Synthetic Instrumental Variables

Posted: 8 May 2019 Last revised: 8 Mar 2024

See all articles by Ratbek Dzhumashev

Ratbek Dzhumashev

Monash University - Department of Economics

Ainura Tursunalieva

Swinburne University

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

Dzhumashev, Ratbek and Tursunalieva, Ainura, Synthetic Instrumental Variables (August 28, 2021). Available at SSRN: https://ssrn.com/abstract=3370143 or http://dx.doi.org/10.2139/ssrn.3370143

Ratbek Dzhumashev (Contact Author)

Monash University - Department of Economics ( email )

Wellington Road
Clayton, Victoria 3
Australia

Ainura Tursunalieva

Swinburne University ( email )

450 Burwood Rd
Hawthorn, Springvale 3122
Australia

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