Randomization as an Instrumental Variable

Abstract

This paper discusses how randomized social experiments operate as an instrumental variable. For two types of randomization schemes, the fundamental experimental estimation equations are derived from the principle that experiments equate bias in control and experimental samples. Using conventional econometric representations, we derive the orthogonality conditions for the fundamental estimation equations. Randomization is a multiple instrumental variable in the sense that one randomization defines the parameter of interest expressed as a function of multiple endogenous variables in the conventional usage of that term. It orthogonalizes the treatment variable simultaneously with respect to the other regressors in the model and the disturbance term for the conditional population. However, conventional `structural' parameters are not in general identified by the two types of randomization schemes widely used in practice.