The purpose of this paper is to estimate a complete, theoretically plausible system of demand equations on microdata, using the rich detail of these data to investigate the impact of demographic variables on demand behavior. The system which we estimate is the quadratic expenditure system (QES) introduced by Howe, Pollak and Wales. We evaluate four methods for incorporating demographic variables into the demand system. Three of these procedures imply parameter restrictions while the fourth does not. Tests on the restrictions imply that, for our data, unrestricted estimation yields significantly greater explanatory power.