Abstract
This study examines how state merit-based scholarships individually and simultaneously with prepaid tuition plans influence the interstate migration of college-bound freshmen. State freshman migration percentages were examined over a 10-year period. Results of an interrupted time-series model suggested that students generally respond to merit-based tuition aid in accordance with our initial prediction based on factors influencing student choice in attending postsecondary institutions. More specifically, many students choose to attend an in-state college in order to be eligible for state merit-based scholarships. Moreover, for home states that adopted both merit-based scholarships and prepaid tuition contracts, student out-migration was further reduced over time.
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Notes
Time-series designs are similar to regression-discontinuity (RD) designs, which have recently received attention in the educational policy literature (e.g., Lesik 2006; Moss and Yeaton 2006). Technically, the RD design is a pre-post, comparison group design where individuals are assigned to treatment or control groups on the basis of a pre-intervention cut score. Scores above and below the cutoff are subsequently compared to determine treatment effects (Cook and Campbell 1979). Time-series designs depend on repeated observations over time and the introduction of a planned treatment that creates some type of hypothesized discontinuity in intercepts and slopes compared before and after the treatment was introduced.
The set of adopters at the time of the study consisted of 15 states; however, Tennessee did not issue its first monetary rewards until Fall, 2004. Therefore, any change due to it merit-based program could not be determined, since 2004 was the final year data on migration rates were available. New Jersey also implemented a pilot merit-based program in 1998 (i.e., Outstanding Scholars Recruitment Program), but the program is estimated to represent only 8% of its total aid package (citation). Other states have also developed merit-based programs in the last 2–3 years. For example, Montana passed a merit-based program in February, 2005, Massachusetts adopted its merit program in 2005, and Hawaii offered merit-based tuition support beginning in Fall, 2007.
Our estimates of student migration percentages take in to consideration the total number of students attending institutions in the states in relation to the total number of students enrolled at each time interval. This provides a control on increases or decreases in the size of the student population (so that the percentages are always in relation to changing growth in states’ college enrollments at each interval. With regard to the residency and migration of college freshmen, IPEDS collects data on (1) college enrollment in each state, (2) the number of college goers attending college anywhere, and (3) the number of each state’s freshmen enrolled in in-state institutions. To calculate “leavers,” we subtract the total number of each state’s residents enrolled anywhere (residents in college) from the number of each state’s freshmen enrolled in in-state institutions (stayers). Subsequently, to get the percentages of out-of-state freshmen, the difference between the two was divided by the total number of each state’s freshman students residing in a particular state when enrolled in an institution anywhere.
We also investigated tuition levels as a time-varying covariate within states. Temporal variation in tuition levels did not affect individual state migration trajectories.
We examined the proposition that the trend for states that adopted merit-based programs included a quadratic term for acceleration or deceleration of the rate of student migration change, but the quadratic term did not contribute to explaining policy changes after implementation (β = −0.05, t-ratio = −1.09, p > .20). The power to detect the linear effect was 0.9, and the power to detect the quadratic effect was 0.4.
We assessed the difference in slope coefficients for non-adopting states and states that adopted merit-based tuition plans. There was no differential effect in explaining student migration patterns prior to policy implementation (β non-adopting = 0.44, β adopting = 0.65, p > 0.10). The slopes for change suggest that states adopting merit-based programs actually had slightly higher rates of migration before adopting than states that did not adopt the policy.
We investigated a number of different types of growth models first (e.g., exponential, cubic, quadratic, logarithmic), to gain some sense of how the trend in the data is best displayed (i.e., in linear or non linear terms). Using several fit indices, we settled on a linear and quadratic term as best in describing the change in states’ migration status over the six data collection points. More specifically, the model with linear and quadratic term fit better than the model with just a linear term (Δχ2 = 33.03, 3 df, p = .000). Adding a cubic term did not improve the description of state trajectories (Δχ2 = 5.08, 4 df, p = .278).
Unlike the structural equation approach to modeling latent growth curves, where time scores are considered model parameters (i.e., factor loadings), in HLM the pattern of time scores (linear, quadratic) are actual data that are entered into the level-1 data set.
We tested for homogeneity of the level-l error structure to determine whether or not a more complex error structure was needed (e.g., autocorrelated errors over the time points). We found the error structure to be homogeneous (χ 2, 12 df = 17.83, p = 0.12).
The set of P + 1 random effects for individual i is a full covariance matrix, T, dimensioned (P + 1) × (P + 1), which is assumed to be multivariate normally distributed, with means of 0, and some variances and covariances between the unit-level residuals (Raudenbush and Bryk 2002).
The addition of a quadratic term for merit adopting was not significant (p > 0.10), suggesting that a linear trend was adequate to describe changes after the policy’s implementation.
The level-1 model remains the same as in Model 2. Between states, the model can be written as
π0 = β00 + β01*(ZPUB4YR) + β02*(TUITION) + r0
π1 = β10 + β11*(ADOPTPP) + β12*(TUITION) + r1
π2 = β20 + r2
π3 = β30 + β31*(ADOPTPP) + β32*(TUITION) + r3
π4 = β40
π5 = β50
π6 = β60.
For a state in which funds became available during an odd-numbered year, the next even-numbered year (e.g., 1998) became the initial status year after policy implementation (coded 0). The first period of possible observed policy change therefore would be in the next even data collection year (e.g., 2000), which would be coded 1. In this case, this migration rate after the policy was implemented would cover a 3-year period, which would seem ample to detect a change in the 2-year migration rate after the initial point of policy implementation.
First, we compared the linear and quadratic slopes representing change over time for non-adopting states with the respective linear and quadratic slopes representing change during the time before policy adoption in those states that adopted the merit-based scholarship policy. We found no significant differences in the size of either linear or quadratic slope coefficients. Second, we examined the construct validity of our coding scheme for determining the effect of policy implementation on student migration by collecting time-series data on other outcomes for which no relationship to policy implementation was proposed (Cook and Campbell 1979). We found that these time-varying covariates (i.e., state unemployment, higher education spending, state per capita income, and tuition levels at the flagship public institution in each state) were unrelated to the specific policy adoption timing in those states that adopted the merit-based policy. More specifically, if each variable shows no statistically significant jump at the specific period identified when a treatment was implemented, then the observed effect on the intended outcome variable (migration) is more plausibly attributed to policy implementation (Cook and Campbell 1979). Even though we found that these variables were unrelated to the timing of the policy’s implementation in adopting states, we did find that state expenditures in higher education were related to the each state’s migration trajectories over time, so we included it in our model along with state unemployment levels.
Within-state variations in per capita income and tuition levels at each state’s flagship public institution were also investigated preliminarily but were dropped from this model since they were not significantly related to migration trends (p > .4).
We also examined possible cubic and quadratic terms to describe the policy-adopting trajectory, but they were not significant (p > .4).
The time-varying covariates in the model (i.e., higher education spending, unemployment, and per capita income) accounted for 17% of the variance in average state level of student migration at the end of the study (2004). After controlling for the covariates, the policy effect contributed an additional 8.4% of the variance accounted for in ending student migration level.
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The authors wish to thank George Marcoulides, Scott Thomas, and two anonymous reviewers for helpful comments on earlier versions of the manuscript.
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Orsuwan, M., Heck, R.H. Merit-Based Student Aid and Freshman Interstate College Migration: Testing a Dynamic Model of Policy Change. Res High Educ 50, 24–51 (2009). https://doi.org/10.1007/s11162-008-9108-5
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DOI: https://doi.org/10.1007/s11162-008-9108-5