Synthetic Instrumental Variables

This paper presents a new method for synthesizing instrumental variables using only the dependent and endogenous explanatory variables of the regression model. We show that a valid instruments can be spanned using the dependent and endogenous variables. Then based on this rationale, we construct an estimator that uses moment conditions stemming from the validity of such synthetic instruments. We demonstrate the consistency of the newly-developed estimator using synthetic variables. A computational algorithm is developed using the moments conditions stemming from the consistency of the estimator. One can use this synthetic instrumental variables method as an alternative to traditional external instruments methods.