FINITE SAMPLE PERFORMANCE OF ORDINARY LEAST SQUARES , INSTRUMENTAL VARIABLES , AND GENERALIZED METHOD OF MOMENTS ESTIMATORS UNDER WEAK INSTRUMENTS AND HETEROSKEDASTICITY: EVIDENCE FROM MONTE CARLO SIM

Adamu Jibrilla , Usiju Peter , Hope Elijah Tumba , Tope Isaiah Omotosho and Felix Bunu Bello
Volume 5 Issue 7

Abstract

This study investigates the finite sample performance of Ordinary Least Squares (OLS), Instrumental Variables (IV), and Generalized Method of Moments (GMM) estimators in the presence of endogeneity, weak instruments, and heteroskedasticity. While the asymptotic properties of these estimators are well established in econometric theory, their reliability in small and moderate samples remains a critical issue for applied research. To address this gap, the study employs a Monte Carlo simulation framework based on a controlled data-generating process that systematically varies instrument strength, sample size, and error variance structure. The performance of the estimators is evaluated using bias, variance, mean squared error (MSE), and coverage probability. The results show that OLS is consistently biased under endogeneity but maintains relatively low variance, making it competitive in terms of MSE when instruments are weak. IV estimation effectively corrects for endogeneity when instruments are strong but becomes highly unstable in the presence of weak instruments, exhibiting substantial bias and inflated variance. GMM demonstrates efficiency gains under heteroskedasticity and outperforms IV in large samples, however, it shares similar vulnerabilities to weak instruments, particularly in small samples. Overall, the findings highlight the importance of the bias–variance trade-off and emphasize that estimator performance is highly dependent on instrument strength and sample size. The study provides practical guidance for researchers on estimator selection and underscores the need for careful diagnostic testing in empirical applications. Keywords: OLS, Instrumental Variables, GMM, Weak Instruments, Monte Carlo Simulation

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