An important purpose in combining time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables. Using exogeneity restrictions and the time-invariant characteristic of the latent variable, we derive (i) a test for the presence of this effect and for the over-identifying restrictions we use, (ii) necessary and sufficient conditions for identification, and (iii) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups or Balestra-Nerlove estimates--particularly, a significantly higher estimate of the returns to schooling.