Among basic aims of empirical research is to separate causal relationships between economic phenomenons. Due to limited possibility for conducting experimental research, analyses based on cross-sectional data are performed instead, which can be characterised as an observational study. Such a study pertains to programs, an intervention or policy analyses that influence economic environment. As a result, natural experiment is created. The key issue for modelling correctness is a distinction between causal factors and their effects. It is in interest to researchers, to measure the average treatment effect on the treated (ATT). The problem becomes more complex, when treatment status is a function of the same observed characteristics as the outcome variable. In such a case, we shall discuss an endogenous nature of the effect. Running public support program or intervening on the market causes an effect on part of, not whole population. Selection phenomena appears, when observed or unobserved characteristics simultaneously influence the fact of being part of the sample and magnitude of the analysed issue. In such situations, selection bias arises often. The selection model is based upon the utility theory. Heckman put in mathematical terms Roy's concepts that assumed that one observes only the selection of best available alternatives. The idea to treat not random selection problem analogously to the functional form specification error as well as to link it with the idea of microeconomics utility theory sets out a framework for the analysis. The treatment effect model is very closely related to sample selection model and may be treated as its more restricted variant. Its advantage is simplicity of modelling and evaluating outcomes, having characteristics of a program. It places additional restrictions on the parameters of the estimated model and undertaking differing assumptions about distribution of the dependent variable. The control function method is an application of the estimator correction due to a not random selection of observation to the sample needed to solve a problem of endogeneity of explanatory variables. It allows for simultaneous inclusion, in the model used for evaluation, of endogenous variables and not random sample selection problems. Moreover, its advantage it that it allows for easy extension to more complex selection processes. Methods for analysing data from an observational study data differ from standard econometric methods. In case when the state under treatment is not based on the nature of units and explanatory variables, then the natural experiment has characteristics of controlled experiment. The situation is more complicated if the effect state is correlated with explanatory variables. In this article is explained for what reason observational study data are influenced by non-random selection. The usage of models concerning the non random selection to analyse data from observational studies is presented. Additionally, it has been shown that the model with sample selection and the model with endogenouos treatment can be both transformed to a common structural form.
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