A lively discussion (here) on the Stata list takes up the question: "This variable has significant effects in the original (logit/probit/heckprobit/whatever) model. But its marginal effect is not significant. Why?"
As the ensuing (and on-going) discussion makes clear, this nuanced discussion involves, among other things, careful attention to precisely what specific hypotheses are being tested in a margins specification versus an "original" specification.
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