This paper investigates the efficiency of four methods of estimating panel data models (Pooling (OLS), First-Differenced (FD), Between (BTW) and Feasible Generalized Least Squares (FGLS)) when the assumptions of homoscedasticity, no autocorrelation and no collinearity are jointly violated. Monte-Carlo studies were carried out at different sample sizes, at varying degrees of heteroscedasticity, different levels of collinearity and autocorrelation all at different time periods. The results from this work showed that in small sample situation, irrespective of number of time length, FGLS estimator is efficient when heteroscedasticity is severe regardless of levels of autocorrelation and multicollinearity. However, when heteroscedasticity is low or mild with moderate autocorrelation level, both FD and FGLS are efficient, while BTW performs better only when there is no autocorrelation and low degree of heteroscedasticity. However, in large sample with short time periods, both FD and BTW could be used when there is no autocorrelation and low degree of heteroscedasticity, while FGLS is preferred elsewise. Meanwhile, Pooling estimator performs better when the assumptions of homoscedasticity, independent of error terms and orthogonality among the explanatory variables are justifiably valid.