Using instrumental variables ("IV") is a classical method to deal with endogeneity of explanatory variables. Since benefiting from aid can be seen as an endogenous explanatory variable of the performance of a firm in a linear regression context, it is natural to use instrumental variables to evaluate the effect of aid.
For the evaluation of State aid, an instrumental variable is a variable that can explain the fact of receiving the aid but has no direct impact on the other unobserved determinants of the outcome that has to be measured. Instrumental variables then allow focusing on the participation in the scheme without interference from the selection effects. For illustrative purposes, one can see the logic of an instrumental variable as follows: In a first step, programme participation is regressed on all the exogenous variables, including the instrumental variables. Second, the participation variable (the variable indicating whether the aid was received) is replaced with the participation as predicted in the first step: this expected participation is not correlated with the unobserved element that also determines the outcome.