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

The identification of production functions from data is an important task in the modelling of economic growth. In this paper, we consider a non-parametric approach to this identification 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 formulate the inverse problem and apply Tikhonov regularization. The inverse problem is discretized by finite elements and solved iteratively via a preconditioned gradient descent approach. Numerical results for the reconstruction of the production function are given and analysed at the end of this paper.