In a new NBER paper, Theodore Joyce notes:
Economists, on the other hand, have corrected mistakes in the original analyses, added new data, offered alternative tests and tried to replicate the association in other countries. Donohue and Levitt have responded to each challenge with more data and additional regressions. Making sense of the dueling econometrics has proven difficult for even the most seasoned empiricists.
Empirical debates can be very tricky. But the bottom line is that a positive, true result becomes more clear the more data and people look at it. If the issue becomes less clear, this favors the null that there is no effect. With GMM, instrumental variables, and interaction terms, you can torture the data to confess to anything, but when others try to replicate your results without the same bias such confessions are rarely observed.