Pondering Piketty – A Simple Analytical Framework

Introduction

When Thomas Piketty’s book (Piketty, 2014) burst upon the international scene less than a year ago, I felt pressure to write a comprehensive review of this aggressive attack on free-market economics. After all, it was based, as its title implies, on an exposition of the essential nature of “capital” – as in “Capitalism” – and had I not spent a lifetime in the grip of capital theory?

So I got the book and began to plough through it. It proved much more tedious than the reviews I had already read had prepared me to expect. Piketty lays out his premises and conclusions in the first few chapters. So, I already realized that his approach was full of fallacies, that it was fundamentally flawed. How does one then proceed to go through the remaining part of the 655 pages knowing there is no redemption, in fact that the rest will be either irrelevant padding or a piling-on of further fallacies.

By the time I made it through the book, the reviews, scholarly and more informal, had accumulated. It is a fair bet that, numerous though they are, all of the criticisms that could be made of the book have been made somewhere. Thus the marginal value of any review I could offer is probably now close to zero.[1] However, as I was thinking about it, I realized that many, if not all, aspects of Piketty’s approach can be expressed in a simple framework which might be of use to some. I cannot say that this has not been done  before, in some form or other, only that I have not seen it, and that, in any case, it may be of value.

I will, therefore, say very little about the details of the book – how it is written and organized. I have already elsewhere delivered a sweeping evaluation, to wit: Piketty is wrong on the data, the economics, and the policy, otherwise this is a valuable book. You might think it a bit too scathingly smug. But, what I have read since writing that, has enforced my view. In addition to his dubious use of aggregates (about which I will have something to say) it now appears that a strong case can be made that Piketty has distorted and/or fabricated data (Magness and Murphy, 2014). And his economics is surely abysmal, to the point of evincing basic misunderstandings of the workings of supply and demand (McCloskey, 2014, 91). On the matter of policy, I need no confirmation of my conviction that his recommendation borders on insanity.

There are, however, two general comments I want to make about the book. First, many, though by no means all, of the reviews I have read, including some by highly critical authors, suggest that Piketty’s book is, for all its faults, admirable; that it is the work of a serious author with integrity and the best of intentions - Intelligent, industrious, but mistaken and misguided. Perhaps I lack the capacity for charitable interpretation, but I do not see it in this way. The book strikes me as pretentious and almost completely devoid of merit. Its tone, for all the superficial self-effacing expressions to the contrary notwithstanding, is arrogant, something particularly galling coming from someone who has not taken the time (in the purported twenty years of incubation that this book endured) to properly understand his subject.

Secondly, and more importantly, the book is clearly mistitled. It should be titled “Inequality in the Twenty-First Century”. It is from start to finish a book about the evil of growing inequality. Yet, while the book mounts a mountain of evidence to support the assertion that inequality is growing (a project that ultimately fails, as many have shown) there is no real effort to support the assertion that inequality, in itself, is bad. Some reviews have addressed the ethical question of how this concern with inequality elevates resentment and envy. But I have not seen any discussion of the fact that time and again Piketty tries to bolster his case by asserting, without a shred of evidence, that social inequality results ultimately in “social instability” (for example, 10, 21). Indeed, Piketty recognizes that inequality in itself may not be a bad thing, but becomes bad when it is unjustified and against the “public interest” (33). And, of course, he knows what is in the “public interest.”

A simple framework

Piketty’s framework consists of a few basic categories that can be captured using the following.

Y = rK + wL

This is an accounting identity, where Y is national income, r the rate of earnings of capital, K, and w is the wage rate, the rate of earnings of labor, L.

Piketty divides the set of all productive resources into two (exhaustive) categories capital, K, and labor, L, whose owners earn r and w per unit respectively. Thus the earnings of K and L are rK and wL respectively. And the shares of K and L are rK/Y and wL/Y respectively – which we may write as s_K and s_L respectively.

