High School Resources, and Peer Group Effects

The Determinants of Undergraduate Grade Point Average: The Relative Importance of
Family Background, High School Resources, and Peer Group Effects
Author(s): Julian R. Betts and Darlene Morell
Source: The Journal of Human Resources , Spring, 1999, Vol. 34, No. 2 (Spring, 1999),
pp. 268-293
Published by: University of Wisconsin Press
Stable URL: https://www.jstor.org/stable/146346
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The Determinants of Undergraduate
Grade Point Average
The Relative Importance of Family
Background, High School Resources,
and Peer Group Effects
Julian R. Betts
Darlene Morell
ABSTRACT
The paper analyzes the Grade Point Average (GPA) of undergraduates at the University of California, San Di ground strongly affects GPA. Graduates of different hig significantly different GPAs, even after controlling for ground. These school effects in part reflect the incidence the level of education among adults in the school neigh ers’ experience in the student’s high school bears a posi cant link to the student’s university GPA, but the effect positive link with GPA emerged for the teacher-pupil r level of education.
I. Introduction
What explains variation in college students’ performance? In the typ-
ical university, measures of student success such as Grade Point Average (GPA) show substantial variation. Of course, to some extent this diversity reflects differ-
ences in the degree of difficulty among different programs of study within the univer- Julian R. Betts is a professor of economics at the University of California, San Diego. Darlene Morell
is the Director of Student Research and Information, Student Affairs, University of California, San
Diego. This research was supported by a grant from the UCSD Chancellor’s Associates. The authors
wish to thank UCSD and Richard Atkinson for their support of this research. They also thank Eric
Kyner and Greg Martin for their expert research assistance, and two referees for helpful suggestions.
The data used in this article can be obtained beginning September 1999 through September 2002 from
Julian R. Betts, Department of Economics, UCSD, La Jolla, CA, subject to the recipient(s) signing a
confidentiality agreement ensuring that the data will not be released to others without permission, or
used to identify individuals in the study.
[Submitted October 1997; accepted April 1998]
THE JOURNAL OF HUMAN RESOURCES * XXXIV * 2
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Betts and Morell 269
sity. But disparities in GPA surely also reflect variations in the level of preparation
of freshmen undergraduates.
It is useful to study the determinants of college GPA because GPA reflects human
capital acquisition at a time when young adults are close to permanent entry into the labor force. Many studies have found a positive and significant link between
college GPA and subsequent earnings. Most recently, Loury, and Garman (1995)
find that weekly earnings of white males in the National Longitudinal Study of the
High School Class of 1972 are predicted to rise by 10.0 percent with a one-point
increase in college GPA. For black males, the corresponding estimate is a 28.7 per- cent increase in earnings, although the point estimate is significant at only the 5.3 percent level. These results are impressive because the earnings equation controls
for college selectivity, the person’s own score on the Scholastic Aptitude Test (SAT and family background. Other studies that have found a positive and significant rela-
tion between college GPA and earnings include Jones and Jackson (1990), Filer
(1983), and Wise (1975). Similarly, Grogger and Eide (1995) report a positive rela-
tion between high school grades and earnings.
This paper seeks to determine the factors underlying variations in student perfor-
mance, measured by GPA, at a major public university. It considers four sets of
explanatory factors:
1. the degree program in which students are enrolled at university,
2. the student’s family background (such as family income and race),
3. the resources of the high school that the student attended prior to enrolling
in university (measured by variables such as the traits of teachers and the
teacher-pupil ratio),’ and
4. the demographic environment in which the student attended high school (for
example, characteristics of the student body and levels of education or in-
come in the community).
This study should prove of interest to two distinct academic communities. First, the study provides a relatively new and novel method for determining the extent to
which high schools vary in effectiveness. Ever since the Coleman Report (1966) was released, the academic community has invested a great deal of effort in an attempt to explain why public schools differ in quality. The vast majority of prior research in this field has measured student success in terms of the test scores of students while
in grade school. Ideally, we would like to follow students after high school to test whether school spending translates into better outcomes for students once they begin their adult lives. The present paper follows students several years past their high
school graduation in an effort to measure the relative effectiveness of high schoo resources in terms of how students fare once they arrive at university.
The second policy community to which this research is directed are college admin-
1. We were unable to obtain measures of school inputs at the level of the student’s high school classroom.
This prevents us from testing for nonlinearities in the relation between school inputs and student outcomes
in university. But on the other hand, using school-level averages overcomes the potential endogeneity bias
that would result from using data at the classroom level if schools change the mix of inputs that go into
each classroom.
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270 The Journal of Human Resources
istrators, who each year sift through tens of thousands of applications for undergra ate admissions in an attempt to identify the best candidates. At many universiti high school GPA and scores on the Scholastic Aptitude Test (SAT) play a key in these admissions decisions. Our research will first test whether high school G and SAT scores provide reliable predictors of GPA. Second, it will test whether o characteristics of the students, or of the high schools from which they graduated improve on simple forecasts of students’ success in university that are based on school grade and test scores alone.
The next section reviews the literature on school quality in detail, and dem strates the new contributions to the literature made by the present paper. Section describes the data. Section IV details the results of reduced form models that an university GPA in terms of high school traits and family background. Sectio examines the extent to which these traits help to forecast university success in m which already condition on SAT scores and high school grades.
II. Literature Review
There now exists a large literature on the role that the characteristic of public schools play in determining students’ test scores. Reviews by Hanus (1986, 1989, 1991, 1996) find that the vast majority of papers in this area have fo surprisingly little correlation between school traits such as class size and stude test scores.
