Thanks for the insightful comment. I hadn’t considered that particular application of Simpson’s paradox. But really, I don’t think this is that likely, is it? I mean, you’re letting me get one statement I like “qualifications correlate with earnings in general” but give up two statements that I find likely: “qualification correlate with earnings for males (resp. females)”.
This paper looks like it says that qualifications are correlated with earnings for each subgroup. See the tables on pages 21 and 22. I say “looks like” since I haven’t actually read it and just skipped to the tables. I hope to get a chance to look at it more in depth soon.
But really, I don’t think this is that likely, is it?
I think that particular reversal is probably unlikely in general, but I can think of several plausible cases when it would exist.
Suppose that IQ positively impacts both education and income. But education has a negative effect on income, because the more educated someone is, the more they will choose to work on abstract tasks which don’t pay as highly. (A salesman earns more than mathematician, say, and the primary function of education is to convince some people that mathematicians are higher status than salesmen.) It looks like the impact of education on income is positive, because of the effect of IQ. (This is basically the same as the reversal effect we discussed, except swapping out sex for IQ.)
Suppose among workers in general, qualification has a positive impact on earnings. For one particular sex at one particular firm, the selection process might be such that qualification has a negative impact on earnings. For small firms in particular, this situation might be likely to arise by chance.
Thanks for the insightful comment. I hadn’t considered that particular application of Simpson’s paradox. But really, I don’t think this is that likely, is it? I mean, you’re letting me get one statement I like “qualifications correlate with earnings in general” but give up two statements that I find likely: “qualification correlate with earnings for males (resp. females)”.
This paper looks like it says that qualifications are correlated with earnings for each subgroup. See the tables on pages 21 and 22. I say “looks like” since I haven’t actually read it and just skipped to the tables. I hope to get a chance to look at it more in depth soon.
I think that particular reversal is probably unlikely in general, but I can think of several plausible cases when it would exist.
Suppose that IQ positively impacts both education and income. But education has a negative effect on income, because the more educated someone is, the more they will choose to work on abstract tasks which don’t pay as highly. (A salesman earns more than mathematician, say, and the primary function of education is to convince some people that mathematicians are higher status than salesmen.) It looks like the impact of education on income is positive, because of the effect of IQ. (This is basically the same as the reversal effect we discussed, except swapping out sex for IQ.)
Suppose among workers in general, qualification has a positive impact on earnings. For one particular sex at one particular firm, the selection process might be such that qualification has a negative impact on earnings. For small firms in particular, this situation might be likely to arise by chance.