instrumenttifunktioon

Instrumenttifunktioon, often translated as instrumental function, is a statistical concept used in econometrics and other fields to address endogeneity. Endogeneity occurs when an explanatory variable in a regression model is correlated with the error term. This correlation violates a key assumption of ordinary least squares (OLS) regression, leading to biased and inconsistent estimates.

An instrumental variable (IV) is a variable that is correlated with the endogenous explanatory variable but is uncorrelated with the error term. The instrumental function is essentially the predicted values of the endogenous variable obtained from a regression where the endogenous variable is regressed on the instrumental variable(s) and any exogenous variables in the original model.

The most common method for using instrumental variables is Two-Stage Least Squares (2SLS). In the first stage, the endogenous explanatory variable is regressed on the instrumental variable(s) and all exogenous covariates. The predicted values from this regression become the instrumental function. In the second stage, the original regression model is re-estimated, but the endogenous variable is replaced by its instrumental function (the predicted values from the first stage). This process effectively removes the variation in the endogenous variable that is correlated with the error term, yielding unbiased and consistent estimates of the other coefficients.

The validity of an instrumental variable requires two key conditions: relevance (the instrument must be correlated with the endogenous variable) and exogeneity (the instrument must be uncorrelated with the error term). If these conditions are not met, the IV estimates will still be biased. The choice of a valid instrument is crucial and often requires strong theoretical justification or careful empirical testing.