But researchers have also examined the determinants of school quality in other ways: they have searched for a link between school traits and both educ attainment and earnings after graduation. The literature on school quality and ings has found mixed results. See for instance Card and Krueger (1992), Betts 1996a), Grogger (1996), and the review by Betts (1996b). Of particular rele to the present paper is a finding by Heckman, Layne-Farrar, and Todd (19 replicating earlier work by Card and Krueger (1992), Heckman and his coau find evidence that school resources are positively related to the earnings o those workers who obtain college degrees. This makes it important to verify w high school resources influence academic success of those who attend colleg is the goal of the present paper.
The impact of public school resources on educational attainment has re relatively little attention. The review by Betts (1996b) finds only 14 published of the link between school resources and educational attainment. Most of these ies have examined only years of education as the outcome variable. Arguabl more interesting to examine whether students receive college degrees, rath the student’s total years of schooling, because it is well known that earnings d strongly on degrees obtained. (This “sheepskin effect,” whereby the econom turns to years of schooling makes nonlinear jumps for those who have obtain school or college diplomas, has been documented by Hungerford and Solon among others.)
Similarly, it is interesting to know how high school characteristics influenc Grade Point Average (GPA) of students once they arrive at university. To t of our knowledge, only one published work has ever examined this questionThis content downloaded from
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Betts and Morell 271
paper, by Raymond (1968), modeled average freshman GPA at West Virginia Un versity as a function of school inputs and demographic traits. The unit of observati for all variables was the county. Raymond finds that spending per pupil, the pupil teacher ratio, and school library resources bear no relation to freshman GPA, though he did find in some specifications that teachers’ salaries were positively link to GPA. He also reports that the demographic traits of the county were significan linked to freshman GPA. It is important to note that this study does not use G at the level of the individual student. Furthermore, it does not control for the ind vidual’s family background, nor does it measure school resources at the actua school attended.
The goal of the project is to model the university GPA of students at the University
of California, San Diego (UCSD), as a function of characteristics of the students at
the time they enter university. This work has both administrative and academic uses.
To academic researchers it will provide some of the first evidence on the role which
individual high schools play in promoting student success in college. Furthermore,
it will be of help to universities in trying to determine what factors should be used
in attempts to predict the likelihood of success should a student be admitted.
We use a rich longitudinal database on undergraduate students enrolled at UCSD
to search for a link between high school characteristics and GPA. The dataset con-
tains detailed information about the actual high school attended, family background
and demographic information on the school and school district that the student last
attended.
Recent work by Morell (1993a,b) establishes that existing databases maintained
at UCSD can be successfully used for research purposes. Her earlier work shows
strongly significant positive links between high school GPA and test scores and
success of undergraduates at UCSD, where success is measured in terms of university
GPA of freshmen and the probability of graduating within six years. Morell’s work
will be extended in several ways. More than one cohort of students will be used.
Second, the research tests whether differences exist between students who come
from different high schools, after controlling for students’ observable traits such as
high school GPA and family background. Third, the paper tests whether high school
resources such as the teacher-pupil ratio and teachers’ credentials are related to stu-
dent outcomes at UCSD. To the best of our knowledge this paper is the first to model
individual students’ university GPA as a function of family background and the traits
of the high school attended.
III. Data
Detailed data on undergraduates who enrolled at UCSD between Fall
1991 and Fall 1993 were obtained from the UCSD Student Information Syste other student information was obtained from the Central Processing data files of Educational Testing Service. Our sample includes all students who enrolled at U during this period who had previously attended California public high schools. excluded transfer students who had transferred to UCSD from a community colle or another four-year post-secondary institution. These information sources, prov for each student a detailed picture of enrollment, GPA by quarter, field of stuThis content downloaded from
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272 The Journal of Human Resources
and background information including the Educational Testing Service (ETS) of the high school last attended and the student’s scores in the math and ver sections of the Scholastic Aptitude (SAT) test.
These data were merged with information on the California public high sch from which the students graduated. Our main source of information was the Cali nia Department of Education, which provided information from the 1992-93 sch year on the level and composition of enrollment at each high school and num and types of teachers. The same source provided two measures of the socioeconom background of the students at each school for 1994. The first, which we use in m of our regressions, is the proportion of students in the school’s attendance area were receiving Aid to Families with Dependent Children (AFDC). The second which we use in the appendix, is the proportion of students who in 1994 rece free or reduced cost meals.
A third source of data was a special tabulation of data from the 1990 Census of
Population, which provides detailed demographic traits for each school district in
California. The two variables from this dataset which we use in the main tables are
median household income in the school district in 1989 and the proportion of the
population older than 20 in the school district who held a Bachelor’s degree or higher
in 1990.
A fourth set of data, provided by the ETS, contains ETS school codes, average
1992 SAT scores (math and verbal) and the number of students writing the SAT,
for each high school in California. These latter variables are used in regressions in
the appendix.
For details on how the various data were merged, see the appendix.
Although some of our information on schools and school districts come from
different years, we believe that the data will provide a highly accurate picture of
school resources and demographic traits for the high schools attended by UCSD
freshmen. Most of the data corresponds to the 1992-93 school year, which is close
to the time when our three cohorts of freshmen are assumed to have graduated
(Spring 1991 through Spring 1993). The district-level demographic data correspond
to 1989 or 1990, depending on the variable, although the school-level information
on AFDC usage and meal assistance correspond to the 1994 school year. Because
the demographic traits of an area are unlikely to change radically over three or four
years, we believe that these proxies for neighborhood characteristics should deliver
a quite accurate depiction of the environment in which each UCSD undergraduate
attended high school.
