Prediction in one of its many forms is the goal of economics as it is of other sciences concerned with the actual world. But prediction may be attempted in so many different ways which are logically distinct that it will probably be best if I begin by discussing and illustrating the basis needed for a full prediction even if this ideal is still a long way from being realized in practical work.

Prediction in this sense requires that we can define the state of the system, or some part of it, in terms of a knowledge of the values of certain variables and that we possess a dynamic theory by means of which we can derive future states of the system by logical implication from a knowledge of the present state. In terms of a saving-investment example which I shall use as an illustration, this means that we have, let us say, a system of relationships connecting saving, investment and income of such a kind that if we know the parameters of the system and the present values of the three variables we can deduce the values which these variables will take in each future period.

If we are to be able to do this it is evident that the values of the variables connected by the relationships of the system must not all relate simply to the levels of those variables in a single period of time. A system of this kind would be static and its solution would yield only the equilibrium values of the variables. In physics it is usual to make this connexion between consecutive periods by reducing to the limit the length of the period and by introducing derivatives of the first and higher orders, i.e. rates of change, accelerations and so forth. In economics on the other hand the differential equations of physics are commonly replaced by finite-difference equations, i.e. dx/dt is replaced by Δx/ Δt, where Δt is some unit period, say the month or the year. In this way past values of at least some of the variables are introduced into the system and a link is thus created between the past and the present and, by extension, between the present and the future.