Instrumental Variable Design

To estimate the causal effect of an independent variable on a dependent variable, the instrument variable design aims to identify a third variable – the instrument – that is correlated with the independent variable and uncorrelated with the dependent variable. Thus, subjects “are assigned at random or as-if at random, not to the key independent variable of interest, but rather to this instrumental variable” (Dunning, 2012, p. 87). “Good” instrumental variables need to fulfill two conditions (see Semadeni, Withers, and Certo, 2014, p. 1072): First, the instrumental variable needs to be relevant, which refers to the strength of the correlation between the instrumental variable and the endogenous independent variable. The stronger the correlation, the better the instrument, and the better the instrument, the more accurate are the estimates and standard errors (see Semadeni, Withers, and Certo, 2014). Second, the instrumental variable needs to be exogenous, which means that the instrumental variable needs to be uncorrelated with the error term. Indeed, even low correlations between the instrumental variable and the error term lead to severely biased estimates (Semadeni, Withers, and Certo, 2014).