The means and standard deviations of the variables used in the main tables appear
in Table Al in the appendix. The student population at UCSD differs from that of
the nation at large. The student population is over-represented by Asian students
and under-represented by all other races and ethnicities, including whites. This re-
flects both differences between the population of San Diego county and the country
as a whole, and the relatively selective nature of UCSD’s undergraduate program.
For instance, according to 1990 Census data, 6.0 percent of the San Diego County
population is black, which is about half the national average. But blacks constitute
only 2.3 percent of the UCSD sample, reflecting the competitive nature of UCSD
admissions, in spite of affirmative action programs that were in place during all years
represented in the study. Therefore, the results reported below do not necessarily
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Betts and Morell 273
reflect patterns at the national level, because of regional variations in the dem graphic background of students, and because selection into UCSD is nonrandom. particular, one referee suggested that some schools might send their best stude to UCSD, although other schools might send their best students to Berkeley an their second best to UCSD. If this selection is correlated in any way with the le of school resources at the two schools, the observed correlation between high scho resources and GPA at UCSD would give a biased picture of the average effect school inputs on university GPA. However, given that this is the first research th to our knowledge has simultaneously modeled university GPA as a function of p sonal, high school and neighborhood traits, we believe that the study makes a tangi contribution.
IV. Reduced Form Estimates of the Total Effect
of School Resources on University GPA
In this section we estimate reduced form models of cumulative uni-
versity GPA. In other words, we do not include high school GPA or SAT scores as
explanatory variables in these regressions, because these variables themselves repre-
sent endogenous outcome variables; by including them we risk understating the total
effect of school resources on students’ university GPA.
The dependent variable in this analysis is the cumulative university GPA, on a
scale of 0 to 4, for the latest quarter in which the student was enrolled. Because our
latest transcript data are from Spring Quarter 1996, and the students in the sample
first enrolled between 1991 and 1993, most students were still enrolled at this time.
Our chief goals in this section will be to test whether personal background is
related to GPA, whether the demographic characteristics of the area in which the
student attended high school influence his or her university GPA, and whether mea-
sures of school resources are significantly related to GPA. We add demographic
characteristics of the neighborhood and school based on the common observation
in the school quality literature that the student’s peer group can influence his or her
rate of learning.2 We choose three measures of demographic traits: the proportion
of students at the school who received AFDC in 1994, the proportion of the popula-
tion above age 20 in the school district who had Bachelor’s degrees or higher in
1990, and the median household income in the school district in 1989, in thousands
of dollars. We use three measures of school resources: the ratio of full-time equiva-
lent teachers to pupils in the high school, the average years of teacher experience,
and the proportion of teachers in the school who hold a Master’s degree or higher.
Before proceeding with detailed regression analysis, we began with two-way plots
of the relation between university GPA and these six variables.3 Each of the plots
using one of the three socioeconomic variables suggested that university GPA rises
with socioeconomic status of the school and neighborhood populations. The relation-
ship, if any, between university GPA and the school inputs was somewhat less clear.
2. See Coleman et al. (1966) and Hanushek (1986).
3. Due to space constraints, these plots are not shown, but are available from the authors, or online from
http://weber.ucsd.edu/-jbetts.
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274 The Journal of Human Resources
The strongest link that emerged between GPA and school resources was for aver teacher experience, where a positive relationship was readily apparent. Simple gressions of mean GPA on a constant and one school trait at a time support conclusion that with the exception of teacher experience, school inputs are not ne as strongly correlated with GPA as are the measures of the socioeconomic trai the school and neighborhood population. The t-statistics on the six explanatory v ables in the series of regressions were: AFDC (-9.2), median income (7.6), ad with college degrees (8.4), teacher-pupil ratio (2.9), teacher experience (6.6), te ers with postgraduate degrees (-1.2).
Of course, none of these relationships may persist after we properly control for t student’s personal background. For this reason we now turn to more formal regre analysis using the individual student, rather than the school, as the unit of observat Because GPA is likely to vary by year of study, it follows that we should condi on the year of study in which the final measure of GPA is observed. We inc dummy variables to indicate observations corresponding to the second through f years of study; students for whom the last year of available data is the first yea study serve as the control group. A student’s GPA may depend on the diffic and/or grading standards in the field in which the student decides to major. Therefo we also condition on the major in which the student is enrolled (Engineering, ence, Arts, Humanities, and Social Sciences, with Undeclared or Missing as th omitted category). We include the following variables to capture the personal bac ground of the student: dummy variables for men, blacks, Hispanics, Asians, an Other (nonwhite) Races, a dummy variable for foreign students, and dummy v ables indicating five categories for the parents’ income, in 1992 prices, with omitted category being parental income below $25,000.4 The justification for inc sion of these variables stems from the frequent observation in the school qua literature that personal and family background tend to be highly correlated with dent achievement, measured in terms of test scores.5
We estimate by Ordinary Least Squares (OLS) the following model, where i notes the student, j denotes the school, GPA refers to the last observation on uni sity GPA, BACK is a vector containing the aforementioned family background v ables, and the YEAR and MAJOR variables are the controls for year of study a major, and m is the number of majors minus one:
5 m
(1) GPAij = c + E YEARjt-x + BACKijA + MAJORkk + ?j
t=2 k=1
background v Table 1, Colu 4. Because studen the raw income v this variable com majority of stude this information in the year in wh 5. See for instan empirical findingThis content downloaded from
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Betts and Morell 275
GPA than females, on the order of 0.06 point. Ethnic minorities also obtain signifi cantly lower GPAs than do whites, with the largest gap arising between black a white students. Of course, we must be circumspect in interpreting correlation b tween GPA and gender or ethnicity as causal.6 Foreign students obtain slightly low GPAs than do citizens, but as will be shown this effect is no longer significant 5 percent once we estimate more complex models. Parental income is a highly si nificant predictor of GPA: students whose parents’ income was in the range $50,000 to $199,999 tended to have a higher Grade Point Average than did studen from less affluent backgrounds. Interestingly, the impact of family income appea to taper off among students whose parents’ income was $200,000 or higher-t GPA of these students was not significantly different from students with parenta income below $25,000.7 As hypothesized, the student’s GPA varies significant across majors, with the lowest GPAs occurring among engineering and science st dents, and the highest GPAs occurring among those enrolled in arts and humanitie This model tends to confirm the test score literature, which has found that person background is an important determinant of academic achievement.
