Capital Theory – A Forgotten Field in the 21st Century

I set out today to write a short post on Capital Theory and promoted further by Cameron Murray (@Rumplestatskin) tweeting that he was writing today a post of definitions of capital.

Post Keynsians often complain that modern economics is practiced as if the Cambridge Capital controversies never happened.  East Anglia may have won the theoretical argument but as Samuelson was publicly admitting defeat privately he was saying so what.

Well it does matter because if you mispecify capital in your modeling you similarly mispecify wages – which can no longer be treated as a marginal return, and so you are likely to get poor results, with a host of ‘unexplained’ residuals dubbed ‘total factor returns’ and ‘puzzles’ over stagnation and productivity.

If critically capital theory lies at the heart of the rot of neoclassical theory sadly post-Keynsians have done very little to displace it with a fully working replacement theory.  The Neo-ricardian/Sraffan advances gradually ran out of steam and the post Keynesian community seemed split between the Italian contingent and the Keynsian rest.  This was no surprise because it was very difficult to integrate a Sraffan  theory which relied on an  infinitely thin slice of time with the dynamic phenomenon of money and aggregate demand.

Many confusing definitions of capital abound.  The old C18th definition as a  ‘stock’ of wealth seems to have been unwisely revivied By Piketty.  Neo-classicism of course still treats it as a factor return on something productive – capital – a benefit. a reward for seemingly natural ownership relations. But capital theory seems to have died death in economics in the last 10 years.  Almost noone is working on it.  Apart from the small troop of neo-ricardians there only remains the even smaller troop of ‘Neo-Austrians’ following in Hicks footsteps (Faber, Kirzner, Stephan, Gehrke) almost unread outside the German speaking world and having far more in common with Bohm-Bawerk and Ricardo than Mises.

Classical authors would have been horrified by any definition of capital as wealth – this they would have seen as mercantalist and misunderstanding the first principles of political economy. Scrooge Mc Duck sitting on a pile of Gold was not employing capital but hoarding wealth.  The most well known definition comes from Ricardo:

“Capital is that part of the wealth of a country which is employed in production, and consists of food,clothing, tools, raw materials, machinery, &c. necessary to give effect to labour.”

This definition – to quote Rubin was ‘the physical definition of the mode of production’  it had a physical characteristic in durable capital and an immaterial one on working capital and wages.  This definition was refined by Say and Torrens and the definition adopted by the political economy club in 1826 became the mature (not vulger) definition adopted by J.S.Mill

What capital does for production, is to afford the shelter, protection, tools and materials which the work requires, and to feed and otherwise maintain the labourers during the process. These are the services which present labour requires from past, and from the produce of past, labour. Whatever things are destined for this use—destined to supply productive labour with these various prerequisites—are Capital.

Capital is a flow of goods from past combinations of land and labour sustaining and assisting labour during the productive process. Profits are the return on this capital which is advanced during capitalist investment.  You can divide the ‘real’ economy into two investment goods (capital), and consumer goods.  This flow of goods concept of capital, was developed further by Jevons, who correctly saw that time spent making a spade was really money spent feeding the working making the spade, the miner mining the iron etc.  Their is considerable continuity in Capital theory up until an ‘American School’ of writers developed the neoclassical theory of capital that Sraffa attacked

Jevons conception was later developed into Austrian Capital theory – though in the process they borrowed a by then discredited conception of the wages fund (seeing it as fixed) from which  the ‘pool of funding’ (after Strigl) for capital investment was funded.  They treated it as a stock rather than a flow.

We get very little of a conception of capital as a ‘real’ as opposed to monetary phenomenon in many of the SFC/Circuitist models favoured by the Post Keynsian community.  Firms are black boxes which pump out money.

The Neo-classical conception of Capital simply defined the real economy and physical components of capital away.  Clark and Knight (following Marshall) saw production and consumption as simultaneous like a forest being managed so that ‘The planting and cutting are, in a way, simultaneous”  The economy was seen as being so big that the firm could be treated as a black box whose internal physical workings were of no consequence.  For students of land and forestry economists such as Faustmann this analogy is absurd as as it underlies the importance of time, physical productivity and economic conditions in time rather than undermining them.  For Knight the analogy was streached even further with his concept of a ‘crusonia tree’ which sustains itself so that all the capitalist has to do is lop bits off with a machete whilst reclined on a desert island a speedboat away from their superyaughts with no perceived input of land,  labour or energy whatsover.

