Since the pioneering work by Stone(1954), a large body of literaturehas developed concerning the estimation of complete demand systems. Becausemost demand systems are nonlinear in either or both parameters and variables,estimation of the parameters of the system is usually carried out usingiterative methods. Here, it is crucial that initial estimates be selectedwith desirable characteristics, both statistically and theoretically.In this paper, we propose an alternative approach that is useful whenthere are many parameters to be estimated in the system. (1) We specify notthe indirect utility function but the direct utility function with a budgetconstraint. As the first order condition for utility maximization, we obtainthe marginal rates of substitution (MRS) equations which serve as our initialestimates of the parameters. These allow us to calculate the unobservablemarginal utility of total expenditure, and also to reestimate all the initialparameters in the system. The appeal of this approach is that it is relativelyeasy to obtain initial estimates whose values satisfy restrictions imposed bytheory. This is because MRS equations measure the relationship between onlytwo commodities, so that the number of parameters to be estimated is smallcompared to that of the whole system.In Section II we provide a detailed discussion of the theoretical model.This is followed by a discussion of the data and the estimation procedure inSection III. In Section IV, we highlight the empirical results by comparingour estimates of marginal budget shares, and elasticities of demand with thoseof previous researchers. Also, we calculate the correlation matrix of thedisturbances to examine the plausibility of an additive utility function.These are followed in Section V by some concluding remarks.