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 reserve 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.