Dear community,
Firm size distributions are often found to follow a Pareto distribution with a power law exponent near 1 (Zipf’s law). Following this literature, we estimate a Pareto distribution for establishment sizes (for Germany) and find a power law exponent less than 1. It was suggested to us that an exponent less than 1 is somehow odd as it implies that the whole economy will be overtaken by a single firm. I understand that a Pareto distribution with a power law exponent less than 1 has no finite mean, but I do not understand how this leads to a process where a single firm overtakes the economy. What is going on in an economy with this kind of firm size distribution? Is there a literature on that?
Best wishes
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Can you a bit more specific on your data set?
What model you are exactly using?
I do not exactly know the answer to the one-firm question, but suspect that this is a consequence of a zero-one theorem in probability theory, in particular, of its version called infinite monkey theorem (see the wikipedia). Loosely speaking, if you have a non-integrable distribution, EVERY firm will either become arbitrarily large or disappear with probability one.