Estimation of the Vintage Cobb-Douglas Production Function for the United States 1900-1960

Abstract

W ITH a number of recent empirical studies presenting evidence in support of the embodiment hypothesis, the vintage aggregate production function appears to be a well established alternative to the aggregate production function which has only disembodied technical progress.' However, this evidence is not wholly satisfactory since the estimation methods used relied upon the conditional estimation of certain crucial parameters of the production function given the values of other (equally important) parameters. It is shown in this paper that for the Cobb-Douglas vintage production function an identification problem arises that may cause serious biases in the estimated parameters if conditional estimation techniques are used with the wrong values of the parameters that are given. A further disquieting aspect of this evidence is that sometimes the parameter that is given is the rate of embodied technical progress which is usually the parameter through which the embodied hypothesis is expressed. In these cases no standard error may be attached to the rate of embodied technical progress and so no direct test of the embodiment hypothesis may be made. A more reliable test of the embodiment hypothesis would be one that is based upon unconditional estimates of the parameters of the vintage production functions and their standard errors. In this paper an attempt is made to obtain such estimates using nonlinear estimation methods. Although the estimates derived are not completely free from conditioning assumptions they do indicate that once cyclical movements in output are adequately treated their evidence alone is not sufficient to support the embodiment hypothesis. Put another way, annual time series data for the United States 1900-1960 do not permit us to distinguish between a vintage Cobb-Douglas production function with a rather high rate of embodied technical progress and one with a very low rate.