[Bruce Weaver]

Fair point in #14, Jeff. I was indeed thinking of OLS models.

[Jeff Wooldridge]

Sara: May I recommend you read one of my books on the difference between a corner solution outcome and a censored outcome? With a corner solution -- which is the original Tobit application -- you see the variable you want to explain. It just happens to have discreetness. Usually the observed pile up is at zero, but sometimes at one or 100. So quantity consumed of alcohol has a corner at zero. Percent of investment in the stock market has corners at zero or one. Censored data is when we do not observe the y we want. For example, income is reported in intervals. I thought this is the situation you are in. The underlying variable you want to model is essentially continuous but it’s reported in intervals. The importance of the assumptions is different for corner solution versus censoring.

[Sara Final]

Thanks a lot for your helpful replies. In fact i have already read the part in one of your books a few times - and i will certainly read it a few more times. At that moment I think I understood it, but then I read another application case and am confused again. Like the paper I mentioned: They justify their use of tobit with censored Data due to the fact that the values can only range from 0 to 100. Since the dependent variable is share of turnover generated by Innovation, there cannot be any values below 0 neither such higher 100 %.
On top of this I wondered wether my case could fit a corner solution. Before the companies are asked about the share of turnover generated by innovation they are asked wether they had introduced any innovation to the market at all in the period considered. The pile up of at zero is due to those companies that answered no to this question. Isn't it similar to a corner solution? However, if so it would only justify left censoring and not double-censoring..
Sorry, I guess I am a little slow on the uptake.

You have already helped me a lot, thank you!