Cream Skimming and Pushout of Students Participating in a Statewide Private School Voucher Program

Cream Skimming Estimation

Our sample for the cream skimming analysis consists of all voucher-eligible students in TPSs (for a sample description, please see Supplementary Appendix Table A1 in the online version of the journal). For an analysis of student movement patterns consistent with the claim of cream skimming, we assess the likelihood of voucher students moving to a private school (the move could be either structural or nonstructural move) in a given year t who are classified as high-achieving, low-discipline, or not an ELL or special education student in the previous year t − 1. We compare this likelihood to all other voucher-eligible students who may make any move without a voucher. We estimate this using achievement as a measure of performance in Equation 1:

Y i t = δ V P i t + θ H A i t − 1 + γ V P i t H A i t − 1 + λ t + μ i t .

(1)

Here, Y i t = 1 if student i makes a move from their public school in between years t − 1 and t. We identify the differential patterns of mobility across students through three indicators. The first ( V P i t ) denotes students who first received a voucher and transitioned into a private school as of year t. The second ( H A i t − 1 ) indicates all students who are high-achieving at time t − 1. We estimated separate models for the different indicators of high-achieving students, including being above the school average, above the state 75th percentile, and above the state 90th percentile. The third ( V P i t H A i t − 1 ) is an interaction between the first two terms, specifically denoting voucher students who were high-achieving in their public school the year prior (t − 1) to making a transition to a private school in year t. We include a series of year fixed effects ( λ t ) to account for unobserved differences in transition rates between years.

In the cream skimming analysis, we want to know whether the rate in which high-achieving students transition from their public school to a private school after receiving a voucher (i.e., voucher users) is different from the rate in which high-achieving students—who are also voucher-eligible—transition from their public school to any other schools without a voucher. We capture this difference in the coefficient (γ) on the interaction term ( V P i t H A i t − 1 ) in Equation 1. A significant and positive γ suggests that higher-achieving students are more likely to receive a voucher and transition to a private school than high-achieving, voucher-eligible students are to make any other school transition without a voucher. The baseline likelihood that all high-achieving students (voucher-using and voucher-eligible) are to make any school transition relative to all low-achieving students is already captured in θ, so γ distinguishes the high-achieving, voucher-using difference in likelihood of transition. This estimate yields descriptive information about whether there are patterns in the data consistent with the claim of private schools cream skimming higher-performing voucher students.

Using this same structural model, we also examine whether students with below-average number of discipline infractions, non-ELL, and non-special education students are more likely to transfer to private voucher schools. In these analyses, a low-discipline, ELL status, or special education status indicator replaces the high-achieving student indicator, H A i t − 1 in both the main effect and interaction term. Here, a significant and positive γ would suggest evidence consistent with the claim that less disruptive or less-costly-to-educate students are more likely to receive a voucher and attend a private school than less disruptive or less-costly-to-educate voucher-eligible students are to switch schools.

Pushout Estimation

Our sample for the pushout analysis consists of all voucher-using students in private schools and all voucher-eligible students in TPSs (for a sample description, please see Supplementary Appendix Table A2 in the online version of the journal). Following a similar approach to our cream skimming analysis, we assess the likelihood of voucher students moving to a TPS (in this case, only a nonstructural move) in a given year t who are classified as low-achieving, or a special education or ELL student in the previous year t − 1. We want to compare this likelihood to all other voucher-eligible TPS students with the same classifications who make a move. We estimated this using achievement as a measure of performance in Equation 2:

Y i t = δ V P i t − 1 + θ L A i t − 1 + γ V P i t − 1 L A i t − 1 + λ t + μ i t .

(2)

Here, Y i t = 1 if student i makes a nonstructural move from their school in between years t − 1 and t. In the pushout model, V P i t − 1 denotes students who are receiving a voucher and enrolled in a private school as of year t − 1. The term L A i t − 1 indicates all students who are low-achieving at time t − 1. We estimated separate models for different indicators of low-achieving students, including being below the school average, below the state 25th percentile, and below the state 10th percentile. The interaction between the first two terms, V P i t L A i t − 1 , denotes voucher students who were low-achieving in their private school at time t − 1. We also included year fixed effects ( λ t ).

