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Beginning with Poisson and compound Poisson models, which involve strong assumptions, a variety of possible stochastic models and their implications are discussed. A number of estimators and their properties are considered in the light of uncertainty about the data generation process. The paper also considers the role of tests in sequential revision of the model specification beginr ing with the Poisson case and provides a detailed application of the estimators and tests to a model of the number of doctor consultations.<\/jats:p>","DOI":"10.1002\/jae.3950010104","type":"journal-article","created":{"date-parts":[[2007,7,12]],"date-time":"2007-07-12T10:06:32Z","timestamp":1184234792000},"page":"29-53","source":"Crossref","is-referenced-by-count":1228,"title":["Econometric models based on count data. Comparisons and applications of some estimators and tests"],"prefix":"10.1002","volume":"1","author":[{"given":"A. 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