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Testing Substitution Bias of the Solow-Residual Measure of Total Factor Productivity Using CES-Class Production Functions


  • Peter A. Zadrozny
  • Baoline Chen

    () (Office of Directors Bureau of Economic Analysis)


Total factor productivity (TFP) computed as Solow-residuals could be subject to input-substitution bias for two reasons. First, the Cobb-Douglas (CD) production function restricts all input substitutions to one. Second, observed inputs generally differ from optimal inputs, so that inputs observed in a sample tend to move not just due to substitution effects but for other reasons as well. In this paper, we describe using the multi-step perturbation method (MSP) to compute and evaluate total factor productivity (TFP) based on any k+1 times differentiable production function, and we illustrate the method for a CES-class production functions. We test the possible input-substitution bias of the Solow-residual measure of TFP in capital, labor, energy, materials, and services (KLEMS) inputs data obtained from the Bureau of Labor Statistics for U.S. manufacturing from 1949 to 2001. We proceed in three steps: (1) We combine the MSP method with maximum likelihood estimation to determine a best 4th-order approximation of a CES-class production function. The CES class includes not only the standard CES production functions but also the so called tiered CES production functions (TCES), in which the prespecified groups of inputs can have their own input-substitution elasticities and input-cost shares are parameterized (i) tightly as constants, (ii) moderately as smooth functions, and (iii) loosely as successive averages. (2) Based on the best estimated production function, we compute the implied best TFP evaluated at the computed optimal inputs. (3) For the data, we compute Solow-residual TFP and compare it with the best TFP. The preliminary results show that the MSP method can produce almost double precision accuracy, and the results reject a single constant elasticity of substitution among all inputs. For this data, the Solow-residual TFP is on average .1% lower, with a .6% standard error, than the best TFP and, hence, is very slightly downward biased, although the sampling-error uncertainty dominates this conclusion. In further work, we shall attempt to reduce this uncertainty with further testing based on more general CES-class production functions, in which each input has its own elasticity of substitution, and we shall use more finely estimated parameters

Suggested Citation

  • Peter A. Zadrozny & Baoline Chen, 2005. "Testing Substitution Bias of the Solow-Residual Measure of Total Factor Productivity Using CES-Class Production Functions," Computing in Economics and Finance 2005 378, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:378

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    References listed on IDEAS

    1. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995. "Capital Utilization and Returns to Scale," NBER Chapters,in: NBER Macroeconomics Annual 1995, Volume 10, pages 67-124 National Bureau of Economic Research, Inc.
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    More about this item


    Taylor-series approximation; model selection; numercial solution; tiered CES production function;

    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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