The identication of production functions from data is an important task in the modelling of economic growth. In this paper we consider a nonparametric approach to this identification problem in the context of the spatial Solow model, which allows for rather general production functions, in particular convex-concave ones that have recently been proposed as reasonable shapes. We show the well-posedness of the direct problem, a system of semilinear partial dierential equations and analyze the dependence of the solution on the production function. We then formulate the inverse problem, which in mathematical terms consists in identifying a nonlinearity in a semilinear reaction-diffusion equation, in appropriate functional spaces and examine the properties of the nonlinear operator to be inverted. Since the problem is ill-posed problem we apply Tikhonov regularization, whose specific properties in this context are analyzed. The inverse problem is discretized by nite elements and solved iteratively via a preconditioned gradient descent approach. Numerical results for the reconstruction of the production function are given at the end of the paper.

@TechReport{EBC11,
  author       = {Engbers, R. and Burger, M. and Capasso, V.},
  title        = {Inverse problems in geographical economics: Parameter identification in the spatial Solow model},
  institution  = {WWU Muenster},
  year         = {2011},
  url          = \{/2011/EBC11},
}