Discrete-Time Linear Models

Abstract

In this Chapter we shall analyze discrete-time linear dynamic economic models. We shall explain the meaning of our two adjectives, (i) In discrete-time models the unit of time is one year or one quarter or one month, but at extreme it may be of 30 years (Appendix B). Due to the inherent lags in these models, now the discrete-time approach is preferable to the continuous-time approach, (ii) Roughly speaking, in linear models output is proportional to input. We shall consider nonlinear or continuous-time models (Chapters 4 and 6, respectively) later on. In Section 2.1 the accelerator-multiplier model of the trade cycle is discussed. In Section 2.2 we shall investigate the control of a multisector economy by stock signals. Section 2.3* discusses the role of expectations in a linear control model. The first model is a macromodel, while the second and third ones are not. It is noteworthy that in all the three models prices play a subordinate role (as is the case in Disequilibrium Theory and Non-Price Control) and each needs a nonlinear extension (Chapter 4).