Instrumenttimuuttujamenetelmät

Instrumenttimuuttujamenetelmät, or instrumental variable methods, are a set of statistical techniques used to address endogeneity in regression analysis. Endogeneity occurs when an explanatory variable is correlated with the error term in a model, leading to biased and inconsistent estimates of the causal effect. Instrumental variables are used to overcome this problem by providing an external source of variation that influences the endogenous variable but is not directly related to the outcome variable through unobserved factors.

The core idea is to find a variable, known as an instrument, that satisfies two conditions. First, it must be correlated with the endogenous explanatory variable. This means the instrument has a direct effect on the variable whose causal impact we want to estimate. Second, the instrument must be exogenous, meaning it is uncorrelated with the error term in the main regression equation. This implies the instrument only affects the outcome variable indirectly, through its influence on the endogenous variable.

The most common implementation is the Two-Stage Least Squares (2SLS) method. In the first stage, the endogenous variable is regressed on the instrumental variable(s) and all exogenous variables in the original model. The predicted values from this regression are then used as a proxy for the endogenous variable in the second stage, where the outcome variable is regressed on these predicted values and the other exogenous variables. This process effectively isolates the variation in the endogenous variable that is attributable to the instrument, thus removing the bias caused by endogeneity.

Instrumental variable methods are widely applied in various fields, including econometrics, epidemiology, and political science, to estimate causal relationships when experimental data is unavailable. The validity of the instrumental variable approach hinges critically on the correct identification of instruments that meet the required conditions.