Incremental Capital-Output Ratios and Growth Rates in the Short Run

ONE of the attractive aspects of the Harrod-Domar model is the magnificent simplicity of its variables. This is especially true of the incremental capital-output ratio (ICOR). It has served as a magnet for economists (including the present writer). Many have been unable to resist employing it as a major element in their attempts to understand economic growth. But are ICORs really helpful in understanding growth? How are ICORs ' and growth rates really related? In a recent paper, Ohkawa and Rosovsky2 presented a graph that showed growth rates and ICORs for Japan from 1890 to 1931 (sevenyear moving averages were employed). The remarkable thing immediately apparent from the graph is the inverse relation between the growth rates and the ICORs. In the few cases where this relation does not hold, the changes in growth rates are very small. Is this relation a curiosity that holds only for Japan, or is it likely to hold for other countries? I want to show both on the basis of theory and of empirical evidence that the latter is what we should normally expect. We should expect an inverse relationship between observable ICORs and growth rates, in most cases, for the following reasons: (1) the investment rate is a more stable variable than are other variables affecting growth; (2) the significance of non-capital inputs is greater than that of capital inputs; (3) changes in the level of employment of all inputs affect growth more than investment; and (4) some outputs are related "probablistically" to inputs. On purely a priori grounds, we can say nothing about these relationships. It is possible to invent hypotheses that would lead to the conclusion that ICORs and growth rates are not inversely related. However, it is also possible to reason plausibly, but not necessarily, that ICORS and growth rates are inversely related. It is this type of plausible reasoning that I wish to undertake. We know on the basis of studies by Solow, Aukrust, Fabricant, and others,3 that increases in capital contribute only a small proportion to total growth. The proportion is probably somewhere between ten and 20 per cent. As a consequence, most of the growth rate is accounted for by non-capital inputs. The main burden of the argument is that investment is a much more stable variable than the non-capital inputs. First we will examine the consequences of this assumption, and then argue why it is likely to be so. Consider the case in which output is explained by the Cobb-Douglas production func'On a priori grounds one can distinguish three types of ICORs. Elsewhere, I have made the distinction between the net incremental capital-output ratio and the adjusted incremental capital-output ratio. By the net incremental capital-output ratios (NICORs) I mean the incremental capital-output ratios as they would be on the assumption that the supplies of all other factors are held constant. By the adjusted incremental capital-output ratio (AICOR) I mean the capital-output ratio as it would be if it were adjusted to a given increase in the supply of other factors -for example, a one per cent increase in the labor force. In practice, however, neither of these concepts are actually employed. Instead, we use the actual increase in the capital stock as a ratio of the actual increase in income. In principle, we should not expect that the actual or observable ICOR would behave similarly to the somewhat purer and more restrictive NICOR and AICOR concepts. But the actual ICORs are much easier to employ statistically and have been used to a great extent. Therefore, their behavior is of great interest to us. In the case of both the NICORs and the AICORs we should expect a clear-cut positive relationship between capital and output. That is, as capital increases we should expect output to increase also. In addition, in both these cases we should not expect the capital-output ratio to vary in any special way with the growth rate. However, for practical work we use actual ICORs and it is these that are under consideration in this paper. See the author's Economic Backwardness and Economic Growth, 178. See also the excellent discussion in Gerald M. Meier, Leading Issues in Development Economics (Oxford University Press, 1964), 101 ff. 2 Ohkawa and Rosovsky, "Economic Fluctuations in Prewar Japan," Hitotsubashi Journal of Economics (Oct. 1962), 24. 'R. Solow, "Technical Progress and the Aggregate Production Function," this REVIEW XXXIII (Aug. 1951). See also R. Solow, "Investment and Economic Growth," Productivity Measurement Review, No. 19 (Nov. 1959); Odd Aukrust, "Investment and Economic Growth," Productivity Measurement Review, No. 16 (Feb. 1959); and S. Fabricant, Basic Facts on Productivity (New York: National Bureau of Economic Research, 1959).