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Educational policy analysis archives
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Arizona State University
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Educational policy analysis archives.
n Vol. 12, no. 21 (May 12, 2004).
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b Arizona State University ;
Tampa, Fla. :
University of South Florida.
c May 12, 2004
Income and financial aid effects on persistence and degree attainment in public colleges / Alicia C. Dowd.
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Arizona State University.
University of South Florida.
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1 of 35 A peer-reviewed scholarly journal Editor: Gene V Glass College of Education Arizona State University Copyright is retained by the first or sole author, who grants right of first publication to the EDUCATION POLICY ANALYSIS ARCHIVES EPAA is a project of the Education Policy Studies Laboratory. Articles appearing in EPAA are abstracted in the Current Index to Journals in Education by the ERIC Clearinghouse on Assessment and Evaluation and are permanently archived in Resources in Education Volume 12 Number 21May 12, 2004ISSN 1068-2341Income and Financial Aid Effects on Persistence and Degree Attainment in Public Colleges Alicia C. Dowd University of Massachusetts BostonCitation: Dowd A., (2004, May 12). Income and finan cial aid effects on persistence and degree attainment in public colleges. Education Policy Analysis Archives, 12 (21). Retrieved [Date] from study examined the distribution of financial a id among financially dependent four-year college students an d the effectiveness of different types of financial aid i n promoting student persistence and timely bachelor’s degree at tainment. The findings of descriptive statistical and logistic re gression analyses using the NCES Beginning Postsecondary Students (19 90-94) data show that subsidized loans taken in the first year of college have a positive effect on persistence. The first-ye ar distribution of aid does not close the income gap in bachelor’s deg ree attainment. Living on campus and first-year grade p oint average are the most important predictors of timely degree completion. In the latter half of the twentieth century, the st ates and federal government of the United States developed a complex higher education financing system. This system serves many purposes, among them the stimulation of private investments in higher


2 of 35 education, economic development, and the redress of inequitable access to college for groups that were traditionally excluded. The fi nancing system has many components, including direct subsidies for public c olleges and universities and financial aid for students. Direct operating subsid ies are the foundation on which states offer higher education to all citizens at a much lower price than that offered by the private sector. Further discounts on the sub sidized price are available to eligible students through grants, scholarships, and loans. In addition, a student’s ability to choose a private or public college is su pported, as financial aid is also made available to enroll in the more expensive priv ate sector ( Policy of Choice 2002). (Note 1) Alongside affirmative action, the creation of publ ic colleges and the financial aid system has been a central mechanism f or addressing economic and social inequality in the U.S. However, despite the development of this complex system over half a century, college participation i n the United States continues to show marked differences by family income ( Access Denied 2001; Ellwood & Kane, 1998; Kane, 1999 Chap.4).The higher education financing system serves studen ts from all socioeconomic backgrounds. Not surprisingly, the distribution of benefits among these groups is continually being reshaped amid competing claims fo r resources. The work-study program, grants, and subsidized loans emerged as pa rt of the War on Poverty. The federal subsidized loan program to aid low-income s tudents was institutionalized in 1965 by the Higher Education Act, and today’s Pell grants were established in 1972 as the Basic Education Opportunity Grant. Shortly t hereafter, in 1978 when the Middle Income Student Assistance Act made subsidize d federal loans available without income restrictions, the middle class was a lso firmly established as an important and powerful financial aid constituency ( Hansen & Stampen, 1981). Today, new forms of aid, such as merit-based schola rships and tax credits, appear to favor the middle and upper classes (Heller & Sch wartz, 2002; Kane, 1999; Selingo, 2002). The purchasing power of Pell grants has declined and students must finance a larger share of their education thro ugh loans. This shift in the financing burden to individuals and families has ha d a disproportionate impact on low-income students ( Empty Promises 2002; Heller, 2001). These changes may well represent a severe loss of opportunity for low -income students and failure of the financial aid system to achieve the goal of pro moting equity in higher education enrollments.At the same time, public colleges are under pressur e from state legislatures and the federal government to educate students and produce graduates at lower cost. In an era of increasing demand for college and declining fiscal resources, colleges are expected to operate more efficiently (Zumeta, 2001) State accountability programs commonly identify college graduation rates as a mea sure of institutional performance (Burke, Rosen, Minassians, & Lessard, 2 000; Burke & Serban, 1998). More recently, the federal government has also prop osed tying grant funds to graduation rates (Burd, 2003). As part of this acco untability movement and to increase the capacity of overwhelmed public campuse s, many states are urging colleges to graduate students in a timely way and t o reverse the trend of lengthening times to degree (Knight, 2002; Selingo, 2001). A recent study by the National Center for Education Statistics shows that public four-year colleges graduate students within the tra ditional period at approximately half the rate of private colleges. On average, 26% of students starting out at


3 of 35 four-year public colleges earned a bachelor’s degre e within four years. The graduation rate increases to 57% within six years ( Berkner, He, & Cataldi, 2002, p 23, Table 10). To explain low rates of persistence and degree completion in public colleges, administrators point to the diverse array of purposes and conditions under which students pursue collegiate studies today. Wor king parents who study part-time do not proceed at the pace of full-time s tudents fresh out of high school. In addition, bachelor’s degree completion differs b y income status, whether measured in four years (26% of the lowest income st udents compared to 50% of high-income students) or in six years (54% versus 7 7%) (Berkner et al, 2002, pp. 26-32, Table 10). Timely degree completion is desir able both for students, who face opportunity and direct costs as long as they are en rolled in college, and for taxpayers who subsidize each student’s place in pub lic higher education (Choy, 2002). If efficient educational outcomes are desire d, it is important to evaluate the factors that contribute to those outcomes.This study contributes to such an effort by evaluat ing the relationship between parental income and student outcomes in college, as it is mediated by different forms of financial aid. It takes the strategy of ob serving the progress of public-college students who are in the strongest po sition for timely degree completion and examining the factors that affect th eir persistence and degree attainment. Students who are financially dependent on their parents and enrolled full-time in the public four-year sector constitute the sample selected for analysis. The experiences of this group of students in a stud y of timely degree completion and financial aid are of interest for several reaso ns. Students who are dependent on their parents in their first year of college are following a traditional path to higher education. They are not yet independent adults, wit h family and employment commitments that impede degree attainment in comple x ways that are not easily mitigated by public policy interventions (Adelman, 1999). In addition, as full-time students in four-year ins titutions, their objective is very likely to obtain a degree, a goal that is less clear among community college students who may be seeking short-term vocational training or am ong part-time students who may be “testing the waters” of college. Part-time s tudents are unable to graduate in a traditional four-year period, while full-time stu dents are. Their failure to do so can more accurately be interpreted as due to academic o r financial barriers than to a partial involvement in higher education. The sample selected for analysis reduces variation to the group that has the most time to in vest in their studies and, therefore, the most realistic possibility of completing a bach elor’s degree. Having selected this relatively homogeneous sample, the study then focus es on observing whether parental income is a significant predictor of acade mic outcomes and whether different forms of financial aid reduce outcome gap s associated with income. Finally, given that students in the public sector a re first and foremost beneficiaries of direct operating subsidies from states to colleg es and universities (Note 2) taxpayers have a particular interest in their succe ssful academic attainment. Financial aid expenditures are in a sense marginal costs (albeit very large ones) to reduce financial barriers to participation in a sys tem already established at great cost with a primary purpose of ensuring equitable a ccess to higher education. While the extent to which taxpayer funds should finance e nrollment in expensive private institutions is debatable ( Policy of Choice 2002), it is clear that as states are abandoning low and no-tuition policies (Hauptman, 2 001) the provision of financial


