Within-college human capital and racial ethnic differences in academic performance

Fixed Effects Model

Random effects growth curve models have the limitation of assuming that unmeasured characteristics of individuals are uncorrelated with measured X’s in the estimation equation, and that all stable characteristics of individuals that determine GPA have been included in the model. Fixed effects models do not require the first assumption and control for the unmeasured heterogeneity that might be implicated in the second assumption. In the extreme, if the apparent racial ethnic gap in academic performance were all due to unmeasured factors, then there would be little basis for our paper as the gap would disappear with control for unmeasured heterogeneity (Allison 1994; Halaby 2004).

Table 3 presents a fixed-effects model that investigates this possibility. In the model we include only racial ethnic category by time interactions, year, and changing X variables, including a measure that treats major as time-varying. Several important results appear. First, the black by year interaction (b = .06) is highly significant and is not dissimilar from the effect of being black on GPA slope in the random effects growth curve model (b = .04). Second, the significant coefficient for black by time indicates that the racial gap in academic performance is not a simple function of unmeasured heterogeneity. A real gap persists even after removing the effects of all stable individual characteristics, which is implied in a fixed effects model. Third, two of six estimates of effect for changing X capital variables are significant and positive, consistent with theorizing. Self-assessed academic skills have a small, positive significant effect on GPA. This effect was not significant or negative in the growth curve model. Work hard attributions have a significant positive effect on GPA, consistent with what we found in the growth curve model. Other changing X capital variables that were significant in the growth curve model are generally positive but not significant in the fixed effects model. In part, this may be because fixed effects methods ignore the between-person variation and focus only on the within-person variation, and thus, the standard errors can be considerably higher than those produced by random effects models (Allison 1995).

In summary, the estimates from the fixed effects model give us greater confidence in the estimates from the growth curve model.

DISCUSSION

The academic performance gap has received substantial scholarly attention. Most studies of human capital investigate pre-college explanations for the gap, or in a few panel studies, fixed independent variables. Our paper addresses this lacuna by investigating within-college variations in human capital in three areas: academic and intellectual skills; global and specific self-esteem, academic self-confidence, and student identity; and academic effort and engagement. How do variations during college in these capital areas affect the trajectories of academic performance as measured by semester-by-semester grade point average?

The racial ethnic gap in grades is at its largest in the first college semester and narrows progressively over the remainder of college for all groups. In particular, black students’ gain in GPA substantially narrows the gap with the highest performing racial ethnic groups.

We found that variations in four of nine indicators of within-college capital were significantly associated with increases in GPA. Variations in work hard attributions, the importance of a good student identity, and two measures of specific self-esteem -- self-assessed ability and self-assessed smartness -- had statistically significant but generally small effects on GPA, concentrated in the first and second college years as opposed to the senior year. In the growth curve model, two additional within-college capital factors, self-assessed academic skills and active learning behaviors had small significant effects but in ways opposite our theorizing. A fixed effects model found one of these, self-assessed academic skills, did have significant positive effects on GPA change, consistent with theorizing. The hours spent studying measure had no significant effects on GPA in either model, likely attributable to our lack of a sufficiently fine-grained measure. The fixed effects model clearly shows that we are not simply analyzing unmeasured heterogeneity in the form of omitted, stable, person-specific characteristics. Within college capital variations do help us understand the performance gap but do not explain a large share of the gap. They are a small to modest factor.

Our findings have a number of limitations. The data refer to but one institution. The findings likely generalize to other elite private institutions, but how far beyond that is an open question. Second, the growth curve model invokes a strong assumption for multivariate normality associated with full information maximum likelihood estimation. The distribution of the dependent variable violates that assumption to some extent. However, our experimentation with other functional forms, such as cumulative percentile rank in class, did not produce much difference in findings. Third, several of our measures for time use and academic engagement (i.e., active learning behaviors) are less than optimal. More fine-grained measures might produce stronger results. More generally, future research might explore other indicators of within-college capital and other indicators of the quality of collegiate educational experiences for different racial ethnic groups.

An even larger question begs for attention. To wit: We now know that pre-college factors explain at most a modest portion of the performance gap. Our results suggest within-college factors, while a number of them are statistically significant, explain only a small portion of the academic performance profiles for different racial ethnic groups. Other within-college processes must be at work. What are they and how do they operate? Elsewhere we examined the possible effects of processes associated with a stereotype threat explanation. Our results suggested that, to the extent it operated, it was a small factor in explaining the gap with CLL data (XXXXX 2006). Other prominent possibilities include forms of cultural and social capital in college including diversity in networks, and academic climate as experienced by different racial and ethnic groups. We plan to explore these possibilities in the future with the CLL data.

