Instrumental variables

In statistics, econometrics, epidemiology and related disciplines, the quasi-experimental method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Intuitively, IVs are used when an explanatory (also known as independent or predictor) variable of interest is correlated with the error term (endogenous), in which case ordinary least squares and ANOVA give biased results. When used, a valid instrument changes the explanatory variable (the variable correlated with the endogenous variable) but has no independent effect on the dependent variable and is not correlated with the error term, thus allowing a researcher or analyst to uncover the true causal effect of the explanatory variable on the dependent variable. Instrumental variable methods allow for consistent estimation when the explanatory variables (covariates) are correlated with the error terms in a regression model. Such correlation may occur when: changes in the dependent variable change the value of at least one of the covariates ("reverse" causation), there are omitted variables that affect both the dependent and explanatory variables, or the covariates are subject to measurement error. Explanatory variables that suffer from one or more of these issues in the context of a regression are sometimes referred to as endogenous. In this situation, ordinary least squares produces biased and inconsistent estimates. However, if an instrument is available, consistent estimates may still be obtained. An instrument is a variable that does not itself belong in the explanatory equation but is correlated with the endogenous explanatory variables, conditionally on the value of other covariates. In linear models, there are two main requirements for using IVs: The instrument must be correlated with the endogenous explanatory variables, conditionally on the other covariates. If this correlation is strong, then the...