4 of 35 aid takes on even greater importance in creating lo w-cost opportunities for higher education.Literature ReviewEducational researchers have extensively analyzed t he educational pipeline to identify the mechanisms by which low-income student s and students of color fall behind in their college aspirations (Carter, 1999; McDonough, 1994), enrollment (Heller, 1997; Jackson, 1990; Perna, 2000; St. John & Noell, 1989) and persistence in college among those who do enroll (Braxton, 2000 ; Tinto, 1975, 1987). (Note 3) The effect of tuition pricing and financial aid on persistence has received increasing attention with the development of theories that ass ign an important role to finances in determining students’ college participation deci sions (Bean & Metzner, 1985; Cabrera, Nora, & Castaneda, 1992; Paulsen & St. Joh n, 2002; St. John, Cabrera, Nora, & Asker, 2000; St. John & Starkey, 1995). Emp irical studies utilizing these theories have examined the effects of tuition and a id on within-year persistence (Paulsen & St. John, 2002; St. John, Andrieu, Oesch er, & Starkey, 1994; St. John, Paulsen, & Starkey, 1996)and multi-year persistence (St. John 1989, 1990; Stampen & Cabrera, 1988; Cabrera, Nora, Castaneda, 1993, Titus, 2000). The effect of financial aid on degree attainment ha s received considerably less attention. However, with increasing availability of data from the longitudinal Beginning Postsecondary Students (BPS) surveys, whi ch follow students for up to six years, recent reports by the National Center fo r Education Statistics (NCES) and higher education policy institutes have analyzed a wide range of factors, including student finances, and their association with both p ersistence and degree attainment (Berkner, Cuccaro-Alamin, & McCormick, 1996; Lutz Berkner et al., 2002; Bradburn, 2002; Choy, 2002; Horn & Kojaku, 2001; Ki ng, 2002; Wei & Horn, 2002). (Note 4) This study builds on these reports and educational research by St. John and colleagues (Paulsen & St. John, 2002; St. John, 1990; St. John, 1989; St. John, Andrieu, Oescher, & Starkey, 1994) focusing o n the effect of different forms of financial aid on persistence in four-year colleg es using NCES data, particularly the National Postsecondary Student Aid Study (NPSAS ). It extends the work of these researchers by studying persistence to the se cond year of college and to degree attainment.The study also draws on the findings of recent work analyzing institutional and state-level data (Note 5) in which researchers have introduced new statisti cal techniques for studying persistence, including even t history modeling (DesJardins, Ahlburg, & McCall, 2002; DesJardins, McCall, Ahlbur g, & Moye, 2002), two-stage regression with sample selection (Note 6) (Singell, 2002a), and discontinuity analysis (Bettinger, 2002). These techniques specif ically model the sequential, interrelated nature of students’ enrollment and mul ti-year persistence decisions. The results of these studies indicate that the anal ysis of cross-sectional data using single-stage regression models produces biased esti mates of the effects of financial aid on persistence. This is due to the fa ct that the personal and academic characteristics that lead students to decide to enr oll and persist in certain types of colleges also play a role in determining the level and type of their financial aid awards. Although multivariate analyses include cont rol variables for these characteristics, Dynarski (2002a) argues that varia bles measuring observable student characteristics are unlikely to provide an adequate control for unobserved


5 of 35 characteristics that are correlated with a student’ s college enrollment decisions. This study analyzes the effects of financial aid re ceived in the first year of college on outcomes in subsequent years. Though the outcome s are longitudinal, the analysis is cross-sectional, based on measures obta ined for one cohort at one point in time. This approach is consistent with prior edu cational research analyzing persistence using national data. This study draws o n the new findings and methods introduced largely in the field of economics to und erstand the direction of potential bias in the estimates and to place the findings in the context of prior research on persistence in both academic fields. Thus the liter ature review informs the current study regarding the effects of different types of a id on persistence and degree attainment; the effectiveness of financial aid in i mproving college persistence by low-income students, and the interpretation of resu lts obtained by single-stage logistic regression models.Prior research provides mixed evidence regarding th e effects of different forms of aid on persistence and degree attainment. In studie s of national data, grants, loans, and work-study awards have been found to have posit ive effects on year-to-year persistence (St. John, 1990), but negative effects on within-year persistence (St. John, Andrieu, Oescher, & Starkey, 1994; Paulsen & St. John, 2002). The results of institutional data also provide inconsistent eviden ce. DesJardins, Ahlburg, and McCall (2002) find that loans have a negative effec t on persistence, although this effect diminishes over the years in college. Singel l (2002) finds a positive effect of subsidized loans and an insignificant effect of uns ubsidized loans. Both studies find positive effects of meritand need-based grants. I n addition, Singell finds a negative effect of work-study awards. Bettinger (20 02), who focuses only on federal Pell grants, obtains inconclusive results. Clearly, further research is needed to develop a strong consensus on the effects of differ ent types of aid on persistence. The conclusions of prior researchers suggest the fi nancial aid system is failing to provide equitable access to college for low-income students. Studies of national data find family income to be consistently associat ed with higher levels of persistence, even with multivariate controls for de mographic and academic factors (St. John, 1990). Aid is found to have negative eff ects on persistence among poor and working-class students, but not among higher-in come students (Paulsen & St. John, 2002). In a study of students enrolled in the University System of Maryland, Titus (2000) also found that aid effects on secondyear persistence differ by income group. He concluded that aid amounts are not suffic ient to promote the retention of low-income students. Merit aid, which is often disp roportionately awarded to higher income students (Heller & Schwartz, 2002), is found to have positive effects by DesJardins et al (2002) and by Singell (2002), with Singell also observing a differential effect in favor of higher income stude nts. DesJardins et al find that graduation probabilities do not differ by income le vel, but this may be due to a more limited range of socio-economic status in the insti tutional data they study from the University of Minnesota. The work by Paulsen and St John (2002) and Singell (2002) demonstrates the importance of evaluating di fferences in the effects of aid on students from different income groups. (Note 7) In this study, these differential effects are evaluated by testing the significance o f interaction terms. When Singell (2002) Note 8 and Bettinger (2002) compare the results of statis tical models that do and do not control for sample select ion bias—the bias inherent in not observing the effects of factors of interest on those with characteristics that


6 of 35 systematically remove them from the sample—they fin d statistically and substantively different results. For example, Singe ll’s research indicates that institutional merit-based aid has the largest effec t on second-year enrollment, with an increase of $1,000 predicted to increase the pro bability of reenrollment by 26.4%. This effect is half of what is estimated in a model that does not control for self-selection bias. This follows from the positive correlation of academic ability and persistence. The students who received merit aid we re more likely to persist even in the absence of a scholarship. The difference in res ults is less dramatic for other types of aid, but the single-stage model appears to underestimate the effects of need-based grants and overestimate the effect of su bsidized loans and work-study awards. Bettinger (2002) also finds that an estimat ion strategy that omits from the sample students who may have been eligible but did not apply for federal Pell grants underestimates the positive effects of Pell grants on persistence. This follows from the fact that Pell grant recipients ha ve characteristics associated with withdrawal. Between the two models, the sign of the estimate changes, which indicates misestimation of both the magnitude and t he direction of the effect. Such a misestimation would mask the positive effects of means-tested grant aid and lead to an incorrect conclusion that grant aid is not ef fective in promoting the college participation of low-income students.Finally, Singell (2002) finds that the effects of a id on persistence (or “reenrollment”) smaller than but similar in direction to effects on the initial enrollment decision. These findings indicate that researchers studying p ersistence can turn to the results of enrollment studies to predict the direction of a id effects on what can be conceptualized as students’ “re-enrollment” decisio ns, though with the expectation that the magnitude of the effect is likely to be sm aller. However, the findings of national cross-sectional studies of the effects of aid on enrollment are difficult to generalize, because the findings differ by type of aid and by type of student (Heller, 1997; Nora & Horvath, 1989). Generally the results indicate that aid does promote enrollment, but, in important departures from those findings, Perna (2000) found loans have a highly negative effect on African Amer ican students, and Jackson (Jackson, 1990) found positive effects of grants fo r African American and white students, but not for those of Hispanic descent. Su mmarizing findings of quasi-experimental studies, Dynarski (2002a) shows that this body of research generally demonstrates positive enrollment effects of both grants and loans. Once again, these effects appear to differ by income and racial group. This literature review underscores the methodologic al complexity of estimating the effects of different types of aid on student decisi on-making. Student responses to different forms of aid appear to vary based on thei r income class and other personal characteristics. Whereas some studies find negative effects of aid on persistence, others find that certain types of aid have a positive effect for some groups of students. These methodological challenges and contrasting results indicate that further work is needed in this area. This study contributes to this literature by analyzing the effects of parental inc ome and financial aid on second-year persistence and timely degree attainmen t among full-time dependent students in the four-year college sector. It analyz es national data, the Beginning Postsecondary Students 90/94, which has not previou sly been examined using the methods and sample presented here. Institutional da ta tend to have rich detail on individual student characteristics, academic perfor mance, and aid packages, but typically lack information about student outcomes i n the higher education system as