Table 1, Column 2 shows the econometric results when we simultaneously contro for the socioeconomic environment of the school along with personal backgroun including major and year of study. The student’s GPA tends to drop as the proporti of students in his or her high school who received AFDC rises. Similarly, the propo tion of the adult population with Bachelor’s degrees or higher is positively and s nificantly related to GPA. Median household income in the district was not signifi cantly related to GPA, though, after controlling for personal background. As show in the final row of the table, the hypothesis that these three variables can be join excluded is strongly rejected.9
These findings are significant in two senses. First, they support previous findin in the literature that a student’s environment, or peer group, affects learning. Ev after controlling for parental income and the student’s gender and race, these var ables appear to have an independent effect on how well the student does at universit Second, the predicted impact of marginal changes in the AFDC and college educatio variables is quite high. Consider an increase in either variable of 0.20, in other word a 20 percent increase. As shown in Table Al, this represents a rise of approximately two standard deviations for either variable. Such a rise in the AFDC variable is
6. One possibility that we have not fully explored is whether variations in GPA across ethnicity reflect
variations in the types of courses which students take. The set of dummy variables that we have included
for major field of study cannot control fully for unobserved variations in the degree of difficulty of courses
taken by each student.
7. Experimentation with different ways of categorizing parental income-for instance making $150,000
the lower bound for the highest income category-tended to show the same decline in the impact of family
income on GPA at higher income levels. Graphical analysis confirmed that the impact of parental income
appeared to level off or decline beyond $150,000 or $200,000.
8. We also attempted a more detailed model that controlled for 32 fields of study instead of 5 broad majors.
But an F-test of the simpler model with broad majors was strongly retained against the more detailed
model with department of study. Therefore we chose the simpler model in this and later tables.
9. We chose these three measures of demographic background for the school because they capture the
median socioeconomic status, and at the same time characterize the two extremes of the socioeconomic
distribution. Of course, these and other socioeconomic indicators are quite highly correlated, so that it
would be unwise to claim more than that the socioeconomic environment matters, in plausible directions.
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Table 1
Reduced Form Models of University GPA
Variable 1 2 3 4 Constant
Male
Black
Hispanic
Asian
Other race
Foreign
Income
25-49.999K
50-74.999K
75-99.999K
100-199.999K
200K-Higher
Last year enroll = 2
Last year enroll = 3
2.8678
(94.78)
-0.0645
(-4.79)
-0.4005
(-9.30)
-0.3268
(-14.69)
-0.1241
(-8.24)
-0.1343
(-3.23)
-0.0481
(-2.04)
-0.0413
(-2.19)
0.0381
(2.04)
0.0617
(2.99)
0.1057
(4.99)
0.0504
(1.08)
0.0292
(0.78)
0.3111
(10.78)
2.8342
(64.47)
-0.0681
(-5.09)
-0.3630
(-8.43)
-0.2893
(-12.85)
-0.1140
(-7.56)
-0.1256
(-3.04)
-0.0393
(-1.68)
-0.0362
(-1.93)
0.0340
(1.83)
0.0519
(2.52)
0.0853
(4.02)
0.0223
(0.48)
0.0242
(0.65)
0.3069
(10.71)
2.8611
(34.85)
-0.0680
(-5.08)
-0.3629
(-8.43)
-0.2890
(-12.82)
-0.1143
(-7.57)
-0.1254
(-3.04)
-0.0396
(-1.69)
-0.0362
(-1.93)
0.0339
(1.83)
0.0519
(2.52)
0.0852
(4.02)
0.0223
(0.48)
0.0245
(0.65)
0.3070
(10.71)
2.6931
(42.94)
-0.0685
(-5.12)
-0.3617
(-8.41)
-0.2852
(-12.65)
-0.1139
(-7.56)
-0.1269
(-3.08)
-0.0387
(-1.66)
-0.0355
(-1.89)
0.0340
(1.83)
0.0511
(2.49)
0.0831
(3.92)
0.0167
(0.36)
0.0195
(0.52)
0.3022
(10.54)
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Last year enroll = 4
Last year enroll = 5
Engineering
Science
Arts
Humanities
Social science
Proportion on AFDC
Median household income
Proportion with Bachelor’s
Teacher-pupil ratio
Average teacher experience
Proportion teachers graduate degree
R-squared
Adjusted R-squared
P-value 1 vs. current
P-value 2 vs. 6
Note: Sample size is 5,623. T-statistics appear in parentheses.
