Wednesday, June 11, 2014

Mehrling on Black on Capital

In a post last week, I suggested that an alternative to thinking of capital as quantity of means of production accumulated through past investment, is to think of it as the capitalized value of expected future profit flows. Instead of writing

α = r k

where α is the profit share of national income, r is the profit rate, and k is the capital-income ratio, we should write 

k = α / r

where r is now understood as the discount rate applied to future capital income. 

Are the two rs the same? Piketty says no: the discount rate is presumably (some) risk-free interest rate, while the return on capital is typically higher. But I’m not sure this position is logically sustainable. If there are no barriers to entry, why isn’t investment carried to the point where the return on capital falls to the interest rate? On the other hand, if there are barriers to entry, so that capital can continue to earn a return above the interest rate without being flooded by new investment with borrowed funds, then profits cannot all be attributed to measured capital; some is due to whatever privilege creates the barriers. Furthermore, in that case there will not be, even tendentially, a uniform economywide rate of profit. 

In any case, whether or not we have a coherent story of how there can be a profit rate distinct from the discount rate, it’s clearly the latter that matters for corporate equity, which is the main form of capital Piketty observes in modern economies. Verizon, to take an example at random, has current annual earnings of around $20 billion and is valued by the stock market at around $200 billion. Nobody, I hope, would interpret these numbers as meaning that Verizon has $200 billion of capital and, since the economy-wide profit rate is 10%, that capital generates $20 billion in profits. Rather, Verizon — the enterprise as a whole, its physical capital, its organization and corporate culture, its brand, its relationships with regulators, the skills and compliance (or not) of its workers — currently generates $20 billion a year of profits. And the markets — applying the economy-wide discount factor embodied in the interest rate, plus a judgement about the likely change in share of the social surplus Verizon will be able to claim in the future — assess the present value of that stream of profits from now til doomsday at $200 billion.  

Now it might so happen that the stock market capitalization of a corporation is close to the reported value of assets less liabilities — this corresponds to a Tobin’s q of 1. Verizon, with total assets of $225 billion and total liabilities of $50 billion, happens to fit this case fairly well. It might also be the case that a firm’s reported net assets, deflated by some appropriate price index, correspond to its accumulated investment; it might even also be the case that there is a stable relationship between reported net capital and earnings. But as far as market capitalization goes, it makes no difference if any of those things is true. All that matters is market expectations of future earnings, and the interest rate used to discount them.

I was thinking about this in relation to Piketty’s Capital in the 21st Century. But of course the point is hardly original. Fischer Black (of the Black-Scholes option-pricing formula) made a similar argument decades ago for thinking of capital as a claim on a discounted stream of future earnings, rather than as an accumulation of past investments. 

Here’s Perry Mehrling on Black’s view of capital:
As in Fisher, Black’s emphasis is on the market value of wealth calculated as the expected present value of future income flows, rather than on the quantity of wealth calculated as the historical accumulation of savings minus depreciation. This allows Black to treat knowledge and technology as forms of capital, since their expected effects are included when we measure capital at market value. As he says: “more effective capital is more capital” (1995a, 35). Also as in Fisher, capital grows over time without any restriction from fixed factors. 
For Black, the standard aggregative neoclassical production function is inadequate because it obscures sectoral and temporal detail by attributing current output to current inputs of capital and labor, but he tries anyway to express his views in that framework in order to reach his intended audience. Most important, he accommodates the central idea of mismatch to the production function framework by introducing the idea that the “utilization” of physical capital and the “effort” of human capital can vary over time. This accommodation makes it possible to express his theory in the familiar Cobb-Douglas production function form: y = A(eh)^α(fk)^(1-α), where y is output, h and k are human and physical capital, e and f are effort and utilization, and A is a temporary shock (1995, eq. 5.3). 
It’s familiar math, but the meaning it expresses remains very far from familiar to the trained economist. For one, the labor input has been replaced by human capital so there is no fixed factor. For another, both physical and human capital are measured at market values, and so are supposed to include technological change. This means that the A coefficient is not the usual technology shift factor (the familiar “Solow residual”) but only a multiplier, indeed a kind of inverse price earnings ratio, that converts the stock of effective composite capital into a flow of composite output. In effect, and as he recognizes, Black’s production function is a reduced form, not a production function at all in the usual sense of a technical relation between inputs and outputs. What Black is after comes clearer when he groups terms and summarizes as Y=AEK (eq. 5.7), where Y is output, E is composite utilization, and K is composite capital. Here the effective capital stock is just a constant multiple of output, and vice versa. It’s just an aggregate version of Black’s conception of ideal accounting practice (1993c) wherein accountants at the level of the firm seek to report a measure of earnings that can be multiplied by a constant price- earnings ratio to get the value of the firm. 
In retrospect, the most fundamental source of misunderstanding came (and comes still) from the difference between an economics and a finance vision of the nature of the economy. The classical economists habitually thought of the present as determined by the past. In Adam Smith, capital is an accumulation from the careful saving of past generations, and much of modern economics still retains this old idea of the essential scarcity of capital, and of the consequent virtue attached to parsimony. The financial point of view, by contrast, sees the present as determined by the future, or rather by our ideas about the future. Capital is less a thing than an idea about future income flows discounted back to the present, and the quantity of capital can therefore change without prior saving.
In comments, A H mentioned that Post Keynesian or structuralist economics seem much closer to the kind of analysis used by finance professionals than orthodox economics does. I think one reason is that we share what Mehrling calls the “money view” or, here, the “finance vision” of the economy. Orthodoxy sees the economy as a set of exchanges of goods; the finance vision sees  a set of contractual money payments. 

