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Under the first system, there is a different and independent random sample of<jats:italic>N<\/jats:italic>consumers in each period and each consumer makes only a single purchase decision. Under the second system, the same<jats:italic>N<\/jats:italic>consumers make a purchase decision in each of<jats:italic>T<\/jats:italic>periods. Interestingly, there exists an asymptotic link between these two systems, which has important implications for the estimation of these demand models. The proposed methods are illustrated using simulated and real data. 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