In this paper, we propose a statistical model to characterize the null hypothesis of the random product size distribution for multi-product exporters. It serves as a benchmark to test the empirical facts and model predictions. We ask which stylized facts that characterize multi-product exporters and motivate such theories as core competencies, productivity being a driver of both scope and scale, and economies of scope among others, are spurious, and which are informative. The benchmark model also provides alternative moments to test the validity of these theories.

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