Mehrling continues:
In The Nature of Capital and Income, Irving Fisher (1906) straddled the older world view of economics and the emerging world view of finance by distinguishing physical capital goods (for which the past-determines-present view makes sense) from the value of those goods (for which the future-determines-present view makes sense). By following Fisher, Black wound up employing the same straddle. 
Piketty may be in a similarly awkward position. 


  1. "Are the two rs the same? Piketty says no: the discount rate is presumably (some) risk-free interest rate, while the return on capital is typically higher."

    I didn't read Piketty (yet, I'm waiting for my library to get it). Why wouldn't Piketty say that the two rs are the same? Also, why does Piketty assume that the return on capital is normally higer than the discount rate? Do you agree with him?
    I'm curious, because from my point of view the two rs are actually the same.

  2. As near as I can tell, here is Piketty's model (implicit in the book, explicit in articles with Saez and with Zucman):

    (1) There is a fixed savings rate, net of deprecation. Savings are automatically invested.

    (2) The value of the capital stock is equal to cumulated net investment. Price and valuation changes are not important.

    (3) The return on capital is fixed by technology. (Capital gets its marginal product.) The return on capital is not affected by the capital-output ratio.

    (4) The growth rate of output is fixed. Growth is not affected by investment or the capital stock.

    Everything else follows from those four premises.

    in this story, the interest rate is irrelevant. In fact, there's no role for finance at all. Investment and saving are the identical act of reserving current production from consumption, which is explicitly described as independent of the interest rate. And capital goods do not seem to be valued as a discounted flow of future earnings at all, or if they are, the discount rate is fixed and also independent of the interest rate.

    It's an entirely real-side story. Piketty certainly has read some Marx (even if he downplays that influence now) but there's no sign of Keynes at all, or of Wicksell or Schumpeter. In particular, there's no explanation for why, if the rate of return on capital is consistently greater than the interest rate, you don't see infinite debt-financed investment, with the required real resources coming from either mobilization of unused capacity (Keynes) or inflationary forced saving (Wicksell & Schumpeter).

    Now, to be clear, in the real world, I think the rate of return on fixed capital generally is higher than the interest rate. So why don't we (usually) see runaway investment booms? Because of barriers to entry, liquidity constraints, and aggregate demand -- none of which come into Piketty's story.

    1. An attempt to explain the relationship between physical and financial capital:

      If we assume that different firms have different levels of capital intensity, aka different organic composition of capital, but that the rate of profit and the wage level is the same throghout the economy, we necessariously get the result that fixed capital in the less capital intensive firm looks much more productive. For example,

      Firm A has:
      Fixed capital (machinery) 100$
      Wages: 50$
      for a rate of profit of 10%, its total profits are 15$.
      But since those profits are attributed to capital productivity, that is supposed to be fixed capital, the profitability of A's fixed capital is 15/100 = 15% rate of profit.

      Firm B has:
      Fixed capital (machinery) 50$
      Wages: 100$ (much less capital intensive)
      For a rate of profit of 10%, total profits are still 15$, but relative to fixed capital 15/50 = 30% rate of profit.

      So the fixed capital of low capital intensity firms "looks" much more productive, and this is what is reflected in the "financial capital" value. However Verizon couldn't simply buy tons of this oh so much profitable fixed capital because the relationship between the amount of capital and the total of wages is fixed by technology, so it's extra productivity is just apparent.

  3. In comments, A H mentioned that Post Keynesian or structuralist economics seem much closer to the kind of analysis used by finance professionals than orthodox economics does. I think one reason is that we share what Mehrling calls the “money view” or, here, the “finance vision” of the economy. Orthodoxy sees the economy as a set of exchanges of goods; the finance vision sees a set of contractual money payments.

    Since I have daily exposure to the arguments of finance lobbyists, I have noticed this as well. But it sometimes seems that the 'finance view' does not give a position external to finance from which to criticize the liquidity worship of the financial industry, i.e. to judge the social vs. private benefits of the rules we use to structure the financial market.

  4. Marcus-

    Yes. The goal is to think about the relationship between the network of financial assets and liabilities recorded on balance sheets, on the one hand, and the concrete social activities of production and consumption, on the other. What we get instead is either a “real” view that collapses these two domains into one, with changes in ownership and debt commitments treated as if they were decisions about production and consumption; or else a “finance” view that treats balance-sheet transactions as a closed system. I think the finance view is more correct in the sense that at least it sees half of the problem correctly. The "real" view is a hopeless muddle because it tries to treat the concrete social activity of production and consumption as if it were a set of fungible quantities like money, and money commitments as if they were decisions about production and consumption. The finance view is correct to see the system of contingent money payments recorded on balance sheets as a distinct social activity, and not simply a reflection of the allocation of goods and services. But the purpose of recognizing finance as a distinct thing shouldn't be just to study it in isolation, but rather to explore the specific ways in which it interacts with other kinds of social activity.

    1. I should add that one could think of Sraffa's project as trying to create a consistent "real" accounting that describes production in a rigorous way without smuggling in money-quantities.