Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity
AbstractFourth-order multi-step perturbation (MSP) is described and applied as a general method for numerically solving nonlinear, differentiable, algebraic equations which are first-order conditions of economic optimization problems. MSP is first described at a general level and is, then, applied to estimating production-function models, using annual US total manufacturing KLEMS data from 1949 to 2001. The application continues by comparing total factor productivity based on the best estimated model with standard Solow-residual productivity. The optimization problem is the classic firm problem of maximizing output for a given production function, given input prices, and a given cost of inputs. If started sufficiently closely to the correct solution, usual iterative methods, such as quasi-Newton methods, can quickly compute accurate solutions of such problems. However, finding good starting points can be difficult, especially in high-dimensional problems. By contrast, MSP automatically provides a good starting point and iterates a finite number of times over preset steps so that, unlike in usual iterative methods, convergence or divergence is not an issue. Although, as in any numerical method, MSP accuracy is limited by the problem's condition and floating-point accuracy, in practice, at least as implemented here, MSP can quickly compute solutions of nearly single-precision or higher accuracy.
Download InfoIf 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 53 (2009)
Issue (Month): 6 (April)
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
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.:
- Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995.
"Capital utilization and returns to scale,"
Working Paper Series, Macroeconomic Issues
95-5, Federal Reserve Bank of Chicago.
- Burnside, A Craig & Eichenbaum, Martin & Rebelo, Sérgio, 1995. "Capital Utilization and Returns to Scale," CEPR Discussion Papers 1221, C.E.P.R. Discussion Papers.
- Burnside, C & Eichenbaum, M & Rebelo, S, 1995. "Capital Utilization and Returns to Scale," RCER Working Papers 402, University of Rochester - Center for Economic Research (RCER).
- Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995. "Capital Utilization and Returns to Scale," NBER Working Papers 5125, National Bureau of Economic Research, Inc.
- Baoline Chen & Peter Zadrozny, 2003.
"Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem,"
Society for Computational Economics, vol. 21(1), pages 45-64, February.
- Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Society for Computational Economics, vol. 21(1_2), pages 45-64, 02.
- Vartia, Yrjo O, 1983. "Efficient Methods of Measuring Welfare Change and Compensated Income in Terms of Ordinary Demand Functions," Econometrica, Econometric Society, vol. 51(1), pages 79-98, January.
- Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013.
"Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions,"
Society for Computational Economics, vol. 42(3), pages 307-325, October.
- Maliar, Lilia & Maliar, Serguei & Villemot, Sébastien, 2011. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Dynare Working Papers 6, CEPREMAP, revised Jul 2012.
- Viktoria Blüschke-Nikolaeva & Dmitri Blüschke & Reinhard Neck, 2010.
"Optimal Control of Nonlinear Dynamic Econometric Models: An Algorithm and an Application,"
- Blueschke-Nikolaeva, V. & Blueschke, D. & Neck, R., 2012. "Optimal control of nonlinear dynamic econometric models: An algorithm and an application," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3230-3240.
- Blueschke, D. & Blueschke-Nikolaeva, V. & Savin, I., 2013.
"New insights into optimal control of nonlinear dynamic econometric models: Application of a heuristic approach,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 37(4), pages 821-837.
- D. Blueschke & V. Blueschke-Nikolaeva & Ivan Savin, 2012. "New Insights Into Optimal Control of Nonlinear Dynamic Econometric Models: Application of a Heuristic Approach," Jena Economic Research Papers 2012-008, Friedrich-Schiller-University Jena, Max-Planck-Institute of Economics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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.