Appendix: Drop-out Bias, Response Bias and Missing Data

Registrar’s Office data provided information on students who were not enrolled at the end semester in each survey year. Non-enrollment might occur for multiple reasons including academic or disciplinary probation, medical or personal leave of absence, dismissal or voluntary (including a small number of transfers) or involuntary withdrawal. At the end of the first college year, fewer than one percent of students (n = 12) were not enrolled, about three percent by the end of the second year (n=48) and just over five percent (n= 81) by the end of the senior year. We combined all of these reasons and tested for differences in selected admissions file information of those enrolled versus not enrolled at the end of each survey year. The test variables included racial ethnic group, SAT verbal and mathematics score, high school rank (where available), overall admission rating (a composite of five different measures), parental education, financial aid applicant, public-private non-religious-private religious high school and US citizenship. Of over 40 statistical tests only two produced significant differences (p<.05): at the end of the first year, dropout had SAT-verbal scores of 734 versus 680 for non-dropouts, by the end of the fourth college year those who had left college had an overall admissions rating of 46.0 (on a 0-60 scale) while those in college had an average rating of 49.7. No other differences were significant. We conclude that our data contain very little drop-out bias.

We conducted similar tests for respondents versus non-respondents for each wave for the same variable set plus college major (4 categories, engineering, natural science/mathematics, social science, humanities), whether or not the student was a legacy admission, and GPA in the semester previous to the survey semester. Seven variables show no significant differences or only a few small sporadic differences (one wave but not others), including racial ethnic category, HS rank, admissions rating, legacy, citizenship, financial aid applicant, and major group. Several other variables show more systematic differences. 1. Non-respondents at every wave have lower SAT scores (math.: 9-15 points, roughly one-tenth to one-fifth of a standard deviation; verbal: 18-22 points, roughly one-third of a standard deviation). 2. Non-respondents have slightly better educated parents at waves one and three, but not waves two and four. 3. Non-respondents at every wave are less likely to be from a public high school and somewhat more likely to be from a private (non-religious) high school. 4. Finally, non-respondents have somewhat lower GPA in the previous semester compared with respondents (by about one-quarter of a letter grade).

These differences are somewhat inconsistent or non-synchronous in that they include lower SAT and GPA for non-respondents, but higher parental education and private (more expensive) high schools. In general, the non-response bias is largest in the pre-college wave and smaller in the in-college waves even though the largest response rates are in the pre-college wave. In general, we judge the non-response bias as relatively minor or small on most variables and perhaps modest on SAT measures.

REFERENCES
Allison, Paul D. 1994. “Using Panel Data to Estimate the Effects of Events.” Sociological Methods and Research 23: 174-199.

------. 2005. Fixed Effects Regression Models for Longitudinal Data Using SAS. Cary, NC: SAS Publishing.

Astin. Alexander W. 1993. What Matters in College? Four Critical Years Revisited. San Francisco: Jossey-Bass.

Becker, Gary S. 1975. Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education. New York: National Bureau of Economic Research.

Bandura, Albert. 1982. “The Self and Mechanisms of Agency.” Pp. 3-39 in Psychological Perspectives on the Self, vol. 1, edited by J. Suls. Hillsdale, NJ: Erlbaum.

Bollen, Kenneth A. and Patrick Curran. 2006. Latent Curve Models: A Structural Equation Perspective. Hoboken, NJ: Wiley.

Bourdieu, Pierre. 1986. “The Forms of Capital.” Pp. 241-258 in Handbook of Theory and Research for the Sociology of Education, edited by J. Richardson. Westport, CT: Greenwood Press.

Bowen, William G. and Derek Bok. 1998. The Shape of the River: Long Term Consequences of Considering Race in College and University Admissions. Princeton, NJ: Princeton University Press.

Burke, Peter J. 2004. “Identities and Social Structure: The 2003 Cooley-Mead Award Address.” Social Science Research 67: 5-15.

Bryk, Anthony S. and Stephen W. Raudenbush. 1992. Hierarchical Linear Models: Applications and Data Analysis Methods. Thousand Oaks: Sage.

Coleman, James S. 1988. “Social Capital in the Creation of Human Capital.” American Journal of Sociology 94 Supplement: S95-S120.