0.3798
(13.46)
0.2711
(8.40)
-0.1181
(-6.49)
-0.0619
(-3.57)
0.1014
(2.07)
0.0513
(1.32)
0.0177
(0.89)
0.1366
0.1336
0.3762
(13.42)
0.2724
(8.50)
-0.1097
(-6.06)
-0.0546
(-3.17)
0.1003
(2.06)
0.0578
(1.50)
0.0221
(1.12)
-0.3867
(-4.64)
-0.0003
(-0.38)
0.2855
(3.91)
0.1487
0.1452
0.00000
0.3765
(13.43)
0.2727
(8.51)
-0.1096
(-6.05)
-0.0545
(-3.16)
0.1005
(2.07)
0.0579
(1.50)
0.0222
(1.13)
-0.3856
(-4.62)
-0.0003
(-0.44)
0.3015
(3.59)
-0.7315
(-0.39)
0.1487
0.1451
0.00000
0.3714
(13.24)
0.2690
(8.40)
-0.1079
(-5.96)
-0.0521
(-3.02)
0.1013
(2.08)
0.0602
(1.56)
0.0213
(1.08)
-0.3478
(-4.13)
-0.0004
(-0.48)
0.2706
(3.70)
0.0082
(3.15)
0.1502
0.1466
0.00000
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278 The Journal of Human Resources
predicted to lead to a drop in the student’s university GPA of 0.77 point; a ris 20 percent in the proportion of the adult population with a Bachelor’s or high predicted to lead to a 0.57 point increase in the student’s GPA. These changes quite large, especially compared to the predicted changes in GPA associated w changes in family income.
Having established that both personal background and measures of the socioe nomic environment of the school and school district are significantly linked to s dents’ university performance, we now test whether school resources influence h well students fare once they reach university. To begin with, we estimate a f effect variant of (1), in which each school is assigned its own intercept:
n 5
(2) GPAi = SCHOOLW k + YEARxt + BACKiA
k=l t=2
m
+ E MAJORk + Ej
k=l
where n is the number of schools and m is the number of major fields of study, le one. In this equation, the SCHOOLij variables are dummy variables equal to one j = k, and 0 otherwise. In our regression sample, we have students from 498 Califo nia public high schools. We test that the GPA of all students is the same, regardle of school attended, after controlling for the basic variables in (1):
(3) H0: o = = 02 3 * * = O498
When the model was estimated, the probability value (p-value) on this hypothesis
was 0.0000, indicating that students from different high schools obtain significantly
different GPAs once they arrive at university. Of course, this finding does not prove
that public high schools differ in quality. These measured differences could simply
be capturing neighborhood effects. With this problem in mind, the model in Table
1, Column 2, with its three measures of neighborhood traits, was also estimated with
fixed effects. The null hypothesis that all high schools are equal in quality was again
rejected, with a p-value of 0.0047. Thus, although the measured interschool differ-
ences are weaker after we control for neighborhood traits, the interschool differences
remain highly significant.10
Given evidence that California high schools differ in quality, we now ask whether
proxies for school spending can explain any of these differences, after controlling
for personal background and environmental/peer effects proxied by the three mea-
sures of the socioeconomic environment. As mentioned above, we use three mea-
sures of school resources: the ratio of full-time equivalent teachers to pupils in the
high school, the average years of teacher experience, and the proportion of teachers
10. Another possible criticism of the interpretation that “schools differ in quality” is that our school fixed
effects are merely detecting interpersonal differences, because many schools in our UCSD sample are
represented by just one or two students. Accordingly, Regressions 1 and 2 in Table 1 were both reestimated
with school fixed effects after first removing cases in which fewer than three students had attended the
school. In this smaller sample, of 5,442 students representing 372 schools, the null that all schools are
identical is in both cases rejected with a p-value of 0.0000.
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Betts and Morell 279
in the school who hold a Master’s degree or higher. All three of these variab capture important aspects of school spending.l1
Columns 3-5 of Table 1 list the results when Model 2 is reestimated with the
addition of one of these three measures of school resources. Column 6 shows the
results when all three measures of school inputs are added to Model 2 at once. As
shown in Column 3, the teacher-pupil ratio is not significantly related to a student’s
GPA once he or she arrives at university. In contrast, students who attended schools
with more highly experienced teachers perform significantly better at university. Al-
though highly significant, the effect is meaningful but not large in a policy sense:
an increase of ten years in teachers’ average experience is predicted to increase a
student’s GPA at university by 0.08 point. Finally, GPA is significantly and nega-
tively related to the proportion of teachers in the student’s high school who held
Master’s or Ph.D. degrees.12 As shown in the final column of the table, these results
persist when all three measures of school inputs are added together to Model 2.
We undertook numerous tests of robustness. First, we reestimated the models us-
ing random effects, to take account of the fact that there are in many cases repeated
observations for each school. These models led to highly similar conclusions in terms
of level of significance of the key regressors, and the size of their coefficients.’3 In
the paper we present OLS results rather than random effects results, though, as Haus-
man tests suggested that the latter were inconsistent, with p-values of 0.002 or less.
Second, we tested for nonlinear effects of school resources by adding squares of
each school input to Models 3-6 in Table 1. A reasonable assumption is that due
to diminishing returns the marginal impact of school inputs may decrease as the
input rises, which would result in a negative coefficient on the square of the input.
