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sample selection and corner solution model

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Hi Statalist, I'm currently working on log-linear model to explain FDI stock that takes zero and strictly positive values (the well known gravity model). Because, I have log linearised my model, I have sample selection problem that I can address with Heckman selection model. Moreover, I have a high presence of zero in the stock level (around 60% percent). After discussing with my supervisor, I don't think my zeros are "true zeros". So I have to use double hurdle models.

However, I don't think double hurdle models work well with log linearised dependant variable. Did someone already had the same problem?

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