7 of 35 a whole for those students who transfer. Therefore, they overestimate student attrition (Adelman, 1999, Berkner et al 2002). In t his respect, national data sets are preferable, as they allow the observation of system -wide persistence and degree attainment. Conceptual FrameworkThis study adopts a theoretical perspective describ ed by Beekhoven, De Jong, and Van Hout (2002) that combines “integration-based st udent departure models” (p.577) with rational choice theory to explain stud ent enrollment decisions across the multiple years of baccalaureate study. Tinto’s (1975, 1987) student integration model focuses on the degree of fit between student and institution and the extent to which a student’s goal commitment is reinforced by academic and social integration on campus. Cabrera and colleagues (Cabrera, Castane da, Nora, & Hengstler, 1992; Cabrera, Nora, & Castaneda, 1993) subsequentl y developed an integrated model of college persistence that combined Tinto’s theory with the “student attrition” model of Bean and colleagues (Bean and Metzner, 198 5). Bean’s model differs most prominently from Tinto’s by its inclusion of f actors outside the college environment, such as work and finances, as explanat ory variables. Through empirical testing, Cabrera et al found that the int egrated model provided a better understanding of the persistence process than could be achieved with either model individually.Similarly, Beekhoven, De Jong, and Van Hout (2002) believed that the student integration model would benefit from greater attent ion to the concept of individual agency in decision-making. Therefore, they tested a combined model of student integration theory and rational choice theory. Thro ugh an empirical test using college student data from the Netherlands, they fou nd that their “extended model” performed better than either theory independently. Their model emphasizes that student withdrawal decisions are based on their exp ectations, modified from one year to the next, of successful program completion. These expectations are influenced by the extent to which students fit into the college environment and are satisfied with their experiences, where “fit” and “ satisfaction” are constructs measured by integration theory. As these authors ex press it, “Students trying to integrate into the student community are likely to be rational actors who make cost-benefit analyses” (p. 581). Their empirical re sults are based on a longitudinal data base and provide support for the assertion tha t student integration in one period influences perceptions of the likelihood of graduating. Conversely, positive perceptions of the likelihood of graduation will po sitively affect integration (p. 597). Other researchers (DesJardins, Ahlburg et al., 2002 ; Manski & Wise, 1983; Paulsen & St. John, 2002; Singell, 2002a; Titus, 2000)have elsewhere emphasized the sequential nature of college students’ enrollment d ecisions over time. Rational choice theory (Becker, 1976, 1993; Elster, 1986)explains student enrollment decisions as a process of cost-benefit a nalysis and utility maximization. From this perspective, as the monetary and personal costs of college rise, the benefits must rise commensurately, or a potential s tudent will perceive labor market opportunities as more attractive than higher educat ion. Monetary costs are determined by direct expenses (such as tuition, fee s, and books) and the loss of foregone wages. Personal costs are largely determin ed by a person’s ability to complete and enjoy academic work. Those who are les s academically prepared or


8 of 35 able take longer to learn and endure greater aggrav ation in the process. The use of Beekhoven, De Jong, and Van Hout’s (2002) theoretic al model combining rational choice and student integration theories is particul arly appropriate for the data analyzed in this study. While the student integrati on theories include propositions modeling the effects of students’ motivations, sati sfaction, and institutional commitment, the BPS data are not rich in these vari ables. In combination with rational choice theory, which assumes students will rationally maximize their utility rather than attempting to measure psychological fac tors, these variables may be omitted, albeit with a loss of explanation of the m echanisms on campus that influence students’ institutional experiences and l oyalties. Beekhoven et al omitted measures of commitment and motivation in their comb ined model without loss of explanatory power; in fact, their model explains a greater proportion of variance than either of the theories applied independently. Further, the use of rational choice theory facilitates the integration of results from persistence studies in the field of economics, where it is a dominant theory.Study DesignData and SampleThe U.S. Department of Education National Center fo r Education Statistics (NCES) conducts the Beginning Postsecondary Students (BPS) survey as a longitudinal component of the National Postsecondary Student Aid Study (NPSAS). The BPS, which is a nationally representative survey, includ es only those students who enrolled in postsecondary education for the first t ime in the NPSAS base year; it excludes returning students who had previously stop ped out of college. This study analyzes BPS90/94, which has a NPSAS base year of 1 989-1990 and a follow-up of student outcomes in the spring of 1994. This tim e frame allows for the observation of “second-year persistence” (re-enroll ment in the second year) and “timely” bachelor’s degree completion (within five years). Use of these data to analyze student outcomes complements relatively sho rt-term analyses of within-year persistence. The exclusion of returning students ensures that the data represent a student’s full persistence and stop-out history. The results of a more recent BPS survey covering the period 1996-2001 was not available for this analysis, but those data make possible replication of the study in a more recent time period, which is desirable given changes in fi nancial aid policies and trends in the 1990s. BPS is a stratified and clustered probability sampl e, where the strata represent the different sectors of higher education and the clust ers represent geographic regions ( BPS9094 Technical report 1996).The public four-year doctoral granting and comprehensive sectors (two strata) were included in this sample. Due to the sampling design, this sub-sample is nationally repr esentative of the population of students in these two sectors. Students were retain ed in the sample if they were financially dependent on their parents and began th eir studies on a full-time basis at a public four-year institution. The resulting sampl e size for this study is 1,087 cases, which is 67% of the original 1,612 BPS cases who st arted out in public four-year institutions. These sampling decisions restrict the analysis to “traditional” students, as evidenced by the sample’s mean age of 18 years.Persistence is defined in this study as full-time e nrollment in the second year of the BPS survey (academic year 1990-91) at a public or p rivate four-year institution. This


9 of 35 definition sustains the focus of this study on stud ents who are on a traditional path towards the bachelor’s degree, as well as the focus on public institutions because only a small proportion of the sample transferred t o private colleges. This definition omitted those who left college or moved to part-tim e status (15%) and those who transferred to public two-year colleges (4%) or pri vate postsecondary (not baccalaureate) institutions. These students were co nsidered to have left the persistence track for timely bachelor’s degree comp letion. Those who transferred to private four-year colleges in the second year (.006 %) were treated as on track, given the higher rates of degree attainment in the private sector. This definition of persistence, which captures reenrollment behaviors in the second year of college that keep students on track for timely bachelor’s d egree completion, differs from other measures that focused on institutional retent ion or within-year persistence. Based on this definition, 78% of the BPS90/94 sampl e persisted from the first to the second year of college. Seventy-one percent were en rolled in the third year of the survey (with or without stop-out in year 2) and 63% were enrolled in the fourth year. Approximately 2% transferred each year to the priva te sector. Fifty-five percent of students obtained their bachelor’s degree within fi ve years. Thirty-nine percent of the sample was enrolled in the fifth year of the su rvey, which, depending on stop-out behaviors, may or may not have been the fi fth year of study for the student.MethodsThe analysis focuses on the following research ques tions: (a) What is the distribution of different types of financial aid am ong dependent students in the public four-year sector by parental income quartile ? (b) What is the influence of parental income and financial aid on reenrollment i n the second year of study at a four-year college? (d) What is the influence of par ental income and financial aid on timely (within five years) bachelor’s degree comple tion? Analyses of complex survey data, such as BPS, may b e “model”or “design”-based (Hosmer & Lemeshow, 2000; Thomas & Heck, 2001). Des ign-based analyses adjust estimates to reflect the sampling structure by using sample probability weights, the intra-class cluster coefficient, and r obust measures of standard errors, while model-based analyses proceed as if the data w ere collected as a simple random sample. This study presents a design-based a nalysis. (Note 9) This approach is of particular importance when estimatin g differences in means and proportions, where the sampling “design effect” has a particularly large impact, greater than on the estimation of regression coeffi cients (Hosmer & Lemeshow, 2000, p. 220). (Note 10) The estimation of means for variables in this stud y is subject to design effects in the range of .9 to 2.0 (Note 11) The sampling weight for cross-sectional and retrospective analyses of data from the 1994 follow-up (BPS94AWT) is applied (National Center for Educatio n Statistics, 1996). The analysis is conducted using Stata statistical softw are, version 7. Descriptive statistics are analyzed by income quart ile to characterize the relationship between income, financial aid, and oth er variables included in the regression analyses. (Note 12) Logistic regression analyses were conducted to observe the effects of factors bearing on student p ersistence and timely bachelor’s degree attainment. Income was entered first as the sole predictor. Groups of additional variables were then entered sequentially to observe their mediating effect


10 of 35 on income. A final model includes interaction terms of the different forms of aid by parental income to test for differences in the effe cts of aid by income, following recent results that the effects of aid differ by in come group (Singell, 2002; Paulsen & St. John, 2002).The magnitude of the effect of the predictor variab les is reported as odds ratios, with standard errors indicated as robust z statisti cs ( Stata 2001, User's Manual, section 23.11), and as “delta p” (change in the pro bability) statistics (Peterson, 1985).The changes in the probability of the positive depe ndent outcome are reported for variables that were significant in the final step o f the sequential regression. The “delta p” values are reported for a change from the minimum to maximum value for all variables (Note 13) and for a one-unit change at the mean for continuo us variables. For dichotomous variables, the change fr om the minimum to maximum value represents a comparison between membership in one of two groups (e.g. on or off campus residence). These changes are estimat ed with dichotomous covariates held at their modal values (as proposed by Long, 1997)and continuous covariates held at their means. (Note 14) Statistically significant differences are reported at p<.05 based on two-sided tests, with th e significance of design variables (race and income quartile) adjusted for multiple ca tegories. The direction of insignificant effects that are expected by theory a nd prior research to be significant are noted if p<.10. (Note 15) Several goodness-of-fit measures are presented. Som e statisticians argue that likelihood ratio (LR) statistics should not be used for models that include weighting and clustering, because under these conditions a “p seudo-likelihood” is estimated rather than a true likelihood (Hosmer & Lemeshow, 2 000; Scribney, 1997a, 1997b). Long (1997), on the other hand, notes the heuristic nature of logistic goodness of fit statistics and argues that the measures may appropr iately be calculated using the pseudo-likelihoods. Consistent with Long, the follo wing LR statistics are reported: the LR chi squared, McFadden’s Rsquared, and the ad justed McFadden’s Rsquared (which adjusts for increases due simply to the addition of predictors). Stata provides a Wald chi squared statistic, which is not based on the likelihood ratio, to test the significance of weighted, cluste red models. This value is also reported. (Note 16) Predictor VariablesAll predictor variables in the logistic regression models were measured in the NPSAS base year, the students’ first year of colleg e. Therefore, the predictors are conceptualized as components of the first-year expe rience. These components take on four dimensions in this study: financial, cultur al, social, and academic (as defined below).Some of the variables, such as gender, mother’s edu cation, and race or ethnicity will not change in subsequent years. Other variable s, particularly those measuring financial aid, may well change. Thus, it is importa nt to emphasize that the observed financial effects are based on a student’s situatio n in the first year. Tuition is included to control for the amount of fi nancial aid required to meet higher


