Estimating capital. Robert Gallman edition.

In economics, there is an unfortunate rift between academics and the economists who actually measure the economy. Which means that academic economists give little attention to the extremely important question how economic concepts relate to actual measurements – one reason why so much of their work is naïve (the ‘Ricardian’ household, which cuts consumption when government spending increases and the like). Fortunately, economic historians, who often have to do the measurements themselves, often bridge part of the gap. Robert Gallman has some highly relevant remarks about different ways to measure (nineteenth century USA) capital – and how these relate to the future, the past, uncertainty, savings, consumption foregone and replacement costs. This still  leaves out important parts of the concept of capital like liquidity, ownership and the ‘overlapping generations’ problem – which however does not make these remarks less valuable.

In principle, capital stocks might be valued in any number of ways. In practice, there are only three ways of any importance, two of which exist in two variants. (I refer here to current price estimates; constant price estimates are discussed below [see the article, M.K.].) Capital may be valued at acquisition cost (which I will also refer to as “book value”), at reproduction cost, and at market value.

Acquisition cost corresponds to the notion (expressed above) of the capital stock as piled-up savings. The great difficulty posed by such estimates is that the capital stock of each year is valued in the prices of many years, so that no meaningful comparisons (at least none that comes to my mind) can be made. This difficulty can be overcome by adjusting the data by means of a general price index-a consumer price index would be best-so that all elements of the capital stock of a given year are expressed in the prices of that year. A capital stock so valued retains the sense of acquisition cost: the valuation expresses the capital stock in terms of forgone consumption. The forgone consumption consists of the consumption goods given up in the year of investment, expressed in the prices of the year to which the capital stock estimate refers. Unambiguous comparisons can thus be drawn-with the national product of the same year, for example.

The capital stock may also be valued at reproduction cost. Each item is valued at the cost of the resources that would be required to replicate it in the year to which the capital stock estimate refers, given the factor prices and techniques of production of that year. The capital stock thus has the sense of congealed productive resources, valued consistently, so that a summation has a precise meaning. Such estimates are well adapted to the study of production relationships. They avoid, in some measure, the circularity problem implicit in market value estimates. Compared to acquisition cost estimates, they express the capital stock in terms of current productive resources rather than historical forgone consumption.

The third system values the capital stock in market prices; that is, each item of capital is appraised at the price it would bring in the current market. The market value of a piece of capital is presumably a function of its productivity, its expected life, and the going rate of interest. The capital stock, so valued, expresses the income that capital is expected to earn, discounted back to the year to which the estimate refers. Such a measure would be useful in consumption function applications, as well as in describing the scale and structure of the economy.

Book and reproduction cost measures differ, theoretically, in that the former measures the capital stock in terms of what was given up to obtain it, while the latter measures the capital stock in terms of what would have to be given up in the current year to reproduce it. In an unchanging economy in equilibrium, these measures would be identical. In an economy in which there were no changes except in the price level, they could be made identical by means of the deflation adjustment described above. In the absence of this adjustment, book value would exceed reproduction cost whenever the price level was falling, and vice versa. Changes in relative prices could lead to the divergence of the two measures, even after adjustment. Thus if the prices of capital goods fell relative to the prices of consumption goods, adjusted book value measures would exceed reproduction cost, and vice versa. (All of the above analysis rests on the assumption that the market price of new capital goods equals the reproduction cost of these goods. If that is not the case, matters become more complicated, as will appear.)

Book value measures look to the past – what was given up to obtain capital – while market values look to the future-earnings potential. In an unchanging economy in equilibrium, and with perfect knowledge, book value and market value would differ only in that the former treats each piece of capital as though it were new, while the latter does not. Even in an unchanging economy, fixed capital would gradually wear out. Therefore old fixed capital would sell for less than new fixed capital, and a capital stock expressed in market values would be smaller than one expressed in book values. The disparity could easily be removed by deducting capital consumption from the book value measures, producing estimates of net book value.

The effects of changing prices (levels and relative prices) on the relative magnitudes of net book and market values are presumably much the same as the effects of changing prices on the relative magnitudes of book and reproduction cost values (see above). Once we drop the assumption of perfect knowledge, other opportunities for divergences between capital stock estimates based on these two concepts emerge. Specifically, deviations between the expected life of individual pieces of fixed capital (on which capital consumption allowances rest) and their actual life may arise.