Reconciling Alternative Estimates of the Elasticity of Substitution

A large number of econometric studies have focused on possibilities for capital-labor substitution in U.S. manufacturing. The evidence, however, indicates substantial disagreement over the value of the elasticity of substitution (cr). Studies based on cross-sectional data provide estimates which are quite close to unity, but time series studies generally report lower estimates. Furthermore, estimates of or seem to vary systematically with the choice of functional form: regressions based on the marginal product of capital relation generally produce lower estimates of cr than regressions based on the marginal product of labor relation. A variety of hypotheses have been advanced to explain the diversity of results, including cyclical changes in the utilization of factors (Nerlove, 1967), random measurement errors (Leontief, 1964), systematic variation of input prices with product prices (Nerlove, 1967), embodied and disembodied technical change and problems in the measurement of inputs (Griliches, 1967a; Hildebrand and Liu, 1965), simultaneous equations bias (Maddala and Kadane, 1966; Nerlove, 1967), serial correlation (Griliches, 1967a), and lagged adjustment (Griliches, 1967a; Lucas, 1969; Jorgenson, 1972). In general, empirical studies attempting to take account of these deficiencies have produced unsatisfactory results. Zvi Griliches, for example, finds that "the labor quality variables . . . contribute little in the elasticity-of-substitution context" (1967a, p. 296), while R. E. Lucas, Jr. concludes that lagged adjustment hypotheses "make essentially no contribution to the reconciling of time series and cross-sectional evidence of substitution" (1969, p. 259). In this paper we report results of a rather successful attempt to reconcile the differing estimates of cr. While it may be desirable to consider separately and systematically the contribution of each of the above hypotheses in reconciling the cr estimates, here we limit our concern to two principal areas: (1) data -we attempt to construct time series data on the cost of capital services in a more detailed manner than previous researchers have, taking into account real and nominal rates of return, asset prices, depreciation, tax policies, and compositional changes in aggregate capital between equipment and structures; (2) stochastic specification -we estimate cr by a two-stage least squares (2SLS) procedure to circumvent the problem of simultaneous equations bias by ordinary least squares (OLS). We then compare estimates of abased on six different functional forms, five alternative measures of the rental price of capital services, and two estimation methods. Our most sobering result is that estimates of Cr are extremely sensitive to differences in measurement and data construction. In this respect we concur with Nerlove who finds that "even slight variations in the period or concepts tend to produce drastically different estimates of the elasticity" (1967, p. 58). However, with our preferred set of data we obtain OLS and 2SLS time series estimates of owhich exhibit robustness over a variety of functional forms and time periods, and are consistent with the cross-sectional evidence.