11 of 35 education expenses. Tuition was defined as the annu al in-jurisdiction charge for students enrolled in their home state and as the an nual out-of-jurisdiction rate for students enrolled in other states (12% of the sampl e). The tuition price students faced in years subsequent to the first year is avai lable in the BPS90/94 data. A correlation analysis of tuition across the five yea rs of the survey shows that it is highly correlated at .97-.99, which is consistent w ith the limitation of the sample to four-year institutions and the small proportion of students exiting to the private sector. Therefore, first-year tuition is a good rep resentation of the tuition charges students faced in subsequent years.The financial variables represent different forms o f financial aid, including federal and state grants, institutional needand non-needbased grants, federal subsidized loans, and federal work-study awards. The state gra nt variable does not distinguish between needand merit-based awards, but it should be noted that these data were collected in 1989 prior to the tremendous growth in state merit scholarships. The financial aid measures are entered in dollar amount s, rather than as binary variables indicating receipt of aid. Although resea rchers have previously tested the latter approach to model the effects of aid (Nora, Cabrera, Hagedorn, & Pascarella, 1996; St. John & Starkey, 1995), recent research de monstrates a preference for the use of actual aid amounts (DesJardins, Ahlburg, & M cCall, 2002; Paulsen & St. John, 2002).The cultural group of variables includes indicators of race or ethnicity in four categories: African American (8% of the sample), Hi spanic (4%), Asian (5%), and White (the reference group, 87% of the sample). Whi le these broad categories are likely to mask differences in educational experienc es among students whose cultural heritage differs quite significantly, fine r distinctions are not possible with these data. Gender is included in this group of var iables; females are in the majority, accounting for 53% of the sample.Based on the theoretical notion of “social capital” (Coleman, 1988), which posits that parental education level facilitates human cap ital production through knowledge of college processes, norms, and networks a binary variable indicating whether the student’s mother is a college graduate is included in the analysis. The other variables in this group also represent measur es of a student’s capacity to participate in college social networks. They are de layed enrollment (a time gap between high school and college, or disassociation from one’s age cohort), living on or off campus, and the number of hours spent workin g each week. An index measuring social integration is also included, base d on a four-item scale intended to measure Tinto’s (1975, 1987) theoretical constru ct. These items, which respondents rated on a frequency scale, included ma king contact with faculty outside class; going places with friends from schoo l; spending time in student centers or participating in student programs; and p articipating in school clubs. (Note 17) Three academic variables measure academic experienc es and performance. The first is a binary measure indicating whether the st udent’s college is a doctoral-granting or a comprehensive institution. T he doctoral-granting group (57% of the sample) is likely to enroll stronger student s and to include flagship campuses. Like the social integration index, the academic int egration index is based on a multi-item scale representing Tinto’s (1975, 1987) construct. The items measure:


12 of 35 attending career-related lectures; participating in study groups with other students; talking with faculty regarding academic matters; an d talking with an advisor about academic plans. The third variable is the first-yea r grade point average (GPA). A standardized measure of academic achievement would be desirable in controlling for academic ability. While the Standardized Achiev ement Test (SAT) scores are available in the BPS90/94 data, in the sample analy zed for this study 62% of the cases were missing. Therefore the variable was not included. High school grades are also not available, but the absence of this mea sure is mitigated by inclusion of actual academic performance in college, as indicate d by the GPA. One fifth of the sample was lacking data on one or more variables in the analysis. A missing cases analysis revealed that the data lacke d a GPA for 26% of African American students, in comparison to 12% of students in other racial categories. Therefore, the values of the missing GPA cases were imputed by a linear regression using race and gender as predictors. A s maller proportion of cases (less than 5%) were missing data on the parental income a nd tuition variables. The missing values were similarly imputed. (Note 18) LimitationsThis study has several limitations. First, the anal ysis seeks to understand whether parental income is a determinant of a college stude nt’s persistence and degree attainment, even in the presence of state, federal, and institutional financial aid programs designed to remove financial barriers to c ollege. The BPS90/94 data provides detailed financial information on students ’ financial aid packages only for the first year of study. Data from subsequent years indicate whether or not students received certain forms of aid, but do not reveal ai d amounts. Therefore, the study is limited to understanding the mitigating effects of the first-year financial aid package on parental income effects. This is valuable for an alyzing second-year persistence. However, aid packages and other variables, such as campus residence and work hours, do change over a student’s four-year career, and these changes are not observed here.Second, the intention of this study (and others tha t precede it using similar methods and data bases) is to draw conclusions about the ef fectiveness of financial aid policies in reducing college participation gaps bas ed on family income. Dynarski (2002a) cautions that cross-sectional studies of th e type presented here are not likely to estimate the relevant parameters accurate ly. She argues that variables measuring observable student characteristics are un likely to provide an adequate control for unobserved characteristics that are cor related with “schooling decisions and schooling costs” (p.2). She notes, “This is par ticularly problematic because point estimates in this literature are often quite fragile, even changing sign with small changes in specification” (p.2). These concer ns raise new challenges for higher education researchers studying financial aid policy, who should be careful to test the robustness of their findings across specif ications and to interpret their findings in light of the potential bias of omitted variables and student self-selection into different types of colleges, programs, and fin ancial aid packages. In addition, it highlights the need for strong theoretical framewor ks in order to impose consistency on the interpretation of findings based on studies using different methods and data. The ongoing comparison of findings from the higher education and the economics literature is also likely to improve understanding of the effectiveness of financial aid


13 of 35 policy. With awareness of these limitations, the an alysis of national data bases is worthwhile to establish benchmarking standards for institutional researchers and state-level policy analysts, who can compare result s for similar populations of students enrolled on their own campuses.ResultsDistribution of Outcomes and Aid by Parental IncomeThe distribution of variables included in the regre ssion analysis is reported by parental income quartile in column (4) of Table 1. The descriptive results indicate that rates of persistence from the first to second years of college do not differ by parental income quartile. However, timely bachelor’ s degree attainment does, rising from 47% in the first quartile to 65% in the fourth quartile. Separate analyses by income quartile of persistence to the third through fourth years of study indicate no statistically significant differences in these outc omes. These findings suggest that the difference in degree attainment depends on elig ibility for graduation at the end of the fourth year, not on differences in year-to-y ear persistence. Table 1 Variable Definitions and Descriptive Statistics (1)(2) Estimated Means (3) Std. Error (4)Quartile Means and ProportionsaVariable (measurement units, range) (mean of 0/1 is percent) 1st2nd3rd4th F-testbt-test 1st v.4th Quartile Persistence toyear2, 0/1, yes=1 .7759.013374.979.377.378.8.689 Bachelor’sdegree, 0/1, yes=1 .5470.018046.951.156.364.86.27** Parentalincome ($170-250000) 46955120717161365425121583599 25.03** Tuition ($96-14095)283877.442555274228323232 4.0**Grant federal ($136-5950) 171252.211698174417021700 .02 Grant federal0/1 Received, yes=1 .3047.013431.833.726.929.61.24 Grant state ($100-4900) 103558.121101797.8929.41585 1.07 Grant state0/1 Received, yes=1 .1633.013739.133.726.929.651.44** Grantinstitutional Need($150-15166) 3311246.82991292831894031 1.40


14 of 35 Grantinstitutional need 0/1,Recd, yes=1 .1356.009915.613.88.816.12.65* Grantinstitutional (non-need)($100-9000) 2190246.12100235217632359 .37 Grant institutnl (non-need) 0/1, Recd, yes=1 .0644.00848. Loan federal ($184-4625) 177058.691790175916082002 .60 Loan federal0/1 Received, yes=1 .1929.015838.** Work study ($139-2998) 977.154.72991.81140597.3573.3 1.59 Work study0/1 Received, yes=1 .0762.008820.** White,0/1, yes=1.8653.014778.785.788.992.97.34** African American, yes=1 .0778.011914.** Hispanic, 0/1, yes=1.0367.00674. Asian, 0/1, yes=1.0499.00896. Male, 0/1, yes=1.4696.016643.245.051.648.01.48 Mom college grad, 0/1,yes=1 .2785.016417.518.829.246.224.43** Delay enrollment, 0/1,yes=1 .0458.00754. Live on campus, 0/1,yes=1 .4706.021144.743.047.952.71.80 Social index (1-4)2.475.02132.452.402.512.53 1.32Work hours (0-70)20.40.532619.2119.1620.9022.37 2.1 6* Doctoral institution 0/1,yes=1 .5734.035051.** Academic index, (1-4)2.702.02332.712.602.722.69 1.4 3 GPA (gradepoint average), 0-400 252.922.914251253250255 .60Notes:Observations = 1087, Population size = 433065.81Data: BPS:90/94 NCES. Weight: BPS94AWT.Subpopulation: public 4-year (OFCON1 = 3 or 4)Estimates adjusted for stratification and clusterin g. Number of strata = 2, Number of PSUs = 260aMeans of aid awards are conditional on aid type>0. *p<.05 **p<.01b The Pearson chi-squared statistic has been correct ed for the survey design and converted into an F statistic.The mean tuition charge of tuition and fees was nea rly $3,000, a skewed value in comparison to the median of $2,200. This is due to the presence in the sample of