But capital as black box is the same trap that many Post Keynesian thinkers fall into.  It is untheorised, it just pumps out fruit.

The classical conception of capital has hit the same theoretical buffers as the classical conception of labour.  The relationship between psychical inputs and monetary outputs became no longer linear when you added fixed capital.  Austrians tended to reverse the causality so that capital inputs were causal but this tended to run into similar non-linearities, as Wicksell discovered you could not treat period of production as as measure of capital when capital was reinvested (compound interest), it varied by interest rate. However non-linearities are no reason not to model, rather it is reason to model using non-linear systems.   James Mill, Torrens (in private correspondence) and J.S.Mill all admitted the solution to the great puzzle of capital values in Ricardo (after his death) was that the labour theory of value was correct if you treated fixed capital as realising stored labour values discounted at the interest rate.  In this way capital can be valued (after depreciation) in a same way as an annuity with the same lifespan. Similarly fully durable commodities (land) can be valued as perpetuities.  Similarly neo-austrian theory demonstrates that capital values are always related to the discounted period of production (roundaboutness) rather than linearly.  Mathematically one theory is the exact complement of the other.

If this is a bit much for the reader lets step back and first correct the dimensional errors in neo-classical theory.  To quote Jevons

One main point which has to be clearly brought before the mind in this subject is the difference between the amount of capital invested and the amount of investment of capital. The first is a quantity of one dimension only—the quantity of capital; the second is a quantity of two dimensions, namely, the quantity of capital, and the length of time during which it remains invested.

To be obsessionally correct we must treat capital as a cost and a flow (Money/unit time), as in the phrase ‘return on capital’

Let us define rate of profit/return (on capital advanced) as follows.

ROR=NPV Revenues/NPV Capital Advanced.

Note we are using the precise classical definition above, which seems to be retained by financial economists and accountants but not neoclassical economists.  If you discount land and reduce all capital inputs to discounted labour inputs what do we have – nothing but the standard formula for calculating NPV.  So if you are arguing with the classical theory of value you are denying accountancy theory.

Here we can make a number of conceptual distinctions. If the revenue of a firm is unexpectedly high – because of its franchise value and control of the market – its rate of profits will go up whilst its capital remains the same,  This value can be financialised to an asset (shares) but the return on this is a scarcity rent not a return on capital as a factor.  Indeed in perfect competition there are no profits, profits can be seen as a return on franchise value, there is no such thing as a factor return on ‘capital’ as a factor.

This has been known for a long time, Wicksells pupil Ackermann developed a mathematical model of capital which showed (to Wicksells discomfort – hence Wicksell effects) that you cannot value the capital stock separate from the interest rate.  Robinson, Swan and even Knight acknowledged this well before Sraffa wrote up his own classically based explanation.

What I hope to have demonstrated here is that capital theory, and value theory, are a rich theoretical mine to be explored by Post-Keynsians and that it is likely to produce more realistic and empirically relevant models.  Why dont they do so? I think because PKs have picked up certain theoretical prejudices from their undergraduate days:

1) Sraffa showed there is no such thing as a price-neutral interest rate just multiple own rates – wrong, wrong, wrong, wrong

2) Sraffa showed that you can calculate prices without labour values – wrong, wrong, wrong wrong

This is a misinterpretation of what Sraffa did show. But this post is long enough – another day.

7 thoughts on “Capital Theory – A Forgotten Field in the 21st Century

  1. Douglas was the first Disequilibrium theorist…not Minsky. Attempting to embrace Disequilibrium is “chasing after wind.” You have to live in the real world and create policies that will balance modern technologically advanced economies. This is what Keen has not done and Douglas did over 90 years ago. And that is why Keen, and every other economist for that matter, are nascent Social Crediters. Keen barks at me and calls me “a crashing bore” even though, as he himself complains about DSGE theorists, it takes repetition to get the attention of almost any theoretician caught up in their various theoretical fugues, He petulantly bans me from his sites despite the fact that I have repeatedly praised him for his iconoclasm, agreed with him regarding money, banks, debt, disequilibrium etc.and even apologized for any ungraciousness in that process. My only real “sins” are that I claim (correctly) that he hasn’t declared any integrated policies to fit his conclusions (except a debt jubilee which of course is perfectly reflective of the Gifting paradigm of Social Credit) and so remains the orthodox scientist despite the fact that the signature of both good science and scientific breakthrough is the integration of the scientific method with some aspect of creative imagination/consciousness/policy REFLECTING one of the world’s equivalent ultimate Wisdom tradition’s experiences, i.e Atman, Satori, Tao, Grace….again, all of which such appropriate integrations Douglas did over 90 years ago.

