The Python That Eats Itself by the Tail: A Self-Contradictory Theory of Capitalism

His plea for a radical redistribution of wealth has received an unprecedented welcome from the general public that has long been thirsty for an intellectually respectable excuse for holding the views it naturally does—namely that capitalism spreads wealth unjustly because it does so unequally. Among professional economists, the cohorts that march under the red flag held high by Joseph Stiglitz and the pink one by Paul Krugman, cannot praise the supporting argument highly enough. The press has been inundated with reviews, mostly favourable. The Economist, not known for falling easily for grandiloquence and self-indulgent ambition, has devoted to the book a leader that bordered on the passionate.2 Most surprising of all, non-partisan economists have offered criticisms that point out weaknesses in the statistical grand work and contestable propositions in the argument while passing over without challenge, and indeed in seeming approval, Mr. Piketty’s central thesis. This thesis depends on the permanent excess of the return on capital over the rate of growth of total output, which would lead to a physical impossibility if it persisted beyond the medium term.

1. The Model in a Tight Form

In introducing his model Mr. Piketty sometimes uses fairly relaxed language that leaves some modest room for interpretation, and by way of parameters, which range between high and low values. Lest looseness should serve as a route for escaping from definite conclusion, the model should be stated unambiguously.

Since 1700, the yield or return on capital is said to have been stable at between 4% and 5%. The rate of growth of output was of the order of 1.5% or probably less. The ratio between the stock of capital and total output has varied between 2:1 and 7:1, with America tending towards the lower half of the range and Europe towards the higher one.

Let the model operate with a rate of return on capital of 4.5%, an output growth of 1.5% and a capital: output ratio of 4:1. These parameters are, if anything, friendly to Mr. Piketty’s eventual conclusions. Let the rich own all the capital, get all the return on it, save and re-invest it all, thus increasing the stock of capital at the same 4.5% rate as the rate of return. The poor do all the consumption and save nothing. The prices of consumer and capital goods relative to each other remain constant. No explicit role is assigned to technology. The parameters are said to yield asymptotic results, getting closer to equilibrium values as time passes.

2. How the Model Self-Destructs

Let the model be launched on a test run. After year 1 output grows from 1 to 1.015. The capital of 4 yields a return of 4.5%. The return is re-invested as it comes in so that capital at the end of year 1 amounts to 4.18. In other words, the stock of capital in year 1 absorbs more than the increment of output, but the excess is very slight and has no significant depressing effect on consumption. However, compound interest continues to do its work in year 2 and in all subsequent years until something stops it.

By the end of year 60, total output will have grown to 2.44 and capital to 56.11. To grow at its predetermined rate of 4.5% in year 61, capital would need to grow by 2.52 but, in that year output would only be 2.48. The whole of the year’s output would have been swallowed up by capital. There would be less than nothing left for consumption and the few workers who have held out so far would finally give up and die of hunger. In a sense, the python will have swallowed itself up. The half-way house to this result will have been reached in year 37, with half of output left over for consumption and part of the work force still surviving on meagre rations. All this is, of course, preposterous and lays bare the logical deformity of the model.

3. The Valuation of Capital: Book or Present Value

It seems implicit in Mr. Piketty’s work that the growth of capital is fed by its absorption of a predetermined part of output. We are led to believe that this part consists primarily of capital goods, measured by the prices at which those goods are added to capital. Their valuation may be affected because they are now second-hand goods and also by wear and tear and obsolescence in subsequent years. After any such adjustments, they will figure in the capital stock at book value. Again and again Mr. Piketty stresses that capital must be valued at market prices. We have meaningful market prices for some components of the stock of capital, in particular for securities traded on active markets. The meaningful price on such a market will be the one at which the marginal holder is indifferent between selling and buying part of some of his holding. A strict conception of rationality requires that this price, in turn, should be the present value of the expected future return from the security, discounted by the holder’s rate of time preference. Security prices as present values of expected returns may in turn, be of some help in estimating present values for assets not quoted on markets and may be never traded at all.

Valuing capital at present value would, at first sight, release the model from its baneful link between output and the increment of capital which must come from the absorption in the capital stock of part or even all of the output. A big chunk of the growth of capital over several years, lifting the capital : output ratio from, say, 4:1 to 6:1 or more, could take place simply by virtue of a change in present values. Changes of such magnitude do not look wholly implausible, especially if expected returns on capital increase while time preference and hence the discount rate decreases.

Alas, Mr. Piketty refuses to allow this tempting escape route for saving his model to be used. Courageously, while maintaining that it is present values and not book values that matter, he dismisses wide movements between the two as condemned to be averaged out in the long run. It seems that to preserve the right perspective, we must treat book value and market value as practically interchangeable, and accept that any lasting growth in the capital stock is the result of some of the output being saved and accumulated in the form of additional capital goods. The theory is very much at a dead end of its author’s making.

4. The “Second Fundamental Law of Capitalism”

Mr. Piketty promulgates two fundamental laws of capitalism. He shows little interest in the first, but insists on the importance of the second. He calls it a law, although it is in fact just a truism. It states that the quotient of the national saving rates and the national growth rate i.e. the capital: output ratio is what it is . If the quotient changes for any reason, the equation would not hold unless the capital: output ratio changed accordingly. If it failed so to change, it would not be in equilibrium. It is not clear by what forces equilibrium must be restored. If the truism were really a law there would be forces, such as incentives and the search for efficiency, to pull the quotient toward its equilibrium value. For Mr. Piketty’s model, namely a permanent excess of the rate of return on capital over the growth rate of output, hence a growth of capital relative to output precludes an equilibrium rate. As shown in section 2, capital would keep growing and soon swallow up all output—a physical impossibility. There is also the awkward circumstance that if output growth became completely stagnant, a prospect that some eminent economists do not think wholly implausible, zero growth rate of output combined with a non-zero savings ratio would imply a capital:output ratio asymptotic to infinity. In any case the Second Fundamental Law appears altogether to clash with the basic driver of the model. The basic driver either dominates the Second Fundamental Law, or is overridden by it. Both cannot be right.