15 of 35 flagship public universities, which typically charg e higher tuitions than other public four-year institutions. (Note 19) Students from the highest income families enrolled in higher priced institutions, on average, than oth er students and were disproportionately enrolled in doctoral-granting in stitutions. In the first year, 30% of the sample received a fed eral grant averaging just over $1,700, an amount which is approximately three-quar ters the median tuition price. (The mean financial aid values in Table 1 are repor ted conditional on the receipt of each aid type.) State grants were received by a sma ller proportion of students (16%) and in smaller amounts (approximately $1,000 on average). Fourteen percent of the sample received institutional need-b ased grants with a relatively large mean value just over $3,300, while 6% receive d institutional non-need-based grants averaging nearly $2,200. These sizeable inst itutional awards were clearly an important source of funds for a small percentage of the sample. Eight percent received a federal work-study award averaging nearl y $1,000. Nineteen percent of the sample took subsidized fede ral loans, averaging $1,770. Over 98% of the sample borrowed an amount less than or equal to the Stafford loan maximum for first-year students, which was $2, 625 in 1989. The maximum loan value in this sample is $4,625, which reflects additional loan dollars available to students with high financial need through the Pe rkins program. Note 20 The greater tuition expenses of higher income stude nts are associated with the pattern of first-year aid awards exhibited in Table 1. Students in the fourth income quartile receive awards in proportions and amounts equal to those of the lowest income students. In fact, award amounts in the four th quartile are often greater, though these differences are not statistically sign ificant. This pattern is observed for federal and state grants and both need-based and no n-need institutional awards, with the exception that higher proportions of low-i ncome students receive state grants. Students in the third-income quartile recei ve these types of aid in amounts similar to that awarded low-income students, but sm aller proportions receive state grants and institutional need-based aid.In contrast, federal loans are taken by much larger proportions of low-income students (38% and 27% in the first and second quart iles, respectively) than high income students (8% and 4% in the third and fourth quartiles). Also, while 20% of students in the lowest income quartile receive work -study awards, that proportion falls steeply to 7% in the second income quartile a nd to less than 3% among high income students. Although students in the upper inc ome quartiles do not typically receive work-study, they do work, with students in the fourth quartile reporting 22 hours per week in comparison to 19 hours per week f or those in the 1st quartile. The proportion of white students increases as paren tal income increases, while the proportion of African Americans falls. While higher proportions of Hispanic and Asian students are observed in lower income bracket s, these differences are not statistically significant. The educational level of students’ mothers is significantly higher in the fourth income quartile, with 46% of m others in the fourth quartile having a college degree, in comparison with just 18 % of mothers in the first income quartile. These differences by income group are not associated with differences in academic experiences. No statistically significant differences are observed by income quartile in delayed enrollment, grade point average, or the indices of academic and social integration.


16 of 35 A matrix of Pearson’s correlations (not shown) betw een the variables in Table 1 showed that the federal and state grant, federal lo an, and work-study variables had low to moderate positive correlations, with values in the range of r=.15 to .37. The social and academic integration indexes were positi vely correlated at r=.33. Other values were lower than r=.15. Overall, these result s do not indicate a collinearity problem for the logistic regressions.Factors Affecting PersistenceThe results of the second-year persistence and bach elor’s degree attainment regressions are reported as odds ratios in Tables 2 and 3, respectively, for the sequential steps through the addition of the academ ic variables. As demonstrated by joint tests of significance and the change in th e adjusted Rsquared statistic, the addition of the terms representing the interaction of financial aid with income status was not significant in either model, and the result s of this step are not shown. Table 4 presents the “delta p” statistics for variables s ignificant in the final model, shown in column 5 of Tables 2 and 3. As indicated by the Wald chi-squared tests in Table 2, the persistence model is not significant in colu mn 1, where income is the sole predictor, but becomes significant in column 2 and increasingly so as additional blocks of predictors are added. The McFadden’s Rsqu ared statistics reported in Table 2 indicate that the goodness-of-fit of the pe rsistence model improves with each additional block of predictors, reaching .1432 Table 2 Persistence to Second Year Variables (1)income (2) financial (3) cultural (4) social (5)academic Income quartile21.2841.5651.6061.6701.737 (1.29)(2.19)(2.33)(2.41)(2.59)Income quartile31.1411.5801.6341.4211.471 (0.74)(2.34)(2.48)(1.65)(1.70)Income quartile41.2441.7171.7921.3631.352 (1.09)(2.46)(2.67)*(1.31)(1.19)tuition 1.0151.0161.0301.017 (0.70)(0.73)(1.34)(0.77)federal grant 1.0361.0351.0551.065 (0.88)(0.85)(1.25)(1.50)state grant 1.1921.1981.1801.134 (2.13)*(2.18)*(2.15)*(1.66)inst'l need grant 1.0161.0161.0191.021


17 of 35 (0.60)(0.64)(0.72)(0.80)inst'l grant 1.0051.0091.0181.033 (0.10)(0.18)(0.33)(0.54)federal loan 1.1261.1201.0931.126 (2.29)*(2.20)*(1.69)(2.12)*work study 1.3271.3171.1961.202 (1.91)(1.84)(1.24)(1.37)African American 1.3361.1311.108 (1.05)(0.41)(0.34)Hispanic 0.8550.9640.806 (0.44)(0.10)(0.57)Asian 1.9652.2282.243 (1.71)(2.01)(1.88)male 0.8490.9711.234 (1.10)(0.19)(1.29)Mom college grad 1.4271.300 (1.79)(1.27)delay enrollment 0.2440.238 (4.36)**(4.15)**on campus 2.3042.211 (4.37)**(3.97)**social index 1.2711.175 (1.98)*(1.20)work hours 0.9860.986 (2.74)**(2.80)**Doctoral inst. 1.339 (1.86)academic index 1.253 (1.74)gpa 1.008 (7.17)**Model Statistics


18 of 35 Wald chi2 (df)1.90(3)22.34(10)27.87(14)95.64(14)132 .33(22) Prob>chi2.5937.0135.0148.000.000McFadden’s Rsquared.0016.0165.0211.0831.1432Adjusted McFadden’sRsq -.005-.003-.005.050.103 LR chi2(df)1.801(3)19.069(10)24.455(14)96.107(19)16 5.69(22) Prob>LR.615. prob.7759 Notes: Observations:1087Robust z statistics in parentheses* significant at 5%; ** significant at 1% (multiple comparisons tested jointly and significant joint tests reported at alpha/k for k categories, alpha = .05) NCES Data: BPS:90/94 Weight: BPS94AWT.Subpopulation: public 4-year OFCON1=3or4 Table 3 Bachelor's Degree Attainment Over Five Years Variables (1)income (2)financial (3)cultural (4)social (5)academic Income quartile21.1851.2621.2501.2651.252 (0.97)(1.24)(1.20)(1.19)(1.13)Income quartile31.4571.5851.6231.4841.557 (2.50)*(2.69)*(2.75)*(2.14)(2.29)Income quartile42.0822.1652.1731.8311.940 (3.77)**(3.74)**(3.62)**(2.65)*(2.91)*tuition 1.0491.0481.0611.060 (2.61)**(2.56)*(2.99)**(2.68)**federal grant 0.9950.9991.0111.018 (0.14)(0.02)(0.32)(0.49)state grant 1.1151.1161.1031.068 (1.67)(1.58)(1.39)(0.91)inst'l need grant 1.0271.0231.0261.029 (1.34)(1.15)(1.26)(1.19)inst'l grant 0.9800.9961.0001.013 (0.50)(0.11)(0.01)(0.33)


19 of 35 federal loan 1.0181.0190.9951.021 (0.36)(0.39)(0.10)(0.41)work study 1.0040.9780.9340.927 (0.04)(0.20)(0.59)(0.62)African American 0.6870.6100.630 (1.59)(2.02)(1.77)Hispanic 0.9371.0650.965 (0.18)(0.18)(0.10)Asian 1.2101.3291.233 (0.53)(0.81)(0.56)male 0.5510.5850.657 (4.23)**(3.66)**(2.68)**Mom college grad 1.2531.167 (1.47)(1.01)delayed enroll 0.3160.334 (3.13)**(2.96)**on campus 1.8091.798 (4.20)**(4.04)**work hours 0.9940.995 (1.53)(1.28)social index 1.1861.126 (1.72)(1.14)Doctoral inst. 1.037 (0.23)academic index 1.105 (0.96)gpa 1.008 (7.45)**Model Statistics Wald chi2 (df)17.6(3)32.2(10)53.6(14)91.44(19)142.7 8(22) Prob>chi2.0005.


