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There are various controls detailed in the study.

For example, they checked for some class associations:

> Applicants living in better neighborhoods receive more callbacks but, interestingly, this effect does not differ by race.

and this bit:

> First, we examine whether the race-specific names we have chosen might also proxy for social class above and beyond the race of the applicant. Using birth certificates data on mother’s education for the different names used in our sample, we find little relationship between social background and the name specific callback rates.

> ...

> We also argue that a social class interpretation would find it hard to explain all of our results, such as why living a better neighborhood does not increase callback rates more for African American names than for White names.

This bit likely controls indirectly for class, as well:

> Whites with higher quality resumes receive 30 percent more callbacks than Whites with lower quality resumes, a statistically significant difference. On the other hand, having a higher quality resume has a much smaller effect for African Americans.




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