NEGATIVE COEFFICIENTS AND EIGENVALUES OF ECONOMIC-MODELS

First we compare the magnitude of the Frobenius root of a non-negative matrix with the size of the eigenvalues of a matrix obtained by replacing one or more elements of the first matrix by negative elements. In particular, we present, in general terms, a number of theorems that provide conditions under which the negative elements do have a stabilizing, or at least not a destabilizing, impact on all or on specific subsets of the eigenvalues. Next, using the theorems, we analyse the observed stabilizing impact of the negative model coefficients in some typical examples of macroeconomic models.