term. Unlike , cannot be directly observed. Unlike the random effects model where the unobserved is independent of for all , the fixed effects (FE) model allows to be correlated with the regressor matrix . Strict exogeneity with respect to the idiosyncratic error term is still required. Statistical estimation Fixed effects estimator Since is not observable, it cannot be directly controlled for. The FE model eliminates by de-meaning the variables using the within transformation: where , , and . Since is constant, and hence the effect is eliminated. The FE estimator is then obtained by an OLS regression of on . At least three alternatives to the within transformation exist with variations. One is to add a dummy variable for each individual (omitting the first individual because of multicollinearity). This is numerically, but not computationally, equivalent to the fixed effect model and only works if the sum of the number of series and the number of global parameters is smaller than the number of observations. The dummy variable approach is particularly demanding with respect to computer memory usage and it is not recommended for problems larger than the available RAM, and the applied program compilation, can accommodate. Second alternative is to use consecutive reiterations approach to local and global estimations. This approach is very suitable for low memory systems on which it is much more computationally efficient than the dummy variable approach. The third approach is a nested estimation whereby the local estimation for individual series is programmed in as a part of the model definition. This approach is the most computationally and memory efficient, but it requires proficient programming skills and access to the model programming code; although, it can be programmed even in SAS. Finally, each of the above alternatives can be improved if the series-specific estimation is linear (within a nonlinear model), in which case the direct linear solution for individual series can be programmed in as part of the nonlinear model definition. First difference estimator An alternative to the within transformation is the first difference transformation, which produces a different estimator. For : The FD estimator is then obtained by an OLS regression of on . When , the first difference and fixed effects estimators are numerically equivalent. For , they are not. If the error terms are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator. If