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
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 For one, the labor input has been replaced by human capital so there is no fixed factor.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 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.