20 of 35 McFadden’sRsquared .0130.0219.0384.0696.1248 AdjustedMcFadden’s Rsq . LR chi2(df)19.477(3)32.803(10)57.470(14)104.20(19)1 86.906(22) Prob>LR. prob.5470 Notes: Observations: 1087Robust z statistics in parentheses* significant at 5%; ** significant at 1% (multiple comparisons tested jointly and significant joint tests reported at alpha/k for k categories, alpha = .05) NCES Data: BPS:90/94 Weight: BPS94AWT.Subpopulation: public 4-year OFCON1=3or4 Income is not a significant predictor of persistenc e, with the exception that income quartile 4 is positive and significant in the third step of the model, when the race and gender variables are added. Income quartile 4 i s not significant when social and academic factors are added. Among the financial aid variables, state grants and federal loans have a positive effect, while the effects of other forms of aid are insignificant. With the exception of mother’s colle ge education, the variables measuring social context are significant predictors with substantive effect sizes, where campus residence and social integration both have positive effects, and delayed enrollment and increasing work hours have n egative effects. The social integration index loses significance when the acade mic variables are added and the model controls for GPA, which is a positive and sig nificant predictor. This suggests that social integration promotes academic achieveme nt. Attendance at a doctoral-granting institution and academic integrat ion are positive, but not significant. Gender and the racial indicator variab les are not significant predictors once the tests on individual categories are adjuste d for multiple comparisons. The conversion of the odds ratios of column 5 to ch anges in probability of persistence are presented in the top portion of Tab le 4. These indicate that, with covariates held at their mean or modal values, the probability of persistence increases .14 by living on campus, .05 with an in crease of $1,000 in federal loans, and .16 with an increase of 100 (of 400) GPA points The probability of persistence decreases-.34 by delayed enrollment and -.03 for an increase of 10 hours of work. For continuous variables, the change in probability in persistence from the minimum to the maximum value of that variable is indicated in Table 4 to show the full range of probabilities associated with that factor. Table 4 Odds Ratios from Final Models as Changes in Probabi lity “Delta P” of Persistence, Significant Variables, Fi nal Model, Table 2, Step 5


21 of 35 Variable(1/0)aMinimum to Maximum from:to:deltaP x=0x=10->1Delay enroll0.69110.3475-0.3435Live on campus0.69110.83180.1407 Variable(delta)bChange(d) Centered at MeanMinimum to Maximum from:to:deltaP from:to:deltaP x-d/2x+d/2-+d/2x=minx=maxmin->maxLoan fed ($1000)0.66520.71580.05060.67150.85970.188 1 Work hours (10)0.70560.6761-0.02950.74720.5292-0.21 80 GPA (100)0.60370.76660.16290.24170.87330.6316 “Delta P” of Bachelor’s Degree, Significant Variabl es, Final Model, Table 3, Step 5 Variable (1/0)aMinimum to Maximum from:to:deltaP x=0x=10->1 income q30.46310.57310.1100income q40.46310.62590.1628Male0.46310.3617-0.1013Delay enroll0.46310.2234-0.2396 Live on campus0.46310.60790.1448 Variable(delta)bChange(d) Centered at MeanMinimum to Maximum from:to:deltaPfrom:to:deltaP x-d/2x+d/2-+d/2x=minx=maxmin->maxtuition ($1000)0.44870.47750.02880.38590.7607 0.374 8 GPA (100)0.36900.55990.19090.10720.72910.6219 Notes:a(1/0) Indicates a dichotomous variable. For dichoto mous variables the minimum to maximum change is the difference between membership in the variable group coded zero and the group coded 1 (indicated by the variable label).b(delta) Indicates the unit change of a continuous v ariable. The changes in probability are calculated with the dichotomous covariates indicated in Table 5


22 of 35 held at their modal value and continuous covariates held at their means. Data: BPS:90/94 NCES. Weight: BPS94AWT.Subpopulation:public 4-year (OFCON1=3or4)Factors Affecting Timely Bachelor’s Degree Attainme nt The logistic regression model predicting bachelor’s degree attainment becomes increasingly significant and the goodness of fit im proves with the sequential addition of predictors, as indicated by the Wald chi-squared and McFadden’s Rsquared statistics reported in Table 3. The Rsquared value of .1248, compared to .1432 for the persistence model, indicates the predictors do a poorer job of explaining outcomes over the long term to bachelor’s degree at tainment. The variables measuring parental income in the thir d and fourth quartiles are positive and significant across the models. Among t he financial variables, only tuition is significant. Contrary to theoretical exp ectations and prior empirical results, it has a positive effect, a finding that is likely due to the higher costs of selective flagship institutions. Being male has a significant negative effect, while the racial indicators are not significant when the tests on in dividual categories are adjusted for multiple comparisons. As in the persistence model, campus residence and first-year GPA are positive predictors of success, while delay ed enrollment has a significant negative effect.The conversion of the odds ratios of column 5 to ch anges in probability of persistence are presented in the lower portion of T able 4. These indicate that, with covariates held at their mean or modal values, the probability of bachelor’s degree attainment increases .11 and .16 by being in the 3r d and 4th income quartiles, respectively; .14 by living on campus; .19 with an increase of 100 GPA points; and .03 with an increase of $1000 in tuition and fees. The probability of degree attainment decreases .-10 for men in comparison to women and -.24 for those who delay enrollment instead of starting college with t heir age cohort after high school.DiscussionThe results of this study demonstrate that among fo ur-year public college students who are financially dependent on their parents, fam ily income is not a determinant of second-year persistence, but it is a determinant of bachelor’s degree attainment. State grants and federal subsidized loans received in the first year have positive effects on persistence, but no form of financial ai d is observed to have a significant effect on degree attainment. Thus, financial aid pa ckages as they are distributed in the first year do not offset the advantages of fami ly income for timely degree completion. The most important factors positively a ffecting both persistence and degree attainment are living on campus and academic performance in the first year. The observed benefit of living on campus is consist ent with student integration theory, as it is likely to promote a greater sense of belonging and commitment to an institution. As Beekhoven, DeJong, and VanHout (200 2) argue in linking integration theory to a student’s perception of costs, “if a st udent cannot succeed in feeling at home or ‘fitting in,’ the costs of proceeding will increase. At the same time, the perceived likelihood of success will decrease” (p. 581). These perceptions are important in determining outcomes because they affe ct a student’s willingness to integrate in campus activities and invest in their studies.


23 of 35 Grants certainly do reduce the costs of college, an d theoretically they should be associated with positive effects. Grants tend to ha ve negligible or positive effects in this study, but no form of grant aid is statistical ly significant in either final model. The positive effects of grants are difficult to obs erve and are likely biased downwards because the model cannot fully control fo r the correlation between the receipt of need-based grants and student characteri stics that are negatively associated with persistence (Bettinger, 2002; Dynar ski, 2002a). Students have no reason not to accept the full amount of scholarship and grant aid offered them by financial aid officers. In contrast, students may d ecide to reduce their course load and increase work hours rather than incur debt by t aking student loans, a form of financial aid that is observed to have a positive e ffect. Each student’s decision about loans is likely based on personal risk aversi on, information about loan availability and terms, and expectations for academ ic success and post-baccalaureate earnings. These decisions and va riations in the amount borrowed serve to distinguish the effects of loans even among a group of already enrolled students.The state grant variable has a substantive and stat istically significant positive effect on persistence until the final step when the academ ic variables are entered. The sequential analysis suggests, then, that state gran ts foster academic success, but this positive effect could be due to the inclusion of merit awards for academically prepared students in this aid category. Both Singel l (2002) and DesJardins et al (2002) observe strong positive effects of merit aid on persistence. The same positive effect is not observed for institutional n on-need based grants, another source of aid which would include merit awards. Thi s insignificant result may be due to the relatively small number of students receivin g institutional non-need based grants (5-8% in comparison to 30-39% receiving stat e grants) or to the inclusion of non-merit awards in the variable. Studies of other NPSAS financial data in which researchers also could not clearly disaggregate nee d-based from merit aid have found insignificant and negative effects of grants on within-year persistence (Paulsen & St. John, 2002; St. John et al., 1994). Paulsen and St. John (2002) find a negative and significant delta p of -.04 for a $1 ,000 change in grant aid for students in the lowest income quartile and insignif icant effects for other income groups. The authors interpret this effect as an ind ication that grant aid was inadequate to meet college costs for low-income stu dents. This conclusion is not supported by this study. The difference in the find ings may be due to the exclusion from this study of financially independent students who may not be able to draw on additional family resources in the event they enrol l and then find grant aid to be insufficient to meet their financial needs.Loans have a positive effect on persistence, but no t on degree attainment. Loan-taking patterns among students are likely to h ave shifted after the first year, as students gained a better sense of their prospect s for degree completion and their capacity to combine work and schooling. Students wh o opted out of borrowing in their first year may have taken loans, the most rea dily available form of new aid, in subsequent years to reduce their out-of-pocket cost s. This new borrowing may have had positive effects on degree attainment that are not observed here. The distribution of aid in the first year did not close the gap in timely degree attainment between low and high income students. This implies that the distribution of aid in subsequent years must have improved in favor of low -income students for the aid


