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Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity


  • Chen, Baoline
  • Zadrozny, Peter A.


Fourth-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.

Suggested Citation

  • Chen, Baoline & Zadrozny, Peter A., 2009. "Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2061-2074, April.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2061-2074

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    References listed on IDEAS

    1. Baoline Chen & Peter A. Zadrozny, 2003. "Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem," Computational Economics, Springer;Society for Computational Economics, vol. 21(1_2), pages 45-64, February.
    2. 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.
    3. 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.
    4. Audrino, Francesco & Barone-Adesi, Giovanni, 2006. "A dynamic model of expected bond returns: A functional gradient descent approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2267-2277, December.
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    Cited by:

    1. 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.
    2. 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.
    3. Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 307-325, October.

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