Spatial activity allocation modelling: The dominant eigenvalue and its corresponding eigenvector

For the Garin-Lowry model, criteria are derived for convergence and it is shown how the forecasts are affected by changes in the parameters of the model and by fluctuations in the exogenous variables. Convergence occurs if and only if the dominant eigenvalue is smaller than one. Expressing the upper and lower bounds for the dominant eigenvalue in terms of the parameters of the model yields interpretable convergence conditions. For the sensitivity analysis, the model is rewritten as an eigensystem in which the endogenous variables appear as the elements of the eigenvector corresponding with the dominant eigenvalue (that is, the Perron vector). The sensitivity of the forecasts is analyzed by examining the effects of perturbations in a matrix on the Perron vector.