This seems to be a problem with the Stata code. Disappointing but not really surprising. Stata isn't an easy language to debug and problems like this happen a lot. I wonder how much coding was done by the original author versus being coded by a research assistant.
I think that some of the biggest issues with omitted variables could have been address by using the "new" Stata interaction syntax ("new" in the sense that has been available in Stata since 10 releases ago) instead of rolling their own products and forgetting to include the main effect.
Moretti replication published in AER · HackerTrans
I think that some of the biggest issues with omitted variables could have been address by using the "new" Stata interaction syntax ("new" in the sense that has been available in Stata since 10 releases ago) instead of rolling their own products and forgetting to include the main effect.