  2. Andrew: “1) Sraffa showed there is no such thing as a price-neutral interest rate just multiple own rates – wrong, wrong, wrong, wrong”

    Assume that the price of haircuts is rising at 1% per year relative to the price of wheat (perhaps because there is faster productivity growth in producing wheat).

    Suppose the central bank is targeting 0% inflation measured in wheat (it tries to keep the price of wheat constant over time).

    Suppose a 3% nominal interest rate is compatible with that inflation target.

    Then the real interest rate on wheat would be 3%, and the real interest rate on haircuts would be 2%.

    And if we assume long run super-neutrality of money, a 2% inflation target on wheat would require a 5% nominal interest rate, but the same 3% real interest rate on wheat and the same 2% real interest rate on haircuts. And a 2% inflation target on haircuts would require a 4% nominal interest rate, but the same 3% real interest rate on wheat and the same 2% real interest rate on haircuts.

    In other words, the idea that there are multiple price-neutral real rates of interest, one for each definition of “inflation” (“does “inflation” mean wheat price inflation, haircut price inflation, or some weighted-average basket price inflation?) is true but irrelevant. Just pick one definition of “inflation” to define the real interest rate, and stick with it. Use that same definition to define both the actual real interest rate and the natural real interest rate. It doesn’t matter which definition you choose, as long as you stick with it.

    If that’s what you are saying, I agree.

    (I’ve argued about this with Austrian blogger Bob Murphy, who is good on capital theory, but it’s always difficult to explain this point clearly, so we are not arguing at cross-purposes.

    • Yes I was making a very similar point and that mad ny David Grasner. Sraffa himself made the indexing point in reply to comments on the 1926 article. By the way I think you are wrong on FTPL because it bonds dont depend on primary surpluses but simly a positive value of the MOA – a functional finance point – another post.

      • Andrew: Yep.

        If that’s what Sraffa was saying, then Sraffa was right, and New Keynesian economists would have no problems with it.

        The only people who would have problems with it would be an (Austrian?) economist who said “The central bank should set the *nominal* interest rate equal to the natural rate of interest!”. Because that invites the Sraffian question: “*which* natural rate of interest (i.e. in terms of which good)?”

    • But we arnt talking about own rates but money rates and arbitrage ensures a single unique market rate of money interest is set – of course that has differential impacts on any commodity basket. Sraffa point was solely concerned with the Austrian one of interest being a physical and not a monetary phenomenon and demonstrated that in a world of barter their is no natural rate. No more no less.

  3. There is no actual talking with Austrian economists. Generally, they’re right and that’s that. I spent 8 years on Mish Shedlock’s blog just trying to get them to actually look at cost accounting data, but their reality filters and other orthodox resistance prevented them from doing so. And of course they accused me of being orthodox myself even though I can see the particle of truth and untruth in every legitimate economic theory…even Austrianism.

    Austrianism’s problem is it is the complete inversion of the truth because it points at the actual problem (excess cost) and then declares the enforced effects of that problem as the solution. This despite our ever increasing ability to produce and the fact that for a body of thought to be humane…it must reflect the entirety of human nature…not just some twisted culturally biased mental orthodoxy of homo economicus. Thus it is economic and human alienation itself.

    Austrians and Objectivists, whose mindsets are basically two concentric circles, have Xed their Selves out….poor things. Social Credit on the other hand also looks at the deepest actual problem and resolves its entropic nature with paradigm changing policies that are non-entropic in character plus resolves the unethical problems of economics as well….again something that is not actually relevant or real according to many Austrians.

    The Big Bang (which it turns out is actually an untrue orthodox assumption itself) is however illustrative of economic theorist’s problem. The first cause is always the primary one in temporal universe affairs. Economists fail to go to the first moment of the economic/productive process where costs have already exceeded individual incomes with which to liquidate them. Then they fail to understand that cost, being the most deeply embedded, continuous and thus dynamic factor in all of economics and commerce,….is never NOT in effect. That makes all subsequent causes like interest, rent, profit, monetary inflation, human flaw (Minsky’s actual insight) and asset inflation are either reactionary theories and/or effects of the prior systemic cause of cost inflation and thus the erosion of individual income and profit. All economic theorists are nascent Social Crediters. Sorry.

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