This is based on Baltagi and Liu (2020). (a) Derive the BLUP for an unbalanced one-way error component \(S\) periods ahead. Show that this predictor corrects the GLS prediction by a fraction of the mean of the GLS residuals corresponding to that \(i\) th individual with differing number of observations for each individual over time. (b) Using the unbalanced NLS young women data over the period 1968-1988 employed by Drukker (2003) and available in Stata, estimate the earnings equation using OLS, FE, RE, FE with AR(1), RE with AR(1) and replicate Table 6 of Baltagi and Liu (2020). (c) Forecast the logarithm of wage for the last year available for that individual (not using this last observation in estimation). Using the MSE criteria, show that the RE with AR(1) has the best performance.