FINITE SAMPLE PROPERTIES OF TOBIT AND SAMPLE SELECTION ESTIMATORS UNDER HETEROSKEDASTICITY AND NON-NORMAL ERRORS: EVIDENCE FROM MONTE CARLO SIMULATIONS
Adamu Jibrilla
Volume 4 Issue 1
Abstract
This study investigates the finite sample properties of Tobit and sample selection estimators under violations of key classical assumptions, specifically heteroskedasticity and non-normal error distributions. While these models are widely employed to address censoring and selection bias in empirical research, their reliability critically depends on correct specification of both the variance structure and the underlying error distribution. To assess their robustness, this study employs a comprehensive Monte Carlo simulation framework, implemented in Stata, across varying sample sizes and alternative data-generating processes that reflect realistic empirical conditions. The analysis considers four distinct scenarios: correct specification (homoskedastic normal errors), heteroskedasticity, non-normality (heavy-tailed distributions), and combined misspecification. Estimator performance is evaluated using standard metrics, including bias, root mean squared error (RMSE), standard error accuracy, and confidence interval coverage probabilities. The results show that under correct specification, all estimators perform well, exhibiting negligible bias and valid inference, with the full information maximum likelihood (FIML) estimator demonstrating superior efficiency. However, the findings reveal significant deterioration in estimator performance under misspecification. Heteroskedasticity induces substantial bias and inconsistency in standard Tobit and Heckman estimators, highlighting the critical role of variance specification in nonlinear models. Non-normality primarily affects efficiency and inference, leading to increased estimator dispersion and systematic under-coverage of confidence intervals, even in moderately large samples. The most severe distortions arise under combined misspecification, where both heteroskedasticity and non-normality are present. In this case, all estimators exhibit large bias, inflated RMSE, and a near breakdown of inferential validity, indicating the limitations of conventional parametric approaches. The study recommends that emphasis should be placed on conducting rigorous diagnostic tests and, where necessary, adopting more flexible estimation approaches such as heteroskedastic specifications, semiparametric methods, or robust alternatives. In addition, empirical results should be supported with sensitivity analyses across multiple model specifications to ensure the robustness of conclusions and enhance the credibility of policy and research inferences Keywords: Tobit Model; Sample Selection Model; Heteroskedasticity; Non-Normal Errors; Monte Carlo Simulation
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