Researchers estimating demand systems have often used annual data even though monthly or quarterly data are available. Monthly data may be avoided because with monthly data it becomes more difficult to specify seasonality, autocorrelation is more likely to be significant, and there is a greater chance of finding significant dynamics in demand. This paper shows how to obtain consistent and asymptotically efficient estimates of a demand system using seasonal differenced data. It also shows that several alternative estimators are either inefficient or implausible for demand systems.