changing labour inputs, so any argument that assumes the contrary is unscientific.

      • #29 by Unlearningecon on July 29, 2012 - 10:56 pm

        It is a survey of what business owners say their firms do, not simply an opinion. I don’t know how that cannot be considered ‘hard fact.’

        It is possible in the real world to add capital without changing labour inputs, so any argument that assumes the contrary is unscientific.

        Sraffa’s argument does not assume the contrary. And would you agree that it’s also possible to have to vary both at the same time, such as needing an extra shovel when digging a hole? And hence that the neoclassical theory is unscientific? Your anecdotal data is sufficient to prove a specific point, not a general one.

        You are determined to paint me with some sort of anti-evidence brush the fact is that this is what characterises neoclassical economics, which I am arguing against, yet which you always seem to be defending. The discussion in this post is incredibly abstract, granted, but sometimes you have to do that to take neoclassicism on.

  10. #30 by Robert on July 28, 2012 - 7:40 am

    Daniel Hausman pointed out decades ago why the analogy to Giffen goods fails: http://robertvienneau.blogspot.com/2007/05/daniel-hausman-on-one-aspect-of-ccc.html.

    For some of the problems with neoclassical theory that would arise even if only one capital good would arise, see: http://robertvienneau.blogspot.com/2006/10/interest-rate-unequal-to-marginal_05.html. The linked post parallels what Keen writes from the bottom of page 145 to the end of page 147. Both of us draw on Bhaduri’s decades-old work. For an argument that even disaggregated General Equilibrium models include a market for aggregated capital, in some sense, see: http://robertvienneau.blogspot.com/2012/06/market-for-num-capital-in-general.html.

    I also have many numerical examples of why disaggregated neoclassical theory is nonsense, at least as far the practical conclusions that mainstream economists are mistakenly taught to draw from it: http://robertvienneau.blogspot.com/search/label/Sraffa%20Effects.

    I expect that this post will go into moderation. I also recommend Matias Vernengo on the CCC. I recently enjoyed one of his co-authored papers with the title, “Because I Said So,” that being about all that underlies mainstream policy advice.

  11. #32 by Robert on July 28, 2012 - 9:38 pm

    “Sraffa uses linear activity models, which do not allow for any substitution between inputs.”

    The above is false. Linear combinations of fixed coefficients allows for substitution between inputs. Furthermore, continuously differentiable production functions can be constructed as the limit of linear combinations of fixed coefficients production functions.

    “This is obviously an extreme case. Allowing for smoothness and substitution in production function may rule out reswitching (e.g. Stiglitz, 1973).”

    Sraffa effects encompass more than the reswitching of techniques. For example, capital-reversing is consistent with continuously differentiable production functions or whatever smoothness you desire.

    Stiglitz’s article has not aged well. Propositions of price theory that he said were accepted are still not understood by many mainstream economists today. As we see here.

    “Regarding empirical relevance, Han & Schefold (2006) analyze OECD input-output tables and find that ‘Reverse substitution of labour or reverse capital deepening are observed in about 3.65% of tested cases’. That doesn’t seem to be that much (although I’d need to read the paper more closely).”

    Other demonstrations of the empirical relevance (including simulations) of the empirical relevance of Sraffa effects are available. And, for that matter, Leontief Input-Output analysis is a widely used empirical technique that goes along with Sraffa’s analysis.

  12. #33 by ivansml on July 29, 2012 - 3:00 pm

    @Robert:
    I’m not convinced by Hausman’s quote. First of all, there do exist some neoclassical papers discussing under which condition capital paradoxes may occur (such as that Stiglitz paper), and I’m sure you are familiar with them more than me. Second, even with Giffen good, all we can say is that the phenomenon occurs when preferences posess certain properties, but since we don’t have good theory of preference formation, the ultimate arbiter is empirical evidence. The difference between Giffen good and capital controversies is then a matter of degree, not kind (in the sense that we have better empirical evidence about the former). This doesn’t justify, IMO, sharp difference in interpretation that you and Hausman hold.

    Yes, linear activity models allow for some substitution when you specify multiple activities producing a good, but that’s not case in your examples. And if I’m not mistaken, Samuelson proved that for efficient output vectors a single mix of activities will be used anyway, so the model can be reduced to nonsubstitution case. I also tried to go through you steel/wheat example, but then I came across Dixit (1977) paper, which discusses the same problem (p. 23-25). He shows that the paradox is caused by incorrect definition of marginal product that doesn’t follow from neoclassical theory except under restrictive assumptions (“In other words, the analysis of Bhaduri and Harcourt amounts to saying that the one-good Clark-Solow result is valid only in the one-good Clark-Solow model.”).

