There have been a couple of studies on this, most of which are paywalled, but there is a very interesting Master's thesis "Force-velocity Characteristics of the Leg Muscles and Anaerobic Performance in African-American and Caucasian College-aged Males" (PDF) which studies ~50 college-age males of similar levels of fitness and body composition, and found:
African-American males jumped 8 cm higher on average than the Caucasian
males. The results of this study coincide with the findings of several other studies - Barker et al. compared vertical jump performance in college football players
and found that African-Americans jumped 7.5 cm higher on average than Caucasians.
They also found that the African-Americans had a significantly lower percentage of body
fat and were significantly shorter than Caucasians...
We chose to control for body fat percentage due to the significant effect of body fat
percentage on vertical jump performance revealed by MANCOVA. Because there was
no difference in body composition between the two groups, it is unlikely that this
explains the racial difference in vertical jump performance.
There are a few possible reasons for the difference in vertical jump performance.
African-Americans may have a higher proportion of type II muscle fibers and higher
glycolytic enzyme activities, both of which would enhance anaerobic performance.
However, these variables were not measured in this study. Therefore, it cannot be
concluded that muscle fiber type or enzyme activity are the reasons for the differences in
performance shown here. Another possibility is greater leg length among African-
Americans, which has been found to significantly correlate with vertical jump
performance. Leg length was not measured in this study, but other studies have
reported that African-Americans have greater leg lengths than Caucasians.
There are a great many interesting citations in that paper which corroborate the findings. This 1988 study on 12-14 year olds also found that African-Americans had a higher average vertical leap than Caucasians, with the effect being more pronounced with boys than with girls (where it was still statistically significant).
Another study with similar findings is this one, "A comparison of anaerobic power between black and white adolescent males" from 1988 which studied ~130 high school students (age ~16).
I can't find any meta-analyses on this, but from my searching it looks like black males consistently leap higher than white males - I haven't found a single study where white males jumped higher.