## ABSTRACT

This chapter talks about a modeling problem in which there are M dependent variables, and these dependent variables are constrained to sum to a known, non-stochastic value. The assumption of accurate specification is crucial to this chapter for two reasons: It makes the specification of the model invariant with respect to the choice of the constraint item (CI); In general, the presence of specification error complicates the stochastic properties of the model in such a way that only limited conclusions can be drawn as to the properties of the coefficient estimates. Accurate specification simplifies the stochastic nature of the model and thus allows the derivation of estimates with certain optimal properties. The analysis of non-stochastic explanatory variables will also apply to the case of stochastic explanatory variables which are independent of the error terms, with the results taken as conditional upon the explanatory variables.