Several recent papers have used annual changes and monthly data to estimate demand systems. Such use of overlapping data introduces a moving average error term. This paper shows how to obtain consistent and asymptotically efficient estimates of a demand system using seasonally differenced data. Monte Carlo simulations and an empirical application to the estimation of the U.S. meat demand are used to compare the proposed estimator with alternative estimators. Once the correct estimator is used, there is no advantage to using overlapping data in estimating a demand system.