säätöfunktio

A säätöfunktio, or control function in English, is a concept used in statistical modeling, particularly in econometrics and causal inference. It is employed when dealing with endogeneity, a situation where an independent 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 of the causal effect of interest.

The core idea behind a säätöfunktio is to construct a variable that captures the variation in the endogenous regressor that is *uncorrelated* with the error term. This new variable, the säätöfunktio, is then included in the regression model along with the original endogenous regressor. By controlling for the säätöfunktio, the part of the endogenous regressor that is exogenous is isolated, allowing for unbiased estimation of the coefficients.

A common method for generating a säätöfunktio is through a two-stage least squares (2SLS) procedure. In the first stage, the endogenous regressor is regressed on a set of instrumental variables (IVs) and other exogenous variables in the model. Instrumental variables are variables that are correlated with the endogenous regressor but not directly with the outcome variable or the error term. The predicted values from this first-stage regression then serve as the säätöfunktio. In the second stage, the original regression model is estimated, including the säätöfunktio as an additional covariate.

The use of säätöfunktiot is a powerful technique for addressing endogeneity, but it relies heavily on the validity of the instrumental variables used. If the chosen instruments are weak or violate the exclusion restriction (i.e., they affect the outcome variable through pathways other than the endogenous regressor), the estimates can still be biased. Therefore, careful selection and testing of instruments are crucial when employing this methodology.