Introducing sliding modes in economics

Abstract

We propose a novel technique for modeling Economic theories (Sliding Modes or SM), but widely used as control models in Engineering. This initial experiment treats the inflation as a phenomenon to explain and control. The two main objectives of this work are: first, to contribute to mathematical Economic modelling and second, the analysis of medium-high inflation in Latin American countries, and its undesirable social consequences. Here we propose SM for testing a traditional economic theory like an augmented Phillips curve in the form of a differential equations model. The first models of variable structure with sliding mode control were developed by Emelyanov and other authors as Utkins and Itkis in the early 1950s. Here we explain how a SM model works, its conditions and properties, in a theoretical way. The next step is to estimate values for the parameters of the system; for that, we have chosen the Chilean economy during the period 1985-2009. With the multiequational system and values of the parameters, simulations are held for controlling the variable inflation by means of money emission. The research ends with conclusions limited to the assumptions pertinent to the theory selected and the inherent simplification of this first simulation. Its selection is just a beginning, with the ambition of extending it to other hypothesis and theories testing.