On the Complete Instability of Empirically Implemented Dynamic Leontief Models

Abstract

Abstract On theoretical grounds, real world implementations of forward-looking dynamic Leontief systems were expected to be stable. Empirical work, however, showed the opposite to be true: all investigated systems proved to be unstable. In fact, an extreme form of instability ('complete instability') appeared to be the rule. In contrast to this, backward-looking models and dynamic inverse versions appeared to be exceptionally stable. For this stability-instability switch a number of arguments have been put forward, none of which was convincing. Dual (in)stability theorems only seemed to complicate matters even more. In this paper we offer an explanation. We show that in the balanced growth case—under certain conditions—the spectrum of eigenvalues of matrix D≡ (I–A)−1B where A stands for the matrix of intermediate input coefficients and Bfor the capital matrix, will closely approximate the spectrum of a positive matrix of rank one. From this property the observed instability properties are easily derived. We argue that the employed approximations are not unrealistic in view of the data available up to now.