On the "Importance" of Productivity Change
Abstract
Robert Solow's paper on technical change provides an economic rationale for the so-called total factor productivity residual-the growth rate of real product not explained by the share-weighted growth rates of the real factor inputs. Solow demonstrated that under the assumptions of a Hicks-neutral aggregate production function and competitive equilibrium, the residual is equivalent to the growth rate of the Hicksian efficiency parameter, which in turn is equivalent to the rate at which the aggregate production function is shifting over time. An important implication of this result is that, under the appropriate assumptions, the shift in the production function can be measured using price and quantity data alone, without the need of estimating or assuming the values of such parameters as the elasticity of substitution between capital and labor.' Although the residual is a valid measure of the shift in technology, it does not indicate the true importance of productivity change as a source of economic growth. An increase in total factor productivity will in general lead to an increase in output (as the inputs are used more efficiently) and thus to additional saving and capital formation. Part of the historically observed growth rate of capital stock is, therefore, the result of productivity change, and must be recognized as such when assessing the importance of productivity change as a source of growth. This paper suggests an accounting framework for measuring the importance of productivity change using price and quantities alone. It is based on an intertemporal specification of technology closely related to the framework proposed by Edmond Malinvaud (1953, 1961). An effective rate of productivity change (termed the dynamic residual) is defined to be the residual growth in total consumption not explained by the rate of change of total primary input. This residual is then related to the change in the Malinvaud intertemporal production possibility frontier due to changes in total factor efficiency. Since capital accumulation is endogenous in the intertemporal framework, the dynamic residual measures the impact of annual changes in factor efficiency inclusive of the induced accumulation of capital. It thus provides a measure of the importance of productivity change in economic growth. John R. Hicks and T. K. Rymes have also emphasized the need to measure technical change in a dynamic (capital endogenous) framework,2 but, have implicitly (and explicitly, in the case of Rymes) rejected the conventional residual as a measure of changing technical efficiency. The main result of this paper is, however, that the conventional and dynamic residuals are complements rather than substitutes. They measure different aspects of the same process within a common analytical framework. As will be seen in Table 1, the conventional (atemporal) accounting framework is embedded in a more general *The Urban Institute. I acknowledge the financial support of the National Science foundation in the preparation of this paper. I would also like to thank Larry Epstein, Melvyn Fuss, Dale Jorgenson, and Mieko Nishimizu. IThe recent empirical literature on U.S. productivity change includes Laurits Christensen and Dale Jorgenson (1969, 1970), Edward Denison (1962, 1967, 1974), Jorgenson and Zvi Griliches (1967), John Kendrick (1961, 1973), and Spencer Star. Estimates of the residual have varied greatly: for example, Jorgenson and Griliches (1967) obtain an average annual estimate of 0.10 percent for the period 1945--65, while Kendrick (1973) obtains 2.0 percent for the same period. For a discussion of some of the issues in productivity analysis, see the 1972 Survey of Current Business exchange between Denison and Jorgenson and Griliches. 2Richard Nelson also notes the interaction between productivity change and capital accumulation, but concentrates on the embodied technical change aspects of the problem. See also Denison (1974, pp. I 33-35).
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