The evidence looks to be in favor of this hypothesis. In states that the Heritage foundation says are highly pro-voucher, the proportion of private school students who are minorities is about 3-4% larger than expected. The difference is significant at the p=0.05 level.
In the average state, the proportion of private school students who are minority is about 12%, while the average state is about 28% minority in all K12 schools. So, 3-4% is a meaningful difference.
Methods
For my main specification, I calculate the proportion minority in the private school system for each state by the ratio (black + hispanic private school enrollment)/(total private school enrollment). For other specifications I use just black or just hispanic in the numerator. This variable is constructed using the 2011-12 Private School Survey. That is the LHS variable.
I calculate proportion minority in the whole state's school system by using K12 enrollments from the 2013 American Community Survey (5-year estimates). Again, I divide (black + hispanic total K12 enrollment)/(total K12 enrollment). Other specifications use just black or just hispanic. This is my only control variable.
I use the Heritage Foundation's summary statement on the "warmth" of the state toward voucher programs. This data is the coloring for my previous post's map of the US. This is the RHS variable.
Results
Regression results are reported: for proportion minority, for proportion black, and for proportion hispanic. The Heritage codes are L (low--not pro-voucher), M (medium), and H (high--very pro-voucher).
For all minorities:
. reg propMinorityPrivate propMinorityK12 i.heritCode, robust
Linear regression Number of obs = 50
F(3, 46) = 32.84
Prob > F = 0.0000
R-squared = 0.7282
Root MSE = .03563
---------------------------------------------------------------------------------
| Robust
propMinorityP~e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------+----------------------------------------------------------------
propMinorityK12 | .351919 .0397002 8.86 0.000 .2720067 .4318314
|
heritCode |
L | -.0390712 .0152037 -2.57 0.013 -.0696747 -.0084677
M | -.0338147 .0160216 -2.11 0.040 -.0660646 -.0015648
|
_cons | .049603 .0161733 3.07 0.004 .0170478 .0821582
---------------------------------------------------------------------------------
For just blacks:
. reg propBlackPrivate propBlackK12 i.heritCode, robust
Linear regression Number of obs = 50
F(3, 46) = 21.95
Prob > F = 0.0000
R-squared = 0.6485
Root MSE = .02338
------------------------------------------------------------------------------
| Robust
propBlackP~e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
propBlackK12 | .2662281 .0460961 5.78 0.000 .1734414 .3590148
|
heritCode |
L | -.0160938 .0098537 -1.63 0.109 -.0359283 .0037407
M | -.0077691 .0101268 -0.77 0.447 -.0281533 .0126151
|
_cons | .0348048 .0108619 3.20 0.002 .0129409 .0566687
------------------------------------------------------------------------------
For hispanics:
. reg propHispPrivate propHispK12 i.heritCode, robust
Linear regression Number of obs = 50
F(3, 46) = 34.09
Prob > F = 0.0000
R-squared = 0.8641
Root MSE = .02125
------------------------------------------------------------------------------
| Robust
propHispPr~e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
propHispK12 | .3925201 .0435877 9.01 0.000 .3047827 .4802576
|
heritCode |
L | -.0240462 .0082604 -2.91 0.006 -.0406735 -.0074189
M | -.0262611 .0087771 -2.99 0.004 -.0439284 -.0085938
|
_cons | .0200219 .0086704 2.31 0.025 .0025693 .0374745
------------------------------------------------------------------------------
We might worry that these results are driven by a few outlier states. One approach to study this is to fit the model:
reg privateSchoolMinorityProportion privateSchoolK12Proportion
take the residual--call that u--and consider the regression of the residual on the Heritage foundation coding:
reg u i.heritCode
This regression amounts to comparing three means, and so is amenable to e.g. a box-and-whisker plot.
Below I present a box-and-whisker plot for each Heritage foundation code. This plot suggests that the results are not driven by outliers.
You might be interested where particular states are on this box plot. Below I provide the full table of residuals u. A higher residual means that private schools in that state have many more minorities in them than expected.
Table of residuals for the all minorities regression.
name u heritLMH
Wisconsin .1099837 H
Florida .0987083 H
New Mexico .0819485 L
Utah .0467744 H
Maryland .0376755 L
Pennsylvania .0344789 H
New York .0344213 L
Ohio .0274519 H
Illinois .0212539 M
Wyoming .0198072 L
Massachusetts .0167609 L
Kansas .0133581 L
Arizona .012336 H
Rhode Island .0121191 M
Missouri .0107811 L
Vermont .010573 M
Texas .0099876 L
California .0092868 L
New Jersey .0090006 L
Alaska .0082151 L
Connecticut .0072463 L
Oklahoma .007045 M
New Hampshire .006892 L
Maine .0056219 M
Indiana .0049619 H
Iowa .0011721 H
Tennessee .0010776 L
Minnesota -.0017883 H
North Dakota -.0066554 L
West Virginia -.006853 L
South Dakota -.0070763 L
Virginia -.0079871 L
Nebraska -.00841 L
Montana -.0111706 L
Alabama -.0126081 L
Colorado -.017377 M
Georgia -.0186063 M
Washington -.0195273 L
Idaho -.0213236 L
Michigan -.0232335 L
Oregon -.0233791 L
Kentucky -.0299317 L
Louisiana -.0301021 H
Arkansas -.0332649 L
Hawaii -.0437874 L
North Carolina -.0478889 M
Delaware -.0511637 L
Nevada -.0542302 L
South Carolina -.0901905 L
Mississippi -.0923834 L
In response to a comment of John Kane, here's a map of these residuals. I'm not surprised by the high residual for Wisconsin, but I am surprised by the low residual for Indiana. His remark that southern states tend to have negative residuals is true.
Reflections
In a comment to a previous post, Jay asked whether in areas with private school voucher programs we observe less private school "absorption" of white students. This was in response to my discussion of Saporito and Sohoni's (hereafter S&S's) analysis, which showed that when there is a private school near a neighborhood public school, the public school has fewer white students than would be expected from the attendance zone child racial composition alone.
While I do not intend to be critical, I really think the S&S results are just a repackaging of two really simple facts: (1) white parents go to private schools more than minority parents, and (2) parents tend to live close to their schools.
For example, in an attendance zone that is 50% white and 50% black, and that has both a private and a public school, and assuming more whites go to the private school and that families don't commute too far to drop their kids off at school, purely mechanically the public school has to be more minority than 50%. S&S's results are just showing that this is true.
What they did cannot speak to the more important questions: do private schools actually take away kids that would have went to public schools? Do private schools attract whites from the suburbs to live in the inner city? Are private schools, directly or indirectly, practicing racial segregation, or is all this public-private racial sorting because of income?
If S&S's results are just a repackaging of those two statements, then Jay's hypothesis is just asking: do private schools enroll relatively more minority students when there are voucher programs available. From results presented here, it looks like the answer is yes.
Caveats
Does the Heritage foundation take into account, either implicitly or explicitly, the proportion of private school students that are minority, when it determines how friendly the state is to school choice? I don't think it does, but if it did the results I've shown could be purely because of measurement.
I am also concerned that I uncovered these results using the 2011-12 private schools survey. Surely this could not have been soon enough for the flurry of 2011 legislation on vouchers to kick in? This might attenuate my estimates--or it might suggest that the causal story I'm proposing is not true. The analysis can and should be replicated using public school enrollment figures in the CCD.
Nice! I didn't notice this go up.
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