Curran, Patrick J. and Andrea M. Hussong. 2002. “Structural Equation Modeling of Repeated Measures Data: Latent Curve Analysis.” Pp. 59-86 in Modeling Intraindividual Variability with Repeated Measures Data: Methods and Applications. Edited by D.S. Moskowitz and S.L. Hershberger. Mahwah, NJ: Lawrence Erlbaum Associates.

Curran, Patrick J., Bengt O. Muthén, and Thomas C. Harford. 1998. “The Influence of Changes in Marital Status on Developmental Trajectories of Alcohol Use in Young Adults.” Journal of Studies on Alcohol 59: 647-658.

Enders, Craig K and Deborah L Bandalos. 2001. “The Relative Performance of Full Information Maximum Likelihood Estimation for Missing Data in Structural Equation Models.” Structural Equation Modeling 8: 430–457.

Flowers, L. 2000. “Cognitive Effects of College: Differences between African-American and Caucasian Students.” Ph.D. dissertation, University of Iowa, Iowa City.

Halaby, Charles N. 2004. “Panel Models in Sociological Research: Theory into Practice.” Annual Review of Sociology 30: 507-544.

Jencks, Christopher and Meredith Phillips (Eds.). 1998. The Black-White Test Score Gap. Washington, D. C.: Brookings Institution Press.

Juster, F. Thomas and Frank P. Stafford. 1991. “The Allocation of Time: Empirical Findings, Behavioral Models, and Problems of Measurement.” Journal of Economic Literature 29: 471-522.

XXXXX. 2008. “A Social Portrait of Legacies at an Elite Private University.” Unpublished manuscript, Department of Sociology, Duke University, Durham, NC.

Massey, Douglas S., Camille Z. Charles, Garvey F. Lundy, and Mary J. Fischer. 2003. The Source of the River: The Social Origins of Freshmen at America’s Selective Colleges and Universities. Princeton, NJ: Princeton University Press.

Morgan, Stephen L. and Jal D. Mehta. 2004. “Beyond the Laboratory: Evaluating the Survey Evidence for the Disidentification Explanation of Black-White Differences in Achievement.” Sociology of Education 77: 82-101.

Muthén Bengt and Linda Muthén. 2007. M Plus version 5. Los Angeles: Muthén and Muthén.

Myerson, Joel, M. Rank, F. Raines and M. Schnitzler. 1998. “Race and General Cognitive Ability: The Myth of Diminishing Returns to Education.” Psychological Science 9: 139-142.

Osborne, J. W. 1995. “Academics, Self-Esteem, and Race: A Look at the Underlying Assumptions of the Disidentification Hypothesis.” Personality and Social Psychology Bulletin 21: 449-455.

Pascarella, Ernest T. and Patrick T. Terenzini. 2005. How College Affects Students, Volume 2: A Third Decade of Research. San Francisco: Jossey-Bass.

Rau, William. 2001. “Response: To Replicate or Not to Replicate: Is that Schuman’s Question.” Sociology of Education 74: 75-77.

Rau, William and Ann Durand. 2000. “The Academic Ethic and College Grades: Does Hard Work Help Students to ‘Make the Grade’?” Sociology of Education 73: 19-38.

Reitzes, Donald C. and Peter J. Burke. 1980. “College Student Identity Measurement and Implications.” Pacific Sociological Review 23: 46-66.

Rosenberg, Morris. 1989. Society and the Adolescent Self-Image, Revised Edition. Middletown, CT: Wesleyan University Press.

Rosenberg, Morris, Carmi Schooler, Carrie Schoenbach and Florence Rosenberg. 1995. “Global Self-Esteem and Specific Self-Esteem: Different Concepts, Different Outcomes.” American Sociological Review 60: 141-156.

Royston, Patrick. 2005. “Multiple Imputation of Missing Values: Update.” The Stata Journal 5:1-14.

Rubin, Donald. 1987. Multiple Imputation for Non-Response in Surveys. New York: Wiley and Sons.

Thorndike, R. and J. Andrieu-Parker. 1992. “Growth in Knowledge: A Two-Year Longitudinal Study of Changes in Scores on the College Basic Subjects Examination.” Paper presented at the Annual Meetings of the American Educational Research Association.

Schuman, Howard. 2001. “Comment: Students’ Effort and Reward in College Settings.” Sociology of Education 74: 73-74.

Schuman, Howard, Edward Walsh, Camille Olson and Barbara Etheridge. 1985. “Effort and Reward: The Assumption that College Grades are Affected by Quantity of Study.” Social Forces 63: 945-966.

XXXXX. 2006. “Race, Stereotype Threat, and Classroom Performance: Tests of Social Psychological Mechanisms.” Unpublished manuscript, Department of Sociology, Duke University, Durham, NC.