    @Unlearning:
    For discussion of Giffen good, see above. Lucas AP model with standard assumptions was not succesful empirically. But by now there are several ways how to extend the model to answer equity premium and other puzzles, while the basic intuition of the model (assets whose payoffs have negative covariance with marginal utility will command higher returns) stays valid. New Keynesian models were somewhat succesful empirically before the crisis, and the crisis was not forecast by any other model/forecasters either (see here). Finally, I’d like to say that “usefulness” of the model is not determined only by its empirical success – model that fails match the data can still be useful if the specific way in which it fails helps us to understant the problem better.

  13. #34 by Ron Ronson on July 29, 2012 - 3:07 pm

    ‘The value of capital is based on the expected profit from it, which is partly based on the price of capital.”

    This is stated as though it is some kind of circular reasoning. But surely under capitalism all goods are produced for profit and the laws of the market will create a tendency for the rate of profit to be equal between different industries. This will lead the price of a particular capital goods to be such that it both generates this “standard” rate of profit for its producers, and can be bought by others to be used in production processes that themselves generate the same rate of profit. This can be shown in a very simple model involving not much more than supply and demand. I don’t see why this is at all circular.

    As the factors that determine the rate of profit change (time preference, risk aversion etc) then the prices of capital goods (both real and relative to each other may change) – and that may also cause the production processes chosen in an economy to change. But that is a feature not a bug in any sensible model (and I agree that the neo-classical model as described by Keen does not meet this criteria).

    • #35 by Unlearningecon on July 31, 2012 - 1:04 pm

      This is stated as though it is some kind of circular reasoning. But surely under capitalism all goods are produced for profit and the laws of the market will create a tendency for the rate of profit to be equal between different industries.

      The second sentence is broadly true; the third is not and has never been observed. The first is unrelated.

      This will lead the price of a particular capital goods to be such that it both generates this “standard” rate of profit for its producers, and can be bought by others to be used in production processes that themselves generate the same rate of profit. This can be shown in a very simple model involving not much more than supply and demand. I don’t see why this is at all circular.

      It can be shown in a model – a model that is false. But it doesn’t address the value of capital.

      As the factors that determine the rate of profit change (time preference, risk aversion etc) then the prices of capital goods (both real and relative to each other may change) – and that may also cause the production processes chosen in an economy to change.

      Correct. But it still doesn’t give us a consistent way to measure the value of capital.

      Neoclassical economists assumed that there was no real problem here. They said: just add up the money value of all these different capital items to get an aggregate amount of capital (while correcting for inflation’s effects). But Sraffa pointed out that this financial measure of the amount of capital is determined partly by the rate of profit. This is a problem because neoclassical theory tells us that this rate of profit is itself supposed to be determined by the amount of capital being used. There is circularity in the argument. A falling profit rate has a direct effect on the amount of capital; it does not simply cause greater employment of it.

      In your model prices are not determined by supply and demand but by the conditions of production.

  14. #36 by srini on July 29, 2012 - 9:48 pm

    The debate is NOT about reswitching but about the validity of capital aggregation, the concept of marginal product of capital, its relationship to interest rates, and finally the theory of distribution as and value. Focusing on reswitching is too narrow. Here are my main issues on this topic:

    1) Even if reswitching turns out to be empirically unimportant (and I am not at all convinced about the evidence), the use of aggregate production function is simply invalid. Franklin Fisher. Stilgliz himself who defended his MIT brethren against the Cambridge UK assault, but admits that, “the difficulties of conventional economic models do not lie so much in capital theoretic issues of reswitching as in the questions arising from the heterogeneity of capital.”

    2) You can rescue GE and price theory–although even that requires some restrictive assumptions that are purely macro driven, such as gross substitution–but then you cannot have value theory, which is the main utility of neoclassical analysis–that the factors received their marginal product.

    3) You cannot abstract away from income distribution. Saving is not independent of income distribution (except under restrictive and untenable assumptions).

    4) Growth accounting is flawed and cannot be generally justified.

  15. #37 by Unlearningecon on July 31, 2012 - 1:55 pm

    I don’t think the debate on reswitching is really going anywhere but as srini has noted it’s not the only problem – I never even considered it to be the most interesting conclusion, that being reserved for the fact that distribution must be known before prices can be calculated. I have not seen anybody, here, in the original debate, or in the papers linked, question Sraffa’s method of measurement.

    New Keynesian models were somewhat succesful empirically before the crisis, and the crisis was not forecast by any other model/forecasters either (see here).

    Whoah whoah – no neoclassical models. The crisis isn’t some sort of black swan – that NK models missed it is representative of the fundamental problems with the way they treat the economy (specifically debt, finance and banking).

    I agree that empirical evidence isn’t the only measuring stick – models have to be internally consistent and have parameters for the realism of their causal mechanisms. I just don’t see how any of the models you linked fit those criteria, particularly the latter.

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