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It is at best difficult and expensive to conduct controlled experiments on smoking status in the general population.The researcher may attempt to estimate the causal effect of smoking on health from observational data by using the tax rate for tobacco products as an instrument for smoking.Note also that the exclusion restriction (condition 4) is redundant; it follows from conditions 2 and 3.
Wright, possibly in co-authorship with his son Sewall Wright, in the context of simultaneous equations in his 1928 book The Tariff on Animal and Vegetable Oils.. Suppose we are considering a regression with one variable and a constant (perhaps no other covariates are necessary, or perhaps we have partialed out any other relevant covariates): (the exclusion restriction), then IV may identify the causal parameter of interest where OLS fails.
Because there are multiple specific ways of using and deriving IV estimators even in just the linear case (IV, 2SLS, GMM), we save further discussion for the Estimation section below.
For example, suppose a researcher wishes to estimate the causal effect of smoking on general health.
Correlation between health and smoking does not imply that smoking causes poor health because other variables, such as depression, may affect both health and smoking, or because health may affect smoking.
In statistics, econometrics, epidemiology and related disciplines, the 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 variable of interest is correlated with the error term, in which case ordinary least squares and ANOVA give biased results.
Such correlation may occur 1) when changes in the dependent variable change the value of at least one of the covariates ("reverse" causation), 2) when there are omitted variables that affect both the dependent and independent variables, or 3) when the covariates are subject to non-random measurement error.
Explanatory variables which suffer from one or more of these issues in the context of a regression are sometimes referred to as endogenous.
Students who attend the tutoring program may care more about their grades or may be struggling with their work.
This confounding is depicted in the Figures 1-3 on the right through the bidirected arc between Tutoring Program and GPA.