Piketty’s project is to show that the laws of capitalism imply that s_K/s_L rises without limit, thus destabilizing the society. To do this he posits the fundamental equation that i > y, where i is the rate of interest, also the rate of earnings of K (i = rK/K), and y is the rate of growth of total incomes ([1/t]dY/Y = gY, explained below).[2]

Piketty reasons that if the earnings of K grow more rapidly than earnings in general, this must imply that K’s share is growing, thus increasing inequality. QED.

Let’s consider s_K and s_L in a little more detail.

As a tolerable approximation we can write

g(s_K) = gr + gK – gY

and

g(s_L) = gw + gL – gY

Where g is the instantaneous percentage rate of growth operator (aka, dlog/dt).

If r is constant so that gr = 0 and gK  > gy, s_K will rise.

But if w is constant or positive and gw + gL > gY, s_L will rise.

Clearly, the variables are connected.

g(s_K/s_L) = (gr + gK) – (gw + gL).

If gr = 0, income inequality (s_K/s_L) will rise iff gK > gw + gL, that is, iff capital grows faster than labor plus the increase in wages.

So even with this simple, really simplistic, framework[3], Piketty’s conclusion does not follow unless one discounts the effects of a large increase in the real wage of pure labor. Indeed real wages have risen astronomically over the period of Piketty’s analysis, but presumably he would argue not sufficiently relative to the earnings of capital – a really astounding claim, that suggests further analysis of this framework is necessary.

What Do These Variables Mean? 

The conflation of personal and functional income distribution

By using only two categories, K and L, Piketty stacks the cards. In examining the income earned by K and L he is conflating the personal distribution of income with the functional distribution of income. To say that K earns income is at best a metaphor. It really means the owners of K earn income. And the same is true of L. Labor rents out its services in return for wages. By drawing conclusions about inequality of incomes from this, Piketty seems to think that all capital-owners own only capital (from which they derive their earnings) and, more importantly, all workers own only labor – no capital – exclusively from which they derive their earnings. What happens if workers own capital (for example by way of their pension investments)? Then the earnings of capital relative to the earnings of labor cannot be taken as coterminous of the earnings of capital owners relative to the earnings of workers. He does have a lot to say about who owns capital, but it is confused.

The neglect of human capital

This conflation is particularly egregious, potentially fatal to his argument, for the case of human capital. Piketty explicitly (and cavalierly) excludes  human capital from his consideration. Yet, human capital is arguably the single most important factor in explaining personal earnings. If we include the accumulation of human capital in capital accumulation as a whole, the tendency would clearly be toward a reduction in inequality – even in the narrow sense in which Piketty presents it.

What does capital mean?

Piketty has a sub-section with the same title (45). His answer is patently inadequate.

To use these kinds of aggregates is always to risk incoherence. This is especially true in the case of capital. A nation’s physical productive capital refers to its non-human instruments of production – machinery, raw-materials, minerals, buildings and land (some have a separate category for land). Beer-barrels, blast furnaces, harbor installations and hotel-room furniture are all capital (Lachmann 1956 [1978]). They are “capital-goods.” Clearly this is a category of diverse and heterogeneous items. In fact there are thousands of different sub-categories of physical capital goods and, owing to the persistent improvement of technology, the number is growing even while the composition of sub-categories changes.

Why are capital-goods valuable? They are valuable only because they are able, when grouped in appropriate combinations, and used together with labor services, to produce goods and services that people (consumers) value and are willing to pay for. But the value of any single capital-good is a matter of speculation. What someone will pay for it depends on his forecast of the value of the stream of future revenues that can be earned by employing this capital-good in a productive capital combination.

The value of the total of all capital goods is thus not an observable phenomenon. Yet this is what K is intended to convey. It is meant to be an index of the physical magnitude of the capital of the economy. But since this category of resources is composed of thousands of incommensurate items, the only way such an index can be constructed is by adding them together on the basis of their supposed values and deflating by some suitable price-index. Still, it is not a physical quantity of any observable entity. The value of any single capital-good depends on the flow of prospective revenue it is expected to produce, but, as this revenue is earned over time it must be discounted in order to arrive at the present value of the capital-good. In other words, an interest rate is already implicit in the construction of K; its magnitude depends on the interest rate used to discount the various income streams. Thus for Piketty to argue that the interest rate is the return to capital, is to commit an elementary but significant error (to be discussed further below).

