Multi-step perturbation solution of nonlinear differentiable equations applied to an econometric analysis of productivity
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.
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- 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.
- 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.
- 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, Craig & Eichenbaum, Martin & Rebelo, Sérgio, 1995. "Capital Utilization and Returns to Scale," CEPR Discussion Papers 1221, C.E.P.R. Discussion Papers.
- Baoline Chen & Peter A. Zadrozny, 2003.
"Higher-Moments in Perturbation Solution of the Linear-Quadratic Exponential Gaussian Optimal Control Problem,"
Society for Computational Economics, vol. 21(1_2), pages 45-64, 02.
- Baoline Chen & Peter 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), pages 45-64, February.
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