Comparative Analysis of Parametric and Semi-nonparametric Sample Selection Models Based on Engel Curves Estimates

In the couples of last decades several methods were developed in order to help researchers to overcome the sample selection problem and to estimate econometric models over non-randomly chosen samples consistently. All these methods can be divided into two groups: parametric ones - which impose the strong assumption about the normality of random errors joint distribution - and semi / non-parametric, which do not assume that the distribution is normal and approximate in some way the unknown density and distribution functions instead. The main research objective of this paper is to provide the comparative analysis of the estimates gained by parametric models and popular semi-nonparametric ones on the various simulations in case of two selection equations and determine the conditions when one or another method should be used. Also, an important real data application to the construction of food Engel curve on the data of Russian Longitudinal Monitoring Survey is considered. It is shown that semi-parametric methods reveal the higher performance when the distribution of stochastic components differs a lot from Gaussian, namely it has more than one mode. Conversely, if the mode of random error distribution is unique and differ from normal by heavy tails or skewness, parametric sample selection models help to obtain the estimates close to nonparametric ones or even more precise in terms of mean squared error or confidence intervals.