In fact there is no such thing as a total of productive physical capital. There are only individual forecasts of what each capital-project (composed of capital and labor combinations) will earn. Only in the idealized theory of neoclassical economics, where all of these individual forecasts are identical and exactly match what will actually transpire, a world of equilibrium, can one meaningfully talk of such a total. In the real-world it is precisely the differences between these forecasts, between the visions of different and competing entrepreneurs, that drive the market-process in which many production plans fail and some succeed. It is a process of implicit experimentation, a dynamic process and there is nothing automatic about it.

What is the interest rate?

It follows that there is no such thing as a return to capital in general, an r, that is the rate of earnings on K that is equal to interest. Interest is a reflection of time-preference, of the discount applied, under various circumstance (notably different degrees of perceived risk) to future incomes. It is the cost of borrowing, the price of credit. It is the cost of financing productive projects and represents the sacrifice made for not consuming value now in favor of waiting until later. If such a sacrifice is to be made it must be deemed worth it. So, for a productive project to be undertaken it must earn at least the value of financing it, after all other expenses are paid. Interest is not the return to capital. It is the cost of financing. It is a separate cost of production.

What then does capital earn? Capital earns a rental rate. If the capital-goods were rented from a third party rather than owned, their earnings would be the rents paid for them. If they are owned it is as if the owner is renting the capital-good to himself. It is no different with labor. The value of a worker, in terms of capitalized earnings, depends on how much he can sell his services for over time. Since he is the exclusive owner of himself, his capital-value cannot be alienated from himself, the employer must rent him, he must purchase the worker’s services. If we consider labor to be human-capital, then all capital earns a categorically identical rental rate. The interest cost is never equal to the earnings of “capital” except in the sense of “financial capital” which may be used to finance both capital and labor.

Rather than just two (different types of) categories of earnings, there are very many categories all of the same type, namely, they are all potential sources of income. And their earnings depend on the nature of the productive environment in which they are created and deployed and not on any fundamental and immutable laws of capitalism.

What is profit?

In real-world economies successful entrepreneurs earn profits. Very successful entrepreneurs can earn fortunes – that they sometimes bequeath to their heirs. Profits are a disequilibrium phenomenon. There is no positive equilibrium rate of profit. In equilibrium profits are zero. Profits are the return for being right in an uncertain world. They are a residual after all other expenses have been accounted for – including contractual payments to workers (wages), capital-goods owners (rental earnings) and financiers (interest).  If the entrepreneur is also an owner of the capital-goods she uses, and part-financer of the project, these sources of income will, in practice, be inextricably comingled.

Conclusion

In the light of the realities of the dynamic economic processes that increased the standard of living of millions of people by magnitudes of thousands, it is hard to see what relevance Piketty’s i > y could possibly have. In truth, his is a bankrupt vision, based on a set of flat-earth dogmas that should never have been accorded the esteem it now has.

References

Lachmann, L. M. (1956 [1978]). Capital and its Structure. Kansas City: Sheed, Andrews and McMeel. .

Magness, P. W., & Murphy, R. P. (2015, Spring). Challenging the Empirical Contribution of Thomas Piketty's Capital in the 21st Century. Journal of Private Enterprise.

McCloskey, D, N. (2014), Measured, unmeasured, mismeasured, and unjustified pessimism: a review essay of Thomas Piketty’s Capital in the twenty-first century. Erasmus Journal for Philosophy and Economics, 7, 2: 73-115.

Piketty, T. (2014). Capital in the Twenty-First Century. Cambridge: Harvard University Press.

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[1] I created a folder on my desktop called Piketty Pieces. At this moment it contains 77 separate files, being various reviews (critiques) including a 10-part review by The Economist.

[2] Piketty uses r and g to write r > g, but we need a different notation for reasons that will become obvious.

[3] It is a Ricardian-Marxist (classical) framework with land thrown in with capital.