Linear modelling and optimal control applied to an indexing process

Abstract

Indexing (monetary correction) has great consequences in a national economy under inflation; it has been the object of much theoretical debate, possibly because it sets a positive feedback branch around most of the economic activities. One of its few known examples is studied here, from 108 monthly recorded data. The fundamental issue is the least-squares identification of a SISO linear model for the economy; it permits proof of loop stability, and interpretation of the indexing formula under linear minimum variance control theory. This first result shows, however, unsatisfactory behaviour under a step disturbance; this calls for the adoption of an integrator, prior to the design of the optimal stochastic controller. The superiority of the indexing formula that incorporates the integrator and this controller, over the first one and over one of the legal formulae, is shown by simulation.