In results that are not shown, such a pattern emerges for the teacher-pupil ratio and
teacher experience, but in neither case is the pattern significant. For the teacher edu-
cation variable, the opposite pattern obtains, but again is not significant. We conclude
from this table that nonlinearities are not an important aspect of the data. It remains
possible that nonlinearities in the relation are obscured by the use of school-average
data.
Third, following the suggestion of a referee, we reran Table 1, Column 6 on the
subsamples corresponding to each of the five college majors. In these smaller sam-
11. Each of the three policies-smaller classes, more highly educated and more highly experienced teach-
ers-represents a policy change that will create new costs for a school. Classroom expenditures, which
consist largely of teacher salaries, will move proportionately with the teacher-pupil ratio. On average,
classroom expenditures account for about 60 percent of spending in American public schools. (National
Center for Education Statistics 1991, page 154.) Nonclassroom expenditures can also rise with an increase
in the teacher-pupil ratio if such a change dictates the building of new classrooms. Betts (1996a) estimates
from the March 1993 Current Population Survey that teachers with Master’s degrees command approxi-
mately a 17 percent wage premium over teachers without postgraduate degrees. Similarly, most teacher
salary contracts stipulate that salaries should rise with years of teaching experience.
12. The graphs of mean GPA by school had suggested such a negative relationship, but it was not signifi-
cant.
13. The regressors typically had t-statistics which were 5 to 10 percent lower in the random effects specifi-
cation, but the levels of statistical significance were unchanged in that the absolute t-statistic of the re-
gressors in no case crossed the 5 percent significance level of 1.96. The coefficients were little changed
by the introduction of random effects, with changes typically occurring in the second or third significant
digit. For example, in Table 1, Column 6, the key coefficient (and t-statistic) on average teacher experience
became 0.0114 (3.85) in the random effects specification.
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280 The Journal of Human Resources
ples coefficients sometimes became insignificant, but in 83 percent of cases coef cients maintained the same sign as in the regression using the full sample. Mo the sign reversals occurred in the subsamples of arts and humanities students, w were very small. In no subsample did a coefficient reverse sign with a t-stat above, or even close to, 1.96. We conclude that the observed effects of family, p group, and high school are quite similar across the five college majors.
As a final check on the results, we tested for robustness of the coefficients on school resources to omitted peer group or neighborhood effects. In particular, d the positive coefficient on teacher experience merely reflect a positive correla between teacher experience and the socioeconomic traits of the neighborhood Table 1, we have attempted to control for this possibility using three socioecono indicator variables. We did not include more because the three we have used capt traits of the median and both the upper and lower ends of the socioeconomic s trum. Adding more background controls, which tended to be highly correlated w the three measures already in use, might suggest that individual measures of soc economic status of the school’s and the area’s populations did not matter, whe fact socioeconomic status did matter. Accordingly, we assembled a matrix of variables designed to capture the traits of the student body at each high school the school neighborhood, along with the 24 squares of these variables. We perfor a factor analysis of these 48 variables to identify the principal components of data. We chose the first 14 principal components, as these captured fully 90 per of the variation in the 48 variables. We then repeated the main models in Tab replacing the three measures of socioeconomic background with the 14 princ components from the factor analysis. The results appear in Table A2 in the appen where we also list the 24 variables used.
If the three measures of school resources are merely capturing unmeasured socio-
economic traits of the student body, then in these specifications, the t-statistics on
the school resource variables should fall toward zero. Comparing the results in Table
A2 with Models 3-6 in Table 1, we instead find that the coefficients and t-statistics
on the school inputs are remarkably robust. In particular, the coefficient and level
of significance on average teacher experience are very little changed. This finding
increases our confidence that the results do not suffer heavily from omitted variable
bias.14
How are we to interpret the diverse results from Table 1? First, the finding that
the high school teacher-pupil ratio is not significantly related to GPA is typical of
the literature. Betts (1996b) finds that studies that have measured the teacher-pupil
ratio at the level of the actual school attended have found no link to the student’s
ultimate educational attainment. However, several studies that use district- or state-
level measures of class size as proxies for the class size enjoyed by the individual
student do show significant links.”5 Hanushek (1996) surveys 377 studies of test
14. As an even more stringent test for omitted background variables, we added the 24 variables and their
squares directly to Model 4 in Table A2, in place of the principal components. The results were quite
similar, with coefficients (and t-statistics) on the three measures of school resources as follows: teacher-
pupil ratio -1.4757 (-0.60), teacher experience 0.0092 (2.74) and the proportion of teachers with a gradu-
ate degree -0.2320 (-3.57).
15. Similarly, Betts (1995) and Grogger (1996) find little or no significant link between the teacher-pupil
ratio at the individual’s high school and subsequent earnings.
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Betts and Morell 281
scores and the teacher-pupil ratio and finds that only 15 percent show a positive a significant link; 13 percent of the studies found a negative and significant link, an fully 72 percent of the studies revealed no significant relation. Similarly, in a detai study of American and Asian public schools, Stevenson and Stigler (1992) find th Asian students regularly outperformed American students on standardized tests, y often were taught in much larger classes.
