TOTAL FACTOR PRODUCTIVITY COMPUTED AND EVALUATED USING MULTI-STEP PERTURBATION *

We describe and illustrate a method for computing and evaluating total factor productivity (TFP). First, we describe using the multi-step perturbation (MSP) method to compute TFP based on any k+1-times differentiable production function. We illustrate the method for Cobb-Douglas (CD), constant elasticity of substitution (CES), and tiered CES (TCES) production functions. Thus, we describe and illustrate computing TFP for far more general production functions than the CD production function, which is the basis of the usual Solow-residual computation of TFP. Second, simultaneously, we describe and illustrate a method for choosing the empirically most valid production function and implied TFP. The MSP method computes optimal inputs, hence, input residuals, the differences between observed and optimal inputs. Optimal inputs maximize output, for a given production function, input prices, and input costs. An information criterion (IC) has a log-likelihood term, computed as the determinant of the sample covariance matrix of input residuals, and a parameter-penalty term, which increases with the number of estimated parameters. Usually, the production function -- the model in this case -- which implies the lowest IC is considered the or empirically-most-valid production function among those being considered. In effect, the usual Solow residual sets all input residuals identically to zero, which results in estimated parameters and implied TFP having no degrees of freedom and no statistical reliability. By contrast, we use the MSP method to compute TFP based on the best CD, CES, or TCES model with the lowest IC and compare it with the usual Solow-residual TFP. We do this using a sample of data on capital, labor, energy, materials, and services (KLEMS) inputs, from 1949-2001, obtained from the Bureau of Labor Statistics.