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We propose a novel procedure, built within a Generalized Method of Moments framework, which exploits unpaired observations (singletons) to increase the efficiency of longitudinal fixed effect estimates. The approach allows increasing estimation efficiency, while properly tackling the bias due to unobserved time-invariant characteristics. We assess its properties by means of Monte Carlo simulations, and apply it to a traditional Total Factor Productivity regression, showing efficiency gains of approximately 8-9 percent.