Evaluation of Estimation Methods for Simultaneous Equations Models Across Varying Levels of Data Variability

Simultaneous Equations Model (SEM) is a set of regression equations where bidirectional relationships exist between variables. SEMs are widely used to model complex systems, capture the interdependencies between different variables, and make predictions about future outcomes in a wide range of fields such as economics, markets, or health sciences. In the literature, the performance of numerous methods, both classical and Bayesian, has been widely studied in various aspects such as endogeneity or correlation. To our knowledge, the study of estimator performance under varying levels of data variability in simultaneous equation models is not well-developed. This paper aims to evaluate the performance of methods for estimating SEMs of different sizes, considering the number of variables and the variability of endogenous variables. An experimental study has been conducted applying different estimation methods, including Two Stage Least Squares (2SLS) and the Optimized Bayesian Method of Moments ( $$Bmom_{OPT}$$ ), to evaluate their performance across different SEMs. Based on our computational results, the main finding is that the performance of the methods depends on the variability of the data, with $$Bmom_{OPT}$$ being more accurate at lower levels of variability. These results could interest researchers aiming to apply SEMs in practical cases as they offer insights into selecting the estimation method while considering both the model size and data variability.