ABSTRACTConstrained utility maximization underlies much consumer behavior in economics. Opportunities for solving important problems are ever present. However, most potential applications remain potential because existing software packages are not able to estimate the systems of equations necessary to identify the utility function. At least three features often conspire to make these problems intractable: the size of the system of equations that must be estimated, the lack of any theory for imposing zero restrictions on many of the parameters of the nonadditive utility functions, and the necessity to insure negative definiteness consistent with the axioms of consumer behavior. This paper develops an approach and illustrates the stepwise least squares estimator of a group of equations by application to the demand for food items.