This paper presents estimation of panel data regression models with individual effects. We discuss estimation techniques for both fixed and random effects panel data regression models. We derive two-stage least squares and generalized least squares estimators, and discuss their limitations. Under specified conditions, we investigate the asymptotic properties of the derived estimators, in particular, the consistency and asymptotic normality, and the Hausman test for panel data regression models with large number of cross-section and fixed time-series observations. We show that both estimators are consistent and asymptotically normally distributed and have different convergence rates dependent on the assumptions of the regressors and the remainder disturbances. We also perform simulation studies to see the performance of our estimates for large cross sections. Our simulation results show that the estimator based on the bigger sample is more consistent than the one based on the smaller sample size. We find that the two stage least squares estimator performs better in the presence of endogeneity, while the generalized least squares estimator performs better under strict exogeneity conditions. We also note that the generalized least squares estimator performs better than the ordinary least squares estimator in the absence of correlation between individual effects and the regressors.