XXXXX. 2005. “The Black-White Achievement Gap in the First College Year: Evidence from a New Longitudinal Case Study.” Pp. 187-216 in Research in Social Stratification and Mobility 22, edited by D. Bills. Amsterdam: Elsevier.

StataCorp. 2007. Stata Statistical Software: Release 10. College Station, TX: StataCorp LP.

Stinebrickner, Ralph and Todd R. Stinebrickner. 2003. “Time-Use and College Outcomes.” Journal of Econometrics 121: 243-269.

Maes, Barbara, Lisa Alstadt, Laura Underwood and Michael Boivin. 1996. “Evaluating Changes in Social Attitudes, Character Traits, and Liberal-Arts Abilities during a Four-Year Program at a Christian College.” Research on Christian Higher Education 3: 115-128.

Van Buuren, S., H.C. Boshuizen, and D.L. Knock. 1999. “Multiple Imputation of Missing Blood Pressure Covariates in Survival Analysis.” Statistics in Medicine 18:681-694.

Figure 1. Semester Grade Point Averages by Racial Ethnic Group


Figure 2. Growth Curve Model



Table 1. Measures and Descriptive Statistics by Racial Ethnic Group, Campus Life and Learning Project

		Mean (Standard Deviation) by Racial Ethnic Group
Variable	Metric/Notes	White	Black	Latino	Asian	Bi-Multiracial
Race	Dummy variable for groups; US Census questions	N = 528	227	214	229	57
Female	1 = Female	.48	.71	.48	.45	.64
	0 = Male	(.50)	(.46)	(.50)	(.50)	(.49)
Mother's Education	1 = High school graduate or less	3.43	2.93	3.16	3.19	3.07
	2 = Some college/vocational school	(.99)	(1.21)	(1.15)	(1.05)	(1.18)
Father's Education	3 = College graduate	4.01	3.17	3.60	4.02	3.46
	4 = Some graduate school/Master's Degree	(1.06)	(1.39)	(1.27)	(1.08)	(1.25)
	5 = Higher professional degree (PhD, JD, MD)
US Citizen	1 = US Citizen (native born and naturalized)	.98	.93	.93	.72	.88
	0 = Other	(.16)	(.26)	(.26)	(.45)	(.33)
SAT-Mathematics	Scholastic aptitude test (max. = 800)	723.03	635.46	682.83	760.20	698.65
		(57.30)	(60.16)	(58.48)	(41.40)	(71.02)
Good Student Identity	1 = Not at all important	4.30	4.67	4.52	4.37	4.57
(High School)	2 = Somewhat important	(.80)	(.59)	(.83)	(.93)	(.80)
	3 = Important
	4 = Very important
	5 = Extremely important
Self-Perceived Ability	Sum of two items for abilities in last challenging mathematics and English course (max. = 10)	8.24	7.98	8.27	8.35	8.30
(High School)		(1.20)	(1.11)	(1.11)	(1.12)	(1.06)
High School Confidence:	1 = Not at all confident	3.68	3.43	3.66	3.74	3.48
Mathematics	2 = Somewhat confident	(1.01)	(1.07)	(1.08)	(1.05)	(.95)
High School Confidence:	3 = Confident	2.28	2.33	2.21	2.46	2.07
English	4 = Very confident	(1.03)	(1.06)	(1.03)	(1.06)	(.99)
	5 = Extremely confident
Time Management	1 = Not at all successful	2.78	2.45	2.54	2.52	2.75
(First Year)	2 = Somewhat successful	(.93)	(.95)	(.97)	(.89)	(.89)
	3 = Successful
	4 = Very successful
	5 = Extremely successful
Final Major Field:	Dummy variable for groups; omitted category: natural sciences/engineering
Natural Sciences		.34	.22	.25	.55	.33
		(.47)	(.41)	(.44)	(.50)	(.48)
Social Sciences		.45	.59	.59	.36	.42
		(.50)	(.49)	(.49)	(.48)	(.50)
Humanities		.19	.16	.14	.07	.23
		(.39)	(.37)	(.34)	(.26)	(.42)
Academic Skills	Self-assessed academic skills; 8-item scale (max. = 40)
First Year		29.28	27.83	28.68	28.91	29.37
		(3.98)	(3.43)	(3.83)	(3.75)	(3.93)
