Improved Two Stage Least Square Estimation with Permutation Methods for Solving Endogeneity Problems

Abstract

This study introduces permutation methods for Two Stage Least Square (2SLS) estimation to improve accuracy and address endogeneity in econometric analysis. The research compares traditional 2SLS with newly developed permutation methods, specifically evaluating their efficiency, predictive power, and precision across various datasets. Instrumental variables were used in a two-step process, applying permutation techniques to both the instrumental variable and the estimated endogenous variable. Results indicate that the classic 2SLS method is more efficient and precise in estimating intercepts, showing the least standard deviation in exact p-values (0.2396). However, the Permute $\widehat{X}$ method outperformed in estimating endogenous variables, demonstrating higher accuracy and stability with a standard deviation of 0.1121. The study highlights that while traditional 2SLS is reliable for intercept estimation, permutation methods, particularly the Permute $\widehat{X}$ method, offer significant improvements in handling endogeneity for endogenous variables. These findings suggest that permutation methods could enhance econometric analyses by providing alternative strategies for more accurate and robust estimates. The study’s contribution lies in advancing econometric methodologies by integrating permutation methods into 2SLS estimation, providing empirical evidence of their effectiveness. The research emphasizes the importance of robustness checks and sensitivity analyses in econometric studies, advocating for a tailored approach to selecting estimation methods based on specific data characteristics and research objectives. Future research should further refine these methods and explore their application in diverse econometric contexts.