A variant on the arguments for the invariance of estimators in a singular system of equations

Allocation models, such as consumer demand systems, typically imply a degenerate error structure. The usual approach in estimation is to delete one equation, and to appeal to the results of Barten (1969), for example, that parameter estimates are invariant to the equation deleted. However such proofs of invariance are not straightforward. This paper demonstrates that such systems are observationally equivalent to structures common in the simultaneous equations literature, for which invariance is obvious, and hence provides a more transparent demonstration of conditions for invariance.