However, a second possible explanation is that there is too little variation in t teacher-pupil ratio in California’s high schools to enable us to detect a positive effec even if it exists. As shown in Table Al in the appendix, the coefficient of variation that is, the ratio of the standard deviation to the mean, is only 0.1 in this samp compared to 0.14 for teacher experience and 0.23 for the teacher education variable As with the results for the teacher-pupil ratio, the finding of a perverse but signifi cant relationship between the proportion of teachers with postgraduate degrees an university GPA accords with much of the test score literature. Hanushek (1996 reports that 5 percent of 171 test score studies found a similarly negative and signi cant relation, although only 9 percent reported a positive and significant relatio In addition, another 27 percent of the studies reported a negative but insignifica relationship. One reason why teacher education may not have a large impact student outcomes is that requirements in some locales that teachers obtain a Maste degree within a certain time after beginning teaching merely induces teachers obtain the “certification,” without regard to the program contents. Similarly, t typically automatic pay hike that awaits teachers who obtain a postgraduate deg may induce similar forms of “credentialism.”‘1617
Finally, how should we interpret the one case in which school spending appear to be significantly and positively related to subsequent performance in university students? Are more highly experienced teachers necessarily better teachers? O possible concern is the direction of causation. As documented in Chapter 4 of Mu nane et al. (1991), in some school districts teachers with seniority have first righ to job openings in other schools in the district. This could potentially lead to rever causation: more experienced teachers might migrate to jobs in the schools that hav the best prepared students because these are considered plum jobs. As shown in t school quality literature, often the main characteristic of such schools is the relative high socioeconomic status of students.18
We have already shown in Table A2 that the coefficient on teacher experience robust to inclusion of a large number of socioeconomic traits of the school populati and the neighborhood. But in order to test this possibility of reverse causation further 16. Chapters 7 and 8 of Murnane et al. (1991) argue that both of these policies-mandatory Master’s degrees for teachers in states such as California and New York, and automatic pay hikes for those teache who acquire a Master’s degree-create the wrong set of incentives for teachers.
17. Betts (1996b) finds that most papers which have tested for a link between earnings of students after they leave school and the level of education of their teachers have found no link. None of the three pre ously published papers that have modeled educational attainment as a function of teacher education h found a significant link. For similar evidence using the National Longitudinal Survey of Young Wom see Betts (1996c).
18. Teachers may prefer to teach at such schools not only because students are better prepared academi-
cally, but because violence is less prevalent at such schools. Grogger (1997) establishes that teachers appear
to command slightly higher salaries at violence-ridden schools, perhaps because higher salaries help to
retain teachers who are working under difficult circumstances.
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282 The Journal of Human Resources
Table 2
Models with Alternative Measures of Teacher Experience
Variable 1 2 3
Average teacher experience 0.0082 0.0155
(3.15) (2.84)
Experience in district 0.0043 -0.0067
(2.04) (-1.52)
R-squared 0.1502 0.1493 0.1506
Adjusted R-squared 0.1466 0.1457 0.1468
Note: Sample size is 5,623. T-statistics appear in parentheses. Other regres shown in Table 1.
Table 2 provides models that employ various measures of teacher experience. If the
positive link between students’ subsequent performance at university and teacher
experience merely reflects the migration of teachers with seniority to the best schools
in the district as jobs open up, then only teacher experience gained inside the school
district should matter. (Experience outside the district will not typically increase the
teacher’s seniority within the district.) The first model in the table replicates Model
4 from Table 1. If the observed positive correlation between teacher experience and
students’ GPA at university merely reflects seniority-based movement of teachers,
then we would expect that the average years of teacher experience in the district
should be more highly linked to GPA than total years. But as shown in Model 2,
this is not the case.
Models 1 and 2 are nonnested hypotheses, which cannot be tested against each
other using traditional methods. Instead, in Model 3, we create an artificially nested
model that includes both measures of teacher experience. Davidson and MacKinnon
(1981) developed the J-test as a specification test for one model against a nonnested
alternative. In our case, the t-statistic on one experience variable is interpreted as a
specification test of the model that contains the second measure of experience, and
vice versa. If the added experience variable is significant, it suggests that the original
model is misspecified because it cannot explain some of the variation in GPA cap-
tured by the experience variable used in the alternative model. By this criterion, the
model which hypothesizes that it is teachers’ experience within the district that mat-
ters is rejected at less than 5 percent; the model which hypothesizes that total teacher
experience determines university GPA is retained at better than 10 percent. We con-
clude that the model that uses total experience is correctly specified, although the
model that assumes that only experience within the district matters is misspecified.19
The models and tests represented in Table 2 suggest that teaching experience
outside the district is at least as valuable as teaching experience within the district.
19. An alternate way of specifying 3 is to enter experience within and outside the district as separate
regressors. As implied by the above statement, at the 10 percent level there is no statistically significant
difference between the effectiveness of teaching experience within and outside the school district.
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Betts and Morell 283
This increases our confidence that the positive link observed between university G and high school teachers’ experience represents a genuine causal relationship, rathe than reverse causation related to seniority-based teacher transfers into the be schools.20
The conclusion from this section is that some school resources, in particular teach experience, might be correlated with students’ subsequent GPA at university. But p sonal background and the socioeconomic traits of the school and school district popu tion are much more important determinants of students’ GPA at university.
V. Can High School Resources and Demographic
Traits Improve Predictions of University GPA?
In the previous section the GPA models did not include high school
GPA or SAT scores as predictors of university GPA. Because it is likely that bet schools produce students who obtain higher SAT scores, higher grade school G and higher university GPA, including the former two potentially endogenous va ables as regressors would have reduced the coefficients on the measures of sch resources. The models in the previous section are thus specified correctly if on goal is to measure the total effect of school spending on university achievemen But universities can and do use high school GPA and SAT scores in their admi sion decisions. Therefore, it is important to study whether these variables pred university GPA well, and whether personal background, school traits, or demo graphic characteristics can improve predictions of students’ university GPA. To swer these questions, in this section we estimate models of university GPA whi condition upon high school GPA and SAT scores.
