Abstract: We consider the general problem of estimation and testing from a sequence of overlapping moment conditions generated by incomplete or rotating panel data. The crucial idea of our suggested method is to separate the problem of moment choice from that of estimation of optimal instruments. We propose a cross-sample GMM estimator that forms direct estimates of individual-specific optimal instruments pooling all the information available in the sample. We compare cross-sample GMM with the pooled and expanded GMM estimators discussed in Arellano and Bond (1991) for dynamic linear models with fixed effects. Cross-sample GMM is asymptotically equivalent to expanded GMM and asymptotically more efficient than pooled GMM. Moreover, Monte Carlo experiments and an empirical illustration show that, contrary to expanded GMM, cross-sample GMM performs well in finite samples, even with severe unbalancedness.