kontrollfunksjonsstrategier

Kontrollfunksjonsstrategier, often translated as control function strategies, are a methodological approach used in econometrics and statistics to address endogeneity issues in regression analysis. Endogeneity arises when an independent variable in a model is correlated with the error term, leading to biased and inconsistent parameter estimates. Control function strategies aim to explicitly model and account for this correlation.

The core idea is to transform the endogenous regressor such that the transformed variable is uncorrelated with the error term of the original equation. This is typically achieved by first regressing the endogenous variable on a set of instrumental variables and other exogenous covariates. The residuals from this first-stage regression, known as the control function, capture the part of the endogenous variable that is correlated with the error term in the outcome equation.

This control function is then included as an additional regressor in the original equation. By including the control function, the researcher effectively removes the endogeneity from the original endogenous variable, allowing for consistent estimation of the parameters of interest. This method is particularly useful when valid instruments are difficult to find or when the functional form of the relationship between the endogenous variable and its determinants is known or can be reasonably assumed. The validity of the control function approach relies on correctly specifying the first-stage regression and ensuring that the control function captures all sources of endogeneity.