Since Roy Harrod and Evesey Domar have put the capital: output ratio near the centre of macro-economics, capital has been understood as an enabling condition of output, and the optimal ratio between them is one where the marginal cost of additional capital matches its marginal product. The ratio would, of course, adjust to major changes in the available technology.

Mr. Piketty’s meaning of the ratio as it transpires in his text is quite different. Saving is what it is for all the standard micro-economic reasons that motivate individuals. The growth rate is what it is for the equally standard reasons of individual productivity and demography. The capital:output ratio is not determined by any direct motive, but is the passive resultant of saving and growth. It is a measure of the dominance of capital in the economy. The lesser economic growth there is, the greater will be the stock of capital relative to the economy as a whole. The historical norm seems to be in the region of 6 or 7 of capital to 1 of output at these ratios—the power of capital is overwhelming.

The author looks almost with benevolence on the period 1913-1945, where a terrible world depression was preceded and followed by two terrible world wars to such effect that by 1950 the capital output ratio sank to a low of about 2:1. Although terrible, this was good for equality, which we must take to be a redeeming feature of wars and depressions. (It is difficult to credit even such a ghastly period with capital destruction in such proportions as to bring the ratio down from 6:1 to 2:1, without suspecting the measures of capital of unrealistic volatility. However, let us take the book’s statistics at face value, for the real trouble resides in the theory, and not in the statistics.) In the second half of the 20th century capital amazingly enough has risen back and above the pre-war level. Mr. Piketty’s basic driver, the excess of the return on capital over the growth of output, was apparently at work. There is nothing in the theory to suggest that it should stop in any foreseeable future, except that capital growth would soon be absorbing all the output, leaving nothing for consumption. The python of capital will have at that point eaten itself.

5. The Sinister Future

For no clear reason, Mr. Piketty makes no attempt to forestall this frightening conclusion of two different growth rates, compounded over time, crushing the economic mechanism dictated by his own theory. It is difficult to credit that he does not discern the harvest of destruction that logically follows from what he has sown. Nowhere does he cancel the assumption of two permanently different growth rates. He merely uses the impetus of the sharply rising capital stock in the second half of the 20th century to extrapolate to the sinister future that lies ahead in the 21st. He forecasts the medium to long-term European economic growth to decline from 1.8% to 1%, due to the demographic trend. According to his Second Fundamental Law, this falling economic growth should nearly double the capital : output ratio. Some increase in the share of saving would further push up the ratio to the mid-teens or above. Such an overwhelming weight of capital would be unprecedented and in the spirit of the book, intolerable. The present paper does not aim at forecasting whether Mr. Piketty will prove to be a lucky or unlucky forecaster. There are ample arguments that could be opposed to his pessimistic forecast including those related to irresistible immigration from the South into Europe or to technology borrowing from America.

However, let all that be left unexamined. What is more worthy of examination is the extraordinary order of values that permeates the book. Falling growth would have been self-evidently better than a little less. It is deplored because, as displayed in the Second Law, it implies a rise in the stock of capital hence in the wealth of the rich that is too high anyway. This is the implicit rationale of his proposal for a world wealth tax with a top rate of 10%, a tax whose effect on economic growth does not bear thinking about.

6. All is Well as Greater and Smaller Turn Out to be Mere Conjectures

Some part of the popular appeal of Capital in the Twenty First Century is probably due to the engaging examples taken from great classics such as Jane Austin and Honoré Balzac, not usually found in heavyweight tomes of statistics and theory. Their focal role in the story is astonishing indeed, for the characters are all rentiers and have little to do with capitalism. This, too, tells us something about the perspective adopted by Mr. Piketty.

Bricks, cement, glass, vehicles, machine tools, computers and paraphernalia are produced, purchased and absorbed in the capital stock. The buyer, typically a firm, incorporates them in what is, or will be, a going concern. The point of organising and developing a going concern is that it is expected to be worth more, and with a bit of luck and acumen, a great deal more than the capital goods purchased to equip it before they become part of the organisation and are set to serve it to good purpose. The excess value of the going concern over its cost is the reward of organization.

Alfred Marshall in his Principles3 gives organisation the same rank as the other factors of production, capital, labour and perhaps land and natural resources. It is a bit of a shame that Marshall is almost forgotten. If organisation had no value-product imputable to it, it would not be done. With a “return of capital” tending to run at 4.5%, Mr. Piketty assumes a homogenous income flow. What we should see instead is a reward to organisation, perhaps some compensation for the risk of failure and a pure return on capital. If the composite of such elements adds up to Mr. Piketty’s 4.5% or near it, we might try to let regression analysis tell us how much of it is attributable to the pure return on capital. Failing a convincing result, we are safe enough to judge it at less than the critical 4.5%, and could not be refuted if we guessed it as being less than the rate of growth of the economy.

The return on capital, then, may or may not be greater than the growth rate. Its excess, the driver of the Piketty theory and the ill-concealed cause of its timely destruction under the inexorable march of compound interest, turns out to be a matter of conjecture at best. Mr. Piketty can select his own conjecture but there is no particular reason why anyone should share it with him.