Statistical Analysis of Identities in Random Variables

Abstract

Abstract A random variable of economic interest is sometimes an identity function of two or more separate variables; for example, crop income per acre is the product of price and yield. This article presents a method for partitioning the variance of such a random variable into components that can be associated with the separate random variables in the identity and interactions among them. Under some statistical assumptions on the variables involved, the converse of the partitioning procedure is useful for deriving the variance of a random variable from the moments of the separate variables of the identity.