A comment on consumer demand systems with binding non-negativity constraints

Wales and Woodland (1983) have proposed an econometric model to deal with non-negativity constraints in systems of demand equations. This paper points out the relationship between the Wales-Woodland model and the simultaneous equation/limited dependent variable model of Amemiya (1974). This relationship is important because Amemiya has proposed a simple estimation procedure that can be utilized for some cases of the Wales-Woodland model. The issue of internal consistency (or coherency) for models of this type is discussed. I show that internal consistency for the Wales-Woodland model is equivalent to the second-order condition for systems of demand equations without binding quantity constraints.