Kontrollfunktsioonide

Kontrollfunktsioonide, often translated as control functions, refers to a concept in statistical modeling, particularly in econometrics and biostatistics. It is a method used to address endogeneity, a common problem where an explanatory variable is correlated with the error term in a regression model. This correlation can lead to biased and inconsistent estimates of the model's coefficients.

The core idea behind control functions is to explicitly model the unobserved factors that cause the endogeneity. These unobserved factors are typically represented by a function that is derived from the first-stage estimation of the endogenous variable. This derived function, the "control function," is then included as an additional explanatory variable in the second-stage regression of the main model.

By including the control function, the model attempts to account for the correlation between the endogenous variable and the error term. This allows for the estimation of unbiased and consistent coefficients for the other explanatory variables. The specific form of the control function depends on the assumptions made about the distribution of the error terms. For example, in a linear model with normally distributed errors, the control function is often the conditional expectation of the error term given the observed covariates.

The application of control functions requires a valid instrument or a way to identify the source of endogeneity. It is a powerful technique for dealing with selection bias and other forms of endogeneity that might arise in observational data. However, the effectiveness of the control function approach relies heavily on the correct specification of the underlying model and the distributional assumptions made.