non-overlapping CIs in predicted probabilities after multinomial logit: can we conclude statistically significant difference? I produced the below plot of predicted probabilities after running a multinomial logit model with Stata (full code below). Questions:

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*In 2013 (for example), the 95% CIs for M, F, and U do not overlap. Can I therefore conclude that the expected probabilities are statistically significantly different (at 5% level) for these 3 groups?


*For the F group the CIs do not overlap for 2013 v 2008. Can I conclude the predicted probabilities are statistically significant (5% level) for those 2 years?
I understand if the CIs do overlap, they may or may not be statistically significantly different.
Code:
mlogit gender_n year, vce(cluster person)
margins, at(year = (2008(1)2013))
marginsplot

Plot:

Note: cross posted to Statalist but no responses.

If the 95% confidence intervals for two estimates do not overlap, you can say the two estimates are significantly different, $p < .05$ at least. There are cases where this may not be true, for instance when there is covariance between the estimates, but that shouldn't be the case here, assuming F, M, and U are different groups.
However:

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*It would be better to examine the parameter estimates for your model to find, for instance, the estimated difference between F and U in 2008, the standard error for that difference, and the associated p value.

*I don't know Stata, but you should probably double check that this plot shows confidence intervals and not standard errors (which are about half as wide). It looks like the CIs wouldn't overlap even if these turned out to be standard errors, but good to check!

*If you want to compare specific years here, and didn't plan in advance which two years to compare, you should probably be correcting for multiple comparisons.

