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.

In search of a new economic model determined by logistic growth

“…As we have already mentioned in Introduction, the idea that exponential growth ought to be replaced with the logistic one is slowly but surely becoming more and more accepted by the scientists developing various growth models (see Capasso et al [15], Engbers et al [25], Brass [11], Ferrara and Guerrini [26,27,28,29,30,31], Leach [52], Oliver [54], Tinter [75]) fore more details and references).…”

“…To address the issue Capasso et al [15] (see also Engbers et al [25], La Torre et al [51], Anita et al [4,5,6]) employed a purely heuristic approch to introduce a new general family of production functions of the form…”

The Hamiltonian approach to the problem of derivation of production functions in economic growth theory

“…was recently introduced, employing a heuristic approach, see [20,21,22,23] and the relevant references therein for more details and applications. Note that the production function (4.…”

Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model

“…The logistic growth in other words can be described by spatial Solow model and that was used in [5], where they did identification of production function using (noisy) data that is an ill-posed inverse problem, using non-parametric approach and applied Tikhonov regularization to stabilize the computations. As there is no clear choice which production function will fit the situation best, it was proposed to identify production function from data about the capital distribution of some spatial economy, further they obtained the following optimization problem that has to be minimized.…”