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Inverse problems in geographical economics: parameter identification in the spatial Solow model
Ralf Engbers1, Martin Burger2, Vincenzo Capasso3
1Institute for Computational and Applied Mathematics, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstrasse 62, Münster 48149, Germany ralf.engbers@uni-muenster.de.
This study identifies production functions using a non-parametric approach within the spatial Solow model. The method reconstructs general production functions, including complex convex-concave shapes, from economic data.
Area of Science:
- Economic modeling
- Econometrics
- Applied mathematics
Background:
- Identifying production functions is crucial for economic growth modeling.
- Existing methods may not capture the complexity of real-world production functions.
- The spatial Solow model offers a framework for incorporating spatial dependencies.
Purpose of the Study:
- To develop a non-parametric method for identifying production functions from data.
- To apply this method to the spatial Solow model, accommodating general production function shapes.
- To validate the approach using numerical simulations.
Main Methods:
- Formulation of the production function identification as an inverse problem.
- Application of Tikhonov regularization for solving the inverse problem.
- Discretization of the inverse problem using finite elements.
- Iterative solution via a preconditioned gradient descent approach.
Main Results:
- Successful reconstruction of general production functions, including convex-concave shapes.
- Demonstration of the method's efficacy in the context of the spatial Solow model.
- Analysis of numerical results for production function identification.
Conclusions:
- The proposed non-parametric approach effectively identifies production functions within the spatial Solow model.
- The method is capable of reconstructing complex, realistic production function shapes.
- This work contributes a valuable tool for economic growth modeling and analysis.
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