Should instrumental variables be used as matching variables?

•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.