Summary

The statistical analysis of interdependent dynamic systems has developed separately in different fields of study, particularly in control engineering and in economics. Control engineers have usually formulated their theories in terms of differential equations, giving careful attention to continuously distributed lagged dependencies and other forms of dynamic relationship. Economists have tended to formulate their theories in terms of difference equations, partly because some discrete adjustments do occur in economic systems but often for the less satisfactory reason that their observations are taken at discrete points of time or over discrete time intervals. Both continuous and discrete systems are considered in this chapter. In econometric work predictions are often made of the future values of certain variables in the economic systems, on the assumption that the system and the stochastic properties of the disturbances to it remain unchanged. In both control engineering and economics it is usually more useful to consider conditional predictions on various assumptions concerning the values of those variables which are subject to direct control, or predictions about the changes in the operating performance of the system which would result from a modification of its structure. Such predictions require knowledge of the structural equations and so raise the problems of estimation and identification. In both continuous and discrete systems the problem of identification will often be overcome if careful attention is given to the formulation of the basic model as a system of dynamic behaviour relationships.