Among the many demand specifications in the literature, the Rotterdam model and the Almost Ideal Demand System (AIDS) have particularly long histories, have been highly developed, and are often applied in consumer demand systems modeling. Using Monte Carlo techniques, we seek to determine which model performs best in terms of its ability to recover the true elasticities of demand.In applications, the AIDS model has been used in linearized form, where the linearization is accomplished by the choice of a price index to replace the price aggregator function that is within the full nonlinear model. Since the Rotterdam model also is linear in a very similar form, the comparison of the Rotterdam model and the AIDS model has been the subject of much speculation in the literature. We derive the formulas for the AIDS model's elasticities, when the Törnqvist or two modified versions of the Stone price index are used to linearize the model. We not only compare the resulting linearized AIDS model with the Rotterdam model, but also with the full nonlinear AIDS.

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