Instrumental variables are\u00a0powerful tools used (most often) by economists to infer causality in the absence of an experiment. \u00a0Their use is\u00a0worth the consideration of psychologists hoping to do the same thing.<\/p>\n
Instrumental variables are appropriate for use when a covariate (your independent variable) is thought to be correlated with the error term in a regression equation (by definition, an endogenous variable). \u00a0This is often a concern when an experiment, the “gold standard” for causal analysis, is lacking. \u00a0An appropriate instrument will allow consistent estimation (estimation of a parameter that converges to the true parameter value as a sample increases to infinity) even without the \u201cgold standard.\u201d \u00a0However, without such an instrument, an endogenous variable would be inconsistent and unable to approximate the true value of a parameter.<\/p>\n
Of note, a researcher should have a theoretical explanation of why\u00a0a covariate is related to the error term of a regression equation.\u00a0 For example, are there omitted X variables correlated with the error term?\u00a0 Is there possible measurement error in the X variables?\u00a0 Perhaps there is a problem of reverse causality\u2014Y could be causing X instead of vice versa.\u00a0 A selection bias could also present reverse causality.\u00a0 Any or all of these problems could exist in a given regression equation, the point is, know which one(s) likely exist\u00a0in order to make theoretical sense for the use of an instrumental variable.<\/p>\n
What makes a good instrument?\u00a0 An appropriate instrument (or instruments) consists of a variable (or variables) that is (are) correlated with the aforementioned endogenous variable, but is (are) not<\/i> correlated with the error term of the equation.\u00a0 In other words, an instrument(s) should not relate to the same possible omitted variables or have the same problem with reverse causation as the covariate, predictor variable in question.<\/p>\n