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# Re: st: Restated: shortfall analysis - logit question

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: Restated: shortfall analysis - logit question Date Wed, 02 Jun 2004 12:10:17 -0500

```At 05:30 PM 6/1/2004 +0000, David wrote:
```
```Thank you Stephen.  I will be more specific.  From the logit model I
would like to be able to determine the overall shortfall of
promotions by calculating the expected number of promotions
(predicted from the model) for the minority group and subtracte this
from the actual number of promotions.  Is there a nice Stata
shortcut that does this and also gives a t-Stat for this shortfall?

Thanks everyone (again)
```
Given that you include a dummy variable for African American, I would think that there would be no remaining shortfall, i.e. the dummy variable already adjusts for any shortfall for one race relative to another. If the AA dummy is significant and negative, I think you've already got a test statistic for the shortfall.

To do what I think you want to do - There may be better ways, but my inclination is to approach this as a "what if" sort of problem. Suppose that African Americans had the same compositional characteristics as other groups (e.g. same levels of education, years of job experience, whatever), but the effects of these variables on African Americans stayed the same as they are now. What would the gap be between African Americans and others then?

Put another way, African Americans may get fewer promotions than whites because they have lower levels of education (compositional differences); but they may also get fewer promotions because the effect of education is smaller for whites than it is for blacks (differences in effects). Once you control for differences in composition, how much of a gap (if any) remains between racial groups?

Using an OLS regression framework, I give an example of this approach at

http://www.nd.edu/~rwilliam/stats2/l44.pdf

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Richard Williams, Notre Dame Dept of Sociology
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