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• Including instrumental variables in regression analysis increases inconsistency.
• Using instrumental variables in propensity score estimation maximizes inconsistency.
• Choosing between control variables and instrumental variables is challenging.
I show that for a linear model and estimating a coefficient on an endogenous explanatory variable, adding covariates that satisfy instrumental variables assumptions increases the amount of inconsistency. A special case is an endogenous binary treatment and estimating a constant treatment effect when matching on covariates that satisfy instrumental variables, rather than ignoribility, assumptions. I also establish a general result that implies that regression adjustment using the propensity score based on instrumental variables actually maximizes the inconsistency among regression-type estimators.
Journal: Research in Economics - Volume 70, Issue 2, June 2016, Pages 232–237