Maintaining parameter invariance in seemingly unrelated regressions estimation

Seemingly unrelated regressions (SUR) is an important estimation methodology in demand analysis. While possessing qualities that make it attractive to applied demand analysts, the SUR estimation technique poses several difficulties, including the lack of parameter invariance in some instances e.g. estimation of consumer demand systems with micro-level data. When data includes zero consumption, corrections used to account for censoring may result in different parameter estimates when different share equations are dropped for estimation. This article proposes an alternative estimation objective which results in invariant parameter estimates when imposing adding-up by dropping equations.