QUAIDS (obs 476) is the authors' preferred specification; LAIDS is presented only 'for comparison' and judged misspecified. || 'The importance of the quadratic expenditure terms for many commodities [is] clearly established and suggests that the LAIDS model is misspecified' (p.222) and 'There is strong evidence in favour of including the quadratic terms' (p.225)
Blundell, R., and J. M. Robin (1999): “Estimation in Large and Disaggregated Demand Systems: An Estimator for Conditionally Linear Systems.” Journal of Applied Econometrics 14(3), 209-232