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I have a logit model

$y = \alpha + age + educ + male + year + u$

where y takes the value one if an individual exits unemployment.

When calculating the marginal effects of, say, male, after the logit - I also use stata's ability to calculate the marginal effect at year=2010.

I would like to test whether the marginal effect of male calculated at year=2010 is statistically significantly different from the marginal effect calculated over all values of "year".

Is a wald test the best method?

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Yes, you can do that, but in your model the only reason why male has a different effect on leaving unemployment is because of differences in the overall rate at which people leave unemployment. This is rather mechanical. What you are probably interested in is including interaction effects between male and year.

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  • $\begingroup$ Maarten, this point has been raised at a recent seminar.. but has caused me confusion. I don't understand well the intuition as to why the marginal effect of an interaction between male and (a new dummy) 2010 would be different to the effect of estimating the marginal effect at year=2010.. $\endgroup$ – StephenB Feb 3 '16 at 11:22
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    $\begingroup$ with marginal effects you don't estimate a new model, you just look in a different way at your existing model. So it is not as if you were estimating your logit model for just year = 2010, you just evaluated your model without interaction term at the year 2010. The only thing different in 2010 and 2011 is the intercept, which influences the marginal effects in a mechanical and usually not substantively interesting manner. $\endgroup$ – Maarten Buis Feb 3 '16 at 11:37
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    $\begingroup$ Adding to @MaartenBuis 's explanation: An interaction tests exactly what you are asking about: Is the relationship between one independent variable (here, sex) and the DV different at different levels of another variable (here, year). $\endgroup$ – Peter Flom Feb 3 '16 at 11:48

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