In many fields of study, including statistics and economics, an instrumental variable (IV) refers to an estimation technique or the exogenous variables (variables whose value is independent of other variables in the system) used in the estimation technique. It is common that researchers are interested in studying the causal effect of a binary treatment. In order to ensure comparability across the treatment and control groups, the researchers rely on randomization of the sample population.

At times, however, randomization is not achievable either due to budgetary, political, or even ethical constraints. In such cases, the best practice or strategy is to rely on an instrumental variable. Simply put, the method of using instrumental variables is utilized to estimate causal relationships when a controlled experiment or study is simply not feasible. Instrumental variable methods rely on appropriate **exclusion restrictions**.

### Using Instrumental Variables (IV)

When researchers employ instrumental variables, they rely on two primary assumptions. The first is that the excluded instruments are distributed independently of the error process. The other is that the excluded instruments are sufficiently correlated with the included endogenous regressors. As such, the specification of an IV model states that the excluded instruments affect the independent variable only indirectly. As a result, exclusion restrictions are considered observed variables that impact treatment assignment, but not the outcome of interest conditional on treatment assignment.

If, on the other hand, an excluded instrument is shown to exert both direct and indirect influences on the dependent variable, the exclusion restriction should be rejected.

### The Importance of Exclusion Restrictions

In simultaneous equation systems, or a system of equations, exclusion restrictions are critical.

The simultaneous equation system is a finite set of equations in which certain assumptions are made. Despite its importance to the solution of the system of equations, the validity of an exclusion restriction cannot be tested as the condition involves an unobservable residual. Exclusion restrictions are often imposed intuitively by the researcher who must then convince of the plausibility of those assumptions, meaning that the audience must believe the researcher’s theoretical arguments that support the exclusion restriction.

The concept of exclusion restrictions denotes that some of the exogenous variables are not in some of the equations. Often this idea is expressed by saying the coefficient next to that exogenous variable is zero. This explanation may make this restriction (hypothesis) testable and may make a simultaneous equation system identified.