Abstract
In Arbia and Paelinck (2003a, b), a Lotka-Volterra model (LVM) is applied to the convergence-divergence problem of European regions in terms of incomes per capita. As the latter have to be non-negative, a double logarithmic version may be substituted for the original specification, a modification that removes at least part of the non-linearity of LVMs; this chapter introduces this non-linearity again. Discussion begins with a general section on LVMs, to go on with a mixed linear-logarithmic specification, of which the positivity of the (possible) equilibrium solution is proved, and for which a (sufficient) stability condition is derived.
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We thank Martijn Smit, Vrije Universiteit Amsterdam (VU University Amsterdam), for furnishing us with the digital map necessary to construct this figure.
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Griffith, D.A., Paelinck, J.H. (2011). A Mixed Linear-Logarithmic Specification for Lotka-Volterra Models with Endogenously Generated SDLS-Variables. In: Non-standard Spatial Statistics and Spatial Econometrics. Advances in Geographic Information Science, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16043-1_11
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