Abstract: When the causal relationship between X and Y is specified by a structural equation, the average causal effect of X on Y is the population average rate of change of Y with respect to changes in X, when all other variables are kept fixed. This parameter is not identifiable from the distribution of (X, Y). We give conditions under which the average causal effect is identified as the solution of an integral equation based on the distributions of (X, Z) and (Y, Z), where Z is an instrumental variable.

Key words and phrases: Causal inference, instrumental variable.