Second Year		29.41	28.55	29.04	28.71	29.77
		(4.01)	(3.38)	(3.61)	(4.03)	(3.69)
Fourth Year		32.14	31.51	31.78	31.15	32.32
		(3.80)	(4.31)	(3.95)	(3.64)	(3.51)
Academic Self Confidence	Confidence in most challenging class
First Year	1 = Not at all confident	2.54	2.24	2.41	2.60	2.70
	2 = Very confident	(.97)	(.88)	(.97)	(1.04)	(1.00)
Second Year	3 = Confident	2.55	2.28	2.54	2.59	2.58
	4 = Somewhat confident	(1.04)	(.91)	(.96)	(.99)	(1.01)
Fourth Year	5 = Extremely confident	2.80	2.65	2.85	2.64	3.16
		(1.02)	(1.00)	(1.02)	(.98)	(1.07)
Word Hard Attributions	Succeed in most challenging class because worked hard?
First Year		.80	.76	.80	.76	.86
	1 = Yes	(.40)	(.43)	(.40)	(.43)	(.35)
Second Year	0 = No	.80	.84	.78	.79	.84
		(.40)	(.37)	(.41)	(.41)	(.37)
Fourth Year		.83	.79	.81	.79	.89
		(.38)	(.41)	(.39)	(.41)	(.32)
Active Learning Behaviors	Scale for number of active learning behaviors and activities used to address challenges in most challenging class (max. = 6)
First Year		2.26	2.55	2.44	2.34	2.45
		(1.33)	(1.52)	(1.46)	(1.26)	(1.58)
Second Year		2.21	2.63	2.53	2.44	2.37
		(1.23)	(1.40)	(1.22)	(1.24)	(1.09)
Good Student Identity	Importance of good student identity to overall identity
First Year		4.02	4.40	4.22	4.20	4.55
	1 = Not at all important	(.91)	(.71)	(.93)	(.98)	(.66)
Second Year	2 = Somewhat important	3.89	4.23	4.02	4.16	4.17
	3 = Important	(.99)	(.83)	(.92)	(1.00)	(.93)
Fourth Year	4 = Very important	3.96	4.07	3.97	4.12	4.06
	5 = Extremely important	(.94)	(.89)	(.99)	(.99)	(1.03)
Global Self Esteem	Sum of 3 items (max. = 15)
First Year	Extent to which respondent agrees that:	10.41	10.59	10.39	9.60	9.66
	On the whole, satisfied with self	(2.72)	(2.80)	(2.66)	(2.50)	(2.54)
Second Year	Do not feel useless at times (reflected)	10.64	11.09	10.96	9.99	10.31
	Do not wish could have more self-respect (reflected)	(2.93)	(2.97)	(2.68)	(2.55)	(2.79)
Fourth Year		11.00	11.42	10.95	10.50	10.60
		(2.91)	(2.80)	(2.75)	(2.64)	(2.71)
Hours Spent Studying	Hours spent during a typical week studying or doing homework; recoded from 6 discrete categories to a continuous scale by recoding each value to the midpoint of the category range.
First Year		10.89	10.43	10.17	11.39	11.86
		(5.11)	(5.14)	(5.16)	(5.10)	(4.93)
Second Year		10.73	10.59	10.01	10.72	10.86
		(4.96)	(4.98)	(4.95)	(5.06)	(5.08)
Fourth Year		10.01	9.06	9.30	8.95	9.52
		(5.24)	(5.11)	(5.24)	(5.29)	(4.82)
Self-Assessed Ability	Ability comparisons to other students in most challenging class
First Year		3.26	2.74	3.09	3.40	3.43
	1 = Very much below average	(.86)	(.81)	(.78)	(.90)	(.76)
Second Year	2 = Below average	3.28	2.80	3.16	3.42	3.19
	3 = Average	(.90)	(.88)	(.84)	(.93)	(.91)
Fourth Year	4 = Above average	3.43	3.14	3.27	3.44	3.45
	5 = Very much above average	(.80)	(.85)	(.80)	(.86)	(.76)
Self-Assessed Smartness	Smartness comparisons to average Duke student
First Year	1 = Not nearly as smart as average	3.33	2.99	3.14	3.54	3.25
	2 = Somewhat less smart than average	(.87)	(.77)	(.85)	(.83)	(.78)
Second Year	3 = As smart as the average Duke student	3.38	3.10	3.24	3.52	3.45
	4 = Somewhat smarter than average	(.87)	(.71)	(.79)	(.82)	(.77)
Fourth Year	5 = Much smarter than average	3.57	3.16	3.47	3.68	3.62
		(.80)	(.77)	(.85)	(.76)	(.85)