This paper addresses the problem of input selection in inferential control of multicomponent distillation columns by introducing the concept of consistency. An estimator is consistent when a feedback (multivariable) control system that uses the estimates of the controlled variables guarantees low closed-loop steady-state offset in the true unmeasured controlled variables when disturbances enter the system (and/or set-point changes are considered). A definition of this property is given, and the relations between the estimator consistency and the closed-loop steady-state offset are derived for both single-input-single-output and multi-input-multioutput systems. A multicomponent distillation column case study is presented to show that the selection of the most "precise" inputs does not necessarily guarantee the lowest closed-loop offset in the presence of disturbances, whereas the use of less precise but more "consistent" inputs leads to a well-designed estimator that guarantees a lower closed-loop steady-state offset.