Estimation of Multinomial Sample Selection Models Using Machine Learning and Bayesian Methods

This study is devoted to the use of machine learning methods and Bayesian approach for evaluating econometric models with multinomial sample selection. The model proposed by Heckman has gained wide popularity in applied economics and fundamental econometric science. However, sample selection correction methods suitable for both large and small sample sizes are not sufficiently studied, and the approaches used are limited by a number of assumptions. This fact is a motivation for developing and investigating new approaches proposed in this work. Monte Carlo simulations have demonstrated the advantages of using machine learning models and Bayesian approach compared to classical methods under different data generation assumptions and sample sizes. The application of Bayesian methods allows for more accurate estimates on small sample sizes, while approaches using machine learning algorithms can outperform classical methods both in large and small sample sizes. Furthermore, the application of the proposed approaches was demonstrated on a unique dataset of football players from the five leading European leagues for the 2021/2022 season to evaluate the influence of various factors on the transfer value of football players.