Perturbed Polynomial Path Method For Accurately Computing And Empirically Evaluating Total Factor Productivity
The paper describes and illustrates a method for generalizing the standard computation of period-to-period percentage change of total factor productivity (TFP) to computation of TFP based on a best k-times-differentiable model. A "model" is a k-times-differentiable functional form of a production function, f(Ã—), a parameterization of f(Ã—) over a data sample, and values of constant structural parameters which determine f(Ã—) in the sample. Given f(Ã—) and sample input price and quantity vectors, we use the perturbed polynomial path method to compute the optimal input vector. Thus, a given model and input data imply input residuals (difference between optimal and observed inputs), and hence, â€“2x a normal-distribution log-likelihood function, L, or information criterion extension to account for parameter uncertainty. A model and its implied TFP are statistically reliable when L is finite and are "best" when L is minimized. The standard Solow-residual TFP is based on 1st-order Cobb-Douglas-type approximation of any differentiable production function and share parameters set to input-cost shares, implying observed inputs are always optimal, degrees of freedom are exhausted, so the model and implied TFP have no statistical reliability. In the paper, we illustrate these ideas using U.S. manufacturing industry data from 1949-2001. We develop models based on CES and tiered-CES production functions and compare their implied TFP with benchmark Solow residuals.
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