title: Inverse problems in geographical economics: parameter identification in the spatial Solow model.
abstract: 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.
authors.affiliation: Institute for Computational and Applied Mathematics, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstrasse 62, Münster 48149, Germany ralf.engbers@uni-muenster.de.
authors.forename: Ralf
authors.initials: R
authors.lastname: Engbers
authors.affiliation: Institute for Computational and Applied Mathematics, Westfälische Wilhelms-Universität (WWU) Münster, Einsteinstrasse 62, Münster 48149, Germany.
authors.forename: Martin
authors.identifier: http://orcid.org/0000-0003-2619-2912
authors.initials: M
authors.lastname: Burger
authors.affiliation: Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences (ADAMSS), Department of Mathematics, Università degli Studi di Milano, Via C. Saldini 50, Milano 20133, Italy Gregorio Millan Institute, Escuela Politecnica Superior Universidad Carlos III de Madrid, Avenida de la Universidad 30, Leganes 28911, Spain.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Capasso
keywords: geographical economics; inverse problems; parameter identification; production function; spatial Solow model