The original Levitt paper on crime and abortion had
huge methodological issues and is no longer regarded as valid in the economics community. Also, the more recent 2019 Levitt paper conveniently ignores data after 2014 because the results no longer hold if you use more recent data. The simple fact seems to be that if you squint and hold your computer in a certain direction, the relationship shows up, but for most years and specifications of the key variables, the result does not hold.
Levitt is a bit of a huckster who is more interested in flashy headlines than proper methodology or replicable results. To be fair, that describes much of modern academic economics, which is part of the reason I left.
