IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

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

Listed author(s):
  • 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

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2005 with number 378.

in new window

Date of creation: 11 Nov 2005
Handle: RePEc:sce:scecf5:378
Contact details of provider: Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

in new window

  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.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:sce:scecf5:378. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.