Shifts in a word's valency (such as increases or reductions, e.g. of a verb) are alterations to a core valency. One precondition of valency shift is that the verb provides semantic and conceptual opportunities for this shift. Another precondition is that, in a given language, constructions have already evolved in which these shifts can be actualized. Valency shift is construction inheritance: a given verb inherits a construction for which it had not previously been licensed from another verb that is licensed for this construction. Valency inheritance is the inheritance of a verb's valency by a noun construction. Valency theory and construction grammar are therefore complementary. Our concept of shift and inheritance of valencies and constructions is prototypical and analogical. In this context, the paper discusses identity, polysemy and homonymy of constructions, using the nominative-accusative construction as an example.