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Perturbed Polynomial Path Method For Accurately Computing And Empirically Evaluating Total Factor Productivity


  • Baoline Chen
  • Peter A. Zadrozny


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(×), a parameterization of f(×) over a data sample, and values of constant structural parameters which determine f(×) in the sample. Given f(×) 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, –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.

Suggested Citation

  • Baoline Chen & Peter A. Zadrozny, 2004. "Perturbed Polynomial Path Method For Accurately Computing And Empirically Evaluating Total Factor Productivity," Computing in Economics and Finance 2004 268, Society for Computational Economics.
  • Handle: RePEc:sce:scecf4:268

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    More about this item


    Purterbation methods; Computing productivity index numbers;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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