The Sources of Measured Productivity Growth: United States Fertilizer Mineral Industries, 1936-1960

Abstract

N this study, intrafirm technical progress, or improvements in the state of the arts, are separated from scale economies and productivity changes due to interfirm shifts of resources, by fitting production functions and employing covariance analysis. With a view toward determining the sources of the resulting series of intrafirm technical change, several hypotheses are formulated and tested by using the distributed lag models and other relations. The Covariance Matrix method employed in this study (which method has not been used extensively, partly because the equations are non-linear in the coefficients) has a number of theoretical and statistical advantages over the traditional methods of measuring productivity, such as the single equation least squares method and the factor shares method. First, it permits the separation of technical advance from the contributions of physical factors without building into the empirical model the twin restrictive assumptions of constant returns to scale and competitive factor-pricing both being necessary conditions in the factor shares method ' as used by Solow,2 Kendrick,3 and others. Second, it enables us to dispense with the necessity of (artificially) imposing the condition of constancy (linear or log-linear) on the rate of technical change, as is commonly done in fitting production functions to timeseries data.4 Third, it is supposed to reduce the simultaneous equation bias of single equation least squares regressions 5 and weaken the tendency towards indeterminacy of the production function coefficients due to multicollinearity in aggregate time-series data.6 Last, being computed rather than obtained as a residual, the technical change series is net of random errors which, in the traditional residual methods, are collected in the productivity index.