In the pushout analysis, the coefficient of interest (γ) on the interaction term ( V P i t L A i t − 1 ) in Equation 2 measures the added difference in the relative likelihood by which low-achieving voucher students exit a public school for a private school. To make sense of this estimate, it must be combined with other coefficients to assess patterns consistent with the claim of pushout of voucher students from private schools that is different from other relevant comparison groups.

First, we want to know whether the rate in which low-achieving, voucher-using students transition from their private school to a public school is different from the rate in which low-achieving students—who are also voucher-eligible—transition from their public school to any other schools without a voucher. Because not all voucher students change schools, we must also account for the baseline transfer rate of all voucher students (δ). A significant and positive linear combination of δ and γ compared with θ suggests evidence that lower-achieving voucher-using students are more likely to exit a private school above and beyond the baseline rate of low-achieving, voucher-eligible TPS students who make a transition (θ).

Second, we want to know whether the rate in which low-achieving, voucher-using students transition from their private school to a public school is different from the rate in which high-achieving, voucher-using students transition from their private school to a public school. Here, we must account for θ, which captures the baseline likelihood that low-achieving students are to transition schools, relative to high-achieving students. A significant and positive linear combination of θ and γ compared with δ suggests evidence that lower-achieving voucher-using students are more likely to exit a private school above and beyond the baseline rate of high-achieving voucher-using students who make the same transition (δ). Together, these estimates yield descriptive information about patterns in the data consistent with the claim of private schools pushing out lower-performing voucher students.

Using this same structural model, we also examined whether voucher-receiving ELL or special education students are more likely to transfer out of private voucher schools. In these analyses, an ELL or special education status indicator replaces the low-achieving student indicator, L A i t − 1 in both the main effect and interaction term. Here, a positive and significant estimate of the combination of δ and γ compared with θ would be consistent with the claim that more-costly-to-educate voucher students are more likely to exit a private school relative to the exit rate of more-costly-to-educate voucher-eligible students enrolled in TPSs. Similarly, a significant and positive linear combination of θ and γ suggests evidence consistent with the claim that more-costly-to-educate voucher students are more likely to transition than their less-costly voucher peers.

Cream Skimming Results

We display our cream skimming results in Table 1. The coefficient of interest is the interaction term with statistical significance for these estimates denoted with asterisks. Overall, we find little evidence consistent with the claim that private schools are cream skimming higher-performing, less disruptive, or less-costly-to-educate students from TPS. While all high-achieving students are less likely to transition schools, the differential transition rates for high-achieving voucher students are mostly null across all subjects and achievement thresholds. The other measures we use to assess cream skimming students yield no evidence consistent with the claims of private schools cream skimming less disruptive or less-costly-to-educate students.

Pushout Results

We display our pushout results in Table 2. Italicized estimates indicate a statistically significant difference in the likelihood of low-achieving/more-costly-to-educate voucher students moving from their private school (the sum of the voucher private baseline transition and the interaction term) compared with their low-achieving/more-costly-to-educate voucher-eligible peers who move from a TPS. Bold estimates indicate a statistically significant difference in the likelihood of low-achieving or more-costly-to-educate voucher students moving from their private school (the sum of the low-achieving/ELL/special education main effect and the interaction term) compared with their high-achieving or less-costly-to-educate voucher peers.

Overall, we find that lowest-achieving voucher students are exiting private schools at a modestly higher rate than their similarly low-achieving voucher-eligible TPS peers as well as their higher-achieving voucher private school peers. The transition rate for low-achieving voucher students is higher than their low-achieving, voucher-eligible TPS peers by 1 to 3 percentage points. Considering that voucher students in general are a percentage point less likely to leave private schools, a statistically significant differential transition rate of 2 percentage points only holds for the lowest-achieving students (below the 10th percentile statewide) when looking at the linear combination of these two terms. Low-achieving voucher students are also 3 to 9 percentage points more likely to move from a private school than their higher-achieving voucher peers. This evidence is consistent across all achievement thresholds.

When looking at the potential pushout of ELL and special education voucher students, the evidence is mixed. Voucher ELL students are 2 percentage points less likely to move from their private school as compared with voucher-eligible ELL peers who move from their TPS. Voucher ELL students are also 4 percentage points less likely to make a transition from their private school than their non-ELL voucher peers. Meanwhile, voucher special education students are 3 percentage points more likely to move a transition from their private school than their non-special education peers, though this rate is similar to the rate at which special education students move from a TPS.