In economics, as in other subjects, we meet with a number of different kinds of mathematical relationship. Perhaps the simplest is the definitional relationship which contains only variables linked together by the ordinary signs of arithmetic. Examples of such relationships are: income equals consumption plus saving; the sum of saving by each sector of the economy equals the total saving of the economy; the quantity of some commodity sold multiplied by the average selling price equals the expenditure on the commodity. These equations do not tell us anything about the behaviour of economic agents; they simply indicate the defined relationships between certain terms. When relationships of this kind form part of a system of equations they may be used to eliminate certain variables from the system and thus reduce the degrees of freedom of the system. To go back to the example of the definitional relationship—income equals consumption plus saving—we can obviously write down (income minus consumption) wherever saving appears in a system of relationships, thus reducing the number of variables and of equations.

Evidently, we cannot build up a theory of human behaviour with the aid of definitional relationships alone; in addition we shall need relationships of a behaviouristic or institutional character telling us something of the way in which the different individuals or institutions behave or indicating the technical relationships which subsist between, say, the input of factors of production and the output of product. Examples of such relationships are: the familiar demand and supply relationships; the relationship connecting saving to income and the rate of interest; a relationship indicating the presence or absence of price control, that is the influence of an aspect of the legal system highly relevant to economic behaviour.

The feature of this whole class of relationships is that they involve in addition to the variables which enter into them certain constants or parameters. These parameters will reflect behaviour or technical and legal influences in the actual world. In the overwhelming majority of cases they will have to be estimated from observations.

This sort of parameter will in most cases tell us the extent of the influence of one variable on another.