Definitions are the terms and terminology which are to be used in developing the theory. Words can have many meanings, both inside and outside of the field of investigation. Therefore, a social scientist must state explicitly the meaning of a word as it is to be used in the analysis so that confusion in communication and subsequent development of the logic is avoided. Relationships are a priori conditions which are imposed on the analysis, generally and simply stated in mathematical terms. These mathematical terms are identities, functional relationships, and behavioral relationships.
Identities are tautologies or truisms.
Identities derive from the fundamental proposition that the whole is equal to the sum of its parts. They define the realm of possibilities. They serve to limit the universe to a certain area of possibilities and, in so doing, also define what is not possible. Because the two sides of an identity are equal by definition, no side is dominant and either side may influence the other. It does not say for certain whether a change in income changes expenditure, or whether a change in expenditure changes income.