24 of 35 system to achieve its equity goals. In fact, federa l policies changed during the five-year span covered by the BPS data in a manner favorable to middleand upper-income students, as revisions to the federal formula for calculating financial need allowed the exclusion of home equity (Berkner, 2000; Dynarski, 2002b). The early nineties also marked the beginning of the shi ft in state aid towards upper income students through merit and institutional awa rds (Heller & Schwartz, 2002). These changes, combined with evidence that the effe cts of different forms of aid decline with each subsequent year of study (DesJard ins, Ahlburg et al., 2002), suggest that the benefits of the aid system were no t effectively redistributed in subsequent years to reduce the degree attainment ga p. The effect estimated in this study of an increased probability of persistence of .05 given an increase of $1,000 in loans is consistent with the findings of Singell (2002) who found an increase of .06 (.04 when correcting f or self-selection bias). These findings are contradictory to those of Paulsen and St. John (2002), who found negative effects of loans on within-year persistenc e in the range of -.01 to -.03 for low income and lower middle income students and ins ignificant effects for upper middle and upper income students. DesJardins et al (2002) also find a negative effect of loans on persistence. A test of interacti on effects in this study indicated no significant differences in the effect of loans by i ncome quartile. This may be due to small sample size in the upper quartiles when this comparison is made. In the population examined in this study, loans were taken by relatively large proportions of students in the 1st and 2nd quartiles and small proportions of students in the upper quartiles.The final estimated effect of loans on persistence of a delta p of .05 may be overestimated due to the selection bias created whe n more confident and capable students decide to incur debt. In addition, the pot entially differential effects of the “intangible” components (St. John et al., 2000) of loan-taking by ethnic group have not been examined in this study. There is some evid ence to suggest that students of color are more risk averse than white students ( Baker & Velez, 1996; Linsenmeier, Rosen, & Rouse, 2001).One possible interpretation of the positive effect of loans on persistence is that it is due to a greater likelihood of loan-taking among st udents attending more expensive (and often more prestigious) institutions. However, the receipt of loans in this study is not correlated with the level of tuition and fee s (r=.025). In addition, a supplementary cross-tabulation of the proportion of students taking loans by income quartile and tuition quartile shows the proportion of students taking loans to be similar across tuition quartiles, with no statistic ally significant differences for any income group. The positive effect of loans is consi stent with theoretical expectations, as they lower the costs of college at tendance. The present value of subsidized loans is considerable, approximately equ al to one-third the value of grants, because the federal government pays the cos t of credit while a student is enrolled (Dynarksi, 2002).In addition, loans may enable students to work fewe r hours and become more integrated into college activities, a conclusion pr eviously reached by King (2001) in a study of BPS data covering the years 1996-98. Wor k hours are shown to have a relatively small negative effect on persistence in this study. The effect may be underestimated due to the inclusion of on-campus wo rk hours, which have been


25 of 35 shown to be positive, with off-campus hours in one combined variable (Nora et al., 1996) Recent developments in student integration theory e mphasize the indirect positive effects of aid on persistence (Cabrera, Nora, & Cas taneda, 1993; Nora et al., 1996). This interpretation is supported by the sequ ential regression analysis. Loans are not significant in step 4 when the social varia bles are entered, but are significant in prior steps and regain significance once the control for GPA is added in step 5. This suggests that loans enable social i ntegration, which has a positive effect by enabling better academic performance. The social index variable is significant in step 4, but not in step 5 once GPA a nd the academic integration index are added. When variation due to academic performan ce is controlled, the independent positive effect of loans due to the red uction in costs is once again observed.Male students, who can earn higher wages than femal e students without a bachelor’s degree and therefore have more lucrative opportunities when they stop out of college, have lower predicted probabilities of timely degree attainment. Those who delay enrollment are also less likely to attain their degree within five academic years, an outcome consistent with their prior progr ess at a slower rate than their high school graduation cohort. However, only 5% of the first-time full-time financially dependent students in this study delayed enrollment so this factor affects relatively few.ImplicationsPrior empirical work estimating the effects of fina ncial aid on college student persistence have led to contradictory results. This study contributes to this literature by estimating the effects of different types of aid on the persistence of financially dependent full-time students in the public four-yea r sector using national data. The findings show that subsidized loans have a positive effect on persistence. Grants have a negligible non-significant effect. A review of developments in the econometric modeling of the effects of aid on persi stence (Bettinger, 2002; DesJardins, Ahlburg et al., 2002; Dynarski, 2002a; Singell, 2002a) suggest that the single-stage regression model employed here is like ly to underestimate the effects of grants and overestimate the effects of loans, be cause, as discussed above, it does not fully control for self-selection bias. The effect of loans is estimated here at an increased probability of persistence of .05 with a $1000 increase in loan value. This estimate falls between Singell’s (2002) estima tes of .06 in a single-stage model and .04 in a two-stage model correcting for s elf-selection bias, which suggests the magnitude of the overestimation is not substantial. From a policy perspective, it is important to accur ately estimate the magnitude of the relative effects of subsidized loans and grants Loans have come to play an increasingly prominent role in the financial aid sy stem, and in many states public higher education is not accessible to low-income st udents unless they incur substantial debt (Kipp III, Price, & Wohlford, 2002 ). As loans replace grants in aid packages, firmer estimates of their relative effect s are needed. The application of new modeling techniques in this area is promising, particularly as they may be able identify differential effects of various types of a id on students of different economic classes, cultural backgrounds, and academic abiliti es and over different points in


26 of 35 time of their academic careers.This study examined the persistence and degree atta inment of students who were financially dependent on their parents. As evidence d by the mean age of eighteen, this was a traditional college-going population of young adults who were not raising families of their own or juggling careers while the y pursued their degrees. Nevertheless, in the first year they worked an aver age of 20 hours per week, and only 55% earned their bachelor’s degree within five years. Consistent with student integration theory, living on campus in the first y ear was a substantive and significant positive predictor of degree completion This finding indicates that policy makers who wish to promote timely bachelor’s degree completion should favor policies that enable public college students to liv e on campus. Campus living fosters immersion in the academic environment, the development of peer groups and social networks, and easier access to faculty a nd administrative advisors. In turn, students with these advantages develop a firm er goal commitment and confidence in their ability to complete their degre es. In this population, family income is a determinant of timely bachelor’s degree completion. Financial aid packages as they are dist ributed in the first year did not offset the advantages of family income. Therefore, the distribution of aid had to improve in subsequent years of the data collection in favor of low-income students in order for the aid system to fully achieve its eq uity goals of providing the benefits of higher education to all qualified students regar dless of their financial status. Two financial aid trends indicate that the distribution of aid more likely shifted in favor of high-income students from 1989 to 1994. These are t he increased popularity of state merit aid, which is distributed disproportion ately to wealthier students who benefit from better schooling, and the revisions to the financial aid formula that allowed for the exclusion of home equity and opened the subsidized loan program to more affluent families. If the amount of time public college students spend working to pay tuition and fees can be reduced by more favorable aid packages, it f ollows from both human capital and student integration theory that their graduatio n rates will increase. Similarly, if students who are tempted to live in the parental ho me in order to economize are offered enough aid to cover dormitory costs, they w ill more likely be able to immerse themselves in student life and proceed stea dily towards completion. For those campuses without dormitories, the constructio n of campus housing may in fact be a good investment to improve student retent ion and outcomes. As significant public dollars are spent on public coll eges through operating subsidies, it is important to align financial aid programs to sup port those investments. While existing aid levels appear adequate to promote year -to-year persistence, they do not promote timely degree completion for low-income students. If timely degree completion is truly a priority of state policymaker s, they should look for ways to enable students to spend more time in academic envi ronments pursuing their studies. AcknowledgmentI would like to acknowledge Ronald Ehrenberg and La ura Perna for helpful


