Since the path-breaking work of Stone (1954), demand systems which imply linear Engel curves or linear (quasi-homothetic) preferences have been popular in both theoretical and empirical research. The theoretical attraction of linear preferences lies in the aggregation theorems of Gorman (1953, 1961), while the empirical attraction is ease of interpretation and estimation of the under lying parameters. The most common linear system used in empirical work is the Linear Expenditure System (LES) introduced by Stone. As is well known, this system also assumes additive separability, which is unlikely to provide a reasonable description of consumer behaviour when there is significant relative price variation (see Deaton (1974)).

There have been several generalisations of the LES. Pollak (1971) proposed one which preserved separability and linearity of Engel curves but allowed marginal budget shares to depend on prices. Blackorby et al.(1978) following the work of Diewert (1971) and Brown and Heien (1972) generalise the LES so as to relax the restrictive separability assumptions. However, their generalisa tions of the LES preserve the linearity of Engel (income-consumption) curves which, despite its theoretical attractions, may itself be at odds with the observed patterns of consumers' expenditures. In this paper we propose and estimate a system that allows for non-linear Engel curves and nests both a non-separable generalisation of the LES and the LES itself. The advantage of such a nesting is that it permits a test of linear preferences independently of any further test of separability. The Quadratic Expenditure System of Howe et al.(1980), for example, does nest the LES but does not allow a separate test for additive separability. Rejection of the LES assumptions, implicit in the significance of the quadratic term in such a system, could occur for reasons of non-separable and/or non-linear preferences. There are several other demand systems that do not impose a priori the linearity or separability restrictions. In particular, the Almost Ideal Demand System of Deaton and Muellbauer (1980 b) has the additional computational attraction of being linear in variables. However, like the Translog System of Christensen et al.(1975), it does not easily nest the linear preference model. We have, in this paper, deliberately chosen two levels of aggregation over households, since we suspect the degree of non-linearity in the Engel curve to be more severe in pooled cross-section than in time series data. The wide