Synthetic Instrumental Variables
Posted: 8 May 2019 Last revised: 8 Mar 2024
Date Written: August 28, 2021
Abstract
This paper presents a new method to address the endogeneity problem in linear regression models. First, we show that a valid instrument can be synthesized using the outcome and endogenous regressor variables under certain conditions. Then, we show that the orthogonality condition E( u'z)=0 for an IV z with respect to the structural unobservable u holds, only if the condition E( z0' e^2 )=0 holds for the first-stage equation x=pi z0+e, where z0 is the projection of the z onto the regression plane W( x,y). This moment condition allows us to infer a valid latent IV from the data. One can use such a synthetic IV in traditional estimation methods that employ IVs. Importantly, the synthetic IV method can be used when a valid IV is not available. However, one can also use this method as an alternative to traditional external instruments methods.
Keywords: IV, OLS, Estimator
JEL Classification: C13,C18
Suggested Citation: Suggested Citation