27 of 35 comments on a previous draft of this article.NotesSee Kane (1999) and McPherson & Shapiro (1998) for timely reviews of public higher education finance goals, and the Carn egie Commission ( Who Pays? 1973) for a historic treatment. 1. Hauptman (2001) emphasizes “States spend roughly tw ice as much as the federal government to support higher education” (p. 65) and state student aid averages only about 5% of total state funding for h igher education (p. 73). 2. Economists have also studied the effects of financi al aid on student choices and outcomes, such as enrollment, institutional cho ice, academic performance, and major field of study. See Ehrenber g (forthcoming) for a comprehensive review. 3. Adelman (1999) analyzed several other national long itudinal data bases to construct a detailed portrait of enrollment pattern s and bachelor’s degree attainment. His analysis, which utilized rich high school curriculum data to emphasize the primary relationship between academic experiences and college outcomes, relied on more limited measures o f student finances and is less informative on this topic. 4. With the development of accountability policies, in stitutional researchers have also analyzed individual campus and state system da ta to estimate the effect of financial and other factors on timely degree com pletion. Knight (2002) provides a review of these. 5. See Heckman (1979) and Willis (1979) regarding the concept of self-selection bias. 6. Dynarski (2001) reaches the same conclusion after r eviewing studies showing that different forms of financial aid have differen t effects on enrollment depending on students’ income group. 7. See also Singell (2002b) for additional methodologi cal and empirical work by this author on this topic. 8. There are two exceptions. First, the logistic regre ssions do not adjust for stratification because preliminary analyses showed the strata had little effect on the estimates. This decision enabled use of a wi der range of software features. Second, model-based Pearson correlation c oefficients were obtained because the statistical software used (Sta ta, version 7) does not offer a design-based correlation function. 9. Some argue that it is better not to use sampling we ights in regression analyses, particularly when the weights are a funct ion of the dependent variable. See Winship and Radbill (1994) for a thor ough discussion of this issue. 10. Skinner, Holt, and Smith (1989, Table 2.1, p. 29) s how that a design effect of 1.5 or 2.0 will change a nominal confidence interva l from 95% to an actual interval of 89% or 83%, respectively. Failure to ad just for design effects of this size will considerably inflate findings of statisti cal significance. 11. A design-based F statistic (calculated from the Pea rson chi-squared statistic) is reported as the test of association for categori cal variables (Stata, 2001, svytab, p. 86), while a design-adjusted t-test is r eported to compare means of the continuous variables (Stata, 2001, svymean, p. 69-70). 12. See Peng, So, Stage, and St. John (2002) for a rati onale for presenting the change in probability at other values besides the m ean. 13.


28 of 35 Both Long (1997) and Peng, So, Stage, and St. John (2002) advise against reporting marginal effects for binary response mode ls, given the inherent non-linearity between the predictors and the probab ilities. Peng et al. (p. 270) caution “the concept of marginal probability is not useful for explaining logistic regression models,” whether the marginal effects ar e calculated at the mean or by computing the average over all the observatio ns. The marginal effect is a good summary measure only when the “independent v ariable varies over a region of the probability curve that is nearly line ar” (Long, p. 75). 14. This approach is consistent with the NCES Statistic al Standards (Seastrom, 2002). 15. A comparison of the results obtained for the McFadd en’s adjusted R squared to results of a model estimated without weighting a nd clustering showed that the difference between these values does not exceed .01 for these models. 16. These items measuring social integration were inclu ded in the initial 1989 survey and precede more recent scholarship (see, fo r example, Nora, 2001-2002; Rendon, Jalomo, & Nora, 2000) that has e nriched the conceptualization of social integration. 17. The variables measuring mother’s education and race /ethnicity were predictors to impute 35 cases (3.14%) of parental i ncome. The variables parental income, mother’s education, and living on campus were predictors to impute 52 cases (4.66%) of tuition. 18. The higher cost of flagship institutions is reflect ed in the mean out-of-jurisdiction tuition charge, which was 2.5 t imes the mean in-state tuition. Prestigious institutions are more likely to attract academically talented students who conduct a national college search and travel out of their home state. 19.ReferencesAccess denied: Restoring the nation's commitment to equal educational opportunity (2001). Washington, D.C.: Advisory Committee on Student Financial Assis tance. Adelman, C. (1999). Answers in the tool box: Academic intensity, attend ance patterns, and bacherlor's degree attainment (Monograph). Washington, D.C.: Office of Education al Research and Improvement, U.S. Department of Education. Baker, T. L., & Velez, W. (1996). Access to and opp ortunity in postsecondary education in the United States: A review. Sociology of Education, SI (SI), 82-101. Bean, J. P., & Metzner, B. S. (1985). A conceptual model of nontraditional undergraduate student attri tion. Review of Educational Research, 55 (4), 485-540. Becker, G. S. (1976). The economic approach to human behavior Chicago: University of Chicago Press. Becker, G. S. (1993). Human capital (Third ed.). Chicago: University of Chicago Press. Beekhoven, S., De Jong, U., & Van Hout, H. (2002). Explaining academic progress via combining concepts of integration theory and rational choice theory. Research in Higher Education, 43 (5), 577-600. Beginning Postsecondary Students longitudinal study second follow-up (BPS:90/94) final technical repor t (No. NCES 96-153)(1996). Washington, D.C.: U.S. Dep artment of Education, National Center for Education Statistics. Berkner, L. (2000). Trends in undergraduate borrowing: Federal student loans in 1989-90, 1992-93, and 1995-96 (Statistical Analysis Report No. NCES 2000-151): U S. Department of Education, National Center for Education Statistics.


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32 of 35 subsidies on within-year persistence. Journal of Higher Education, 66 (2), 156-186. Stata User's Guide Release 7 (2001). College Station, Texas: Stata Press. Thomas, S. L., & Heck, R. H. (2001). Analysis of la rge-scale secondary data in higher education research: Potential perils associated with complex sampling designs. Research in Higher Education, 42 (5), 517-540. Tinto, V. (1975). Dropout from higher education: A theoretical synthesis of recent research. Review of Educational Research, 45 (1), 89-125. Tinto, V. (1987). Leaving college: Rethinking the causes and cures of student attrition (Second ed.). Chicago: University of Chicago Press. Titus, M. (2000, May 21-24). The financing of success in higher education: Stude nt aid, expectations, and the persistence of first-time, full-time freshman. Paper presented at the Association for Institution al Research, Cincinnati, Ohio. Wei, C. C., & Horn, L. (2002). Persistence and attainment of beginning students wi th Pell grants (Statistical Analysis Report No. NCES 2002-169). Wa shington, D.C.: U.S. Department of Education, National Center for Education Statistics. Willis, R. J. (1979). Education and self-selection. Journal of Political Economy, 87 (5), S7-S36. Winship, C., & Radbill, L. (1994). Sampling weights and regression analysis. Sociological Methods and Research, 23 (2), 230-257. Zumeta, W. (2001). Public policy and accountability in higher education: Lessons from the past and present for the new millenium. In D. E. Heller (Ed. ), The states and public higher education policy: affordability, access, and accountability Baltimore: Johns Hopkins University Press.About the AuthorAlicia C. DowdGraduate College of EducationUniversity of Massachusetts BostonWheatley Hall100 Morrissey Blvd.Boston, MA 02125-3393Phone: (617) 287-7593Fax: (617) 287-7664E-mail: Alicia C. Dowd is an assistant professor in the hig her education administration doctoral program in the Graduate College of Educati on at the University of Massachusetts Boston, where she teaches research me thods, the political economy of education, and higher education finance. She holds a PhD in educational administration and social foundations f rom Cornell University Dowd’s research focuses on college student outcome equity, methods for evaluating factors that affect student outcomes, community college fin ance, and the effects of financial aid on student persistence in public coll eges and universities. The World Wide Web address for the Education Policy Analysis Archives is Editor: Gene V Glass, Arizona State University


33 of 35 Production Assistant: Chris Murrell, Arizona State University General questions about appropriateness of topics o r particular articles may be addressed to the Editor, Gene V Glass, or reach him at College of Education, Arizona State Un iversity, Tempe, AZ 85287-2411. The Commentary Editor is Casey D. Cobb: .EPAA Editorial Board Michael W. Apple University of Wisconsin David C. Berliner Arizona State University Greg Camilli Rutgers University Linda Darling-Hammond Stanford University Sherman Dorn University of South Florida Mark E. Fetler California Commission on TeacherCredentialing Gustavo E. Fischman Arizona State Univeristy Richard Garlikov Birmingham, Alabama Thomas F. Green Syracuse University Aimee Howley Ohio University Craig B. Howley Appalachia Educational Laboratory William Hunter University of Ontario Institute ofTechnology Patricia Fey Jarvis Seattle, Washington Daniel Kalls Ume University Benjamin Levin University of Manitoba Thomas Mauhs-Pugh Green Mountain College Les McLean University of Toronto Heinrich Mintrop University of California, Los Angeles Michele Moses Arizona State University Gary Orfield Harvard University Anthony G. Rud Jr. Purdue University Jay Paredes Scribner University of Missouri Michael Scriven University of Auckland Lorrie A. Shepard University of Colorado, Boulder Robert E. Stake University of Illinois—UC Kevin Welner University of Colorado, Boulder Terrence G. Wiley Arizona State University John Willinsky University of British ColumbiaEPAA Spanish and Portuguese Language Editorial BoardAssociate Editors for Spanish & Portuguese


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