I don’t know how this is typically measured (or measured in this specific case because I can’t find the actual paper), but do economists generally apply the same dollar threshold to everyone across the country, or do they account for regional cost of living?
Apparently the standard poverty threshold does not vary by region. There is a measure called the "Supplemental Poverty Measure" which does take into account certain cost-of-living adjustments, amongst other things. More info here: https://www.census.gov/content/dam/Census/library/publicatio...
It does not look like this research used that measure. Given the income disparity between urban and rural areas, I'm worried that this could paint a misleading picture about who exactly is suffering here.
(I'm definitely no expert here, just a lay person trying to interpret this.)
I don't think the arbitrary nature is as big of a deal as the first user suggests. If policy makers were truly optimizing for poverty rate reduction of that single metric than Goodhart's law would come into play - but they don't really do that. Other people use other thresholds and I've never seen any evidence that people just below the poverty line getting help is responsible for the shift.