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Inverse problems in geographical economics: parameter identification in the spatial Solow model.

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Summary

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.

Keywords:
geographical economicsinverse problemsparameter identificationproduction functionspatial Solow model

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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.