We begin the formal regression analysis with a variant of (1):
5
(4) GPA = c + HSGPA,ij + SATMjy,n + SATV,jy + E YEARJXt
t=2
+ BACKiA + E MAJORk + gij
k=l
This equation adds the high school GPA, and the math and verbal SAT scores
(HSGPA, SATM and SATV respectively) to (1). This equation allows us to test a
number of hypotheses:
i) Do high school GPA (HSGPA) and SAT scores predict GPA at UCSD well?
Ho: 5 y, = , – 0
ii) Does personal background provide information beyond that obtainable from
high school GPA and test scores? H0: A = 0
Column 1 in Table 3 shows the above model estimated without the personal back-
ground variables. As suggested by Morell’s (1993b) analysis of UCSD’s freshman
20. Furthermore, the robustness tests in Table A2 in the appendix suggest that teacher experience is not
proxying for unmeasured socioeconomic traits of the student body or neighborhood.
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Table 3
Predicting University GPA using High School GPA, Test Scores, and Background Info Variable 1 2 Constant
High school GPA
SAT math
SAT verbal
Male
Black
Hispanic
-0.2758
(-3.38)
0.5272
(29.22)
0.0008
(9.90)
0.0009
(13.07)
-0.1297
(-1.45)
0.5097
(27.36)
0.0009
(10.52)
0.0008
(10.24)
-0.0862
(-6.67)
-0.0553
(-1.34)
-0.0598
(-2.74)
-0 (-2 (2 ( (9 -0 (-6 -0 (-0 -0 (-1This content downloaded from
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Asian -0.0900 -0.0846 – (-6.44) (-6 Other Race -0.0209 -0.0188 (-0.55) (-0 Proportion on AFDC -0.2166 (- Median household income 0.000 Proportion with Bachelor’s 0.38 Teacher-pupil ratio – Average teacher experienc Proportion Teachers Graduate degr R-squared 0.2825 0.2991 0.311 Adjusted R-squared 0.2809 0.2962 0.3 P-Value 1 vs. current P-Value 0.00000 0.0 Previous vs. current 0.00000 Note: Sample size is 5,470. T-statisThis content downloaded from
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286 The Journal of Human Resources
class of 1990, both SAT scores and high school GPA are highly predictive of univ sity GPA. The null hypothesis in i) above is strongly rejected (p-value = 0.000 Nonetheless, fully 72 percent of the observed variation in university GPAs rema to be explained. Furthermore, a one-to-one correspondence does not exist betw high school and university GPA. The model suggests that a one-point increas HSGPA translates into an increase in university GPA of only 0.53 point.21
We next test the hypothesis that the student’s personal background does not a any explanatory power to the model once HSGPA and SAT scores are includ Column 2 of Table 3 shows that the student’s gender and race continue to be hig significant predictors of GPA. (In coefficients not shown, to some extent pare income also remains significant.) An F-test for the joint exclusion of these perso traits rejected the null with a p-value of 0.0000, as shown in the penultimate of the table.22
It is noteworthy that after we condition on high school achievement, there is longer a statistically significant difference between blacks and whites or betw “other races” (nonwhite) and whites. Significant differences persist between whi on the one hand and Hispanics and Asians on the other, although the size of coefficients drop considerably. This finding is similar to that by O’Neill (1990 Neal and Johnson (1996) that earnings differences between blacks and whites largely accounted for by precollege factors such as test scores.
We next test whether, conditional upon high school achievement and perso background, high schools “matter.” In the model:
(5) GPA ij = SCHOOLotk + HSGPA,iJ + SATMijy
j=1
5
+ SATViy, + YEAR tx
t=2
+ BACKJA + Z MAJORJk + ?,
k=l
we test that
(6) H0: ol = a2 = tC3 * * * = ,,.
21. Of course, this apparent dissipation of GPA once the student arrives at university in part reflects
collinearity between HSGPA and the SAT scores. Reestimation of the model without SAT scores increased
the coefficient on HSGPA moderately, to 0.6. As shown in Table Al, high school GPA is on average
about 0.8 point higher than the university GPA.
22. As we have postulated, because the three measures of high school success are positively correlated
with university GPA, the signs and size of the coefficients on the measures of personal background tend
to be smaller than what was found in the reduced form models in Table 1, Column 1.
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Betts and Morell 287
The hypothesis in (6) was strongly rejected, with a p-value of 0.0000.23 We thus
conclude that students from certain high schools obtain a significantly higher univer- sity GPA than do other students, even after controlling for the student’s high school
GPA, SAT scores and observable personal characteristics.
Accordingly, in Column 3 of Table 3 we add the three measures of the demo-
graphic background of people in the school area, and then in Column 4 we also add the three measures of school resources. As shown in the penultimate row in the table, tests of each model against the more complex model to its right in all cases strongly
reject the simpler model. The coefficients and t-statistics on the school and neighbor- hood traits in both Models 3 and 4 are quite similar to our earlier results.
By how much do the GPA predictions improve once we add the measures of
school resources and demographic background of the school? The change in the R2 provides a rough guide. Model 1, which conditions only on high school performance
and major and year of study at university, accounts for about 28 percent of the
variation in GPA. As we add the measures of personal background, demographic
traits and high school resources, we succeed in explaining slightly over 31 percent of the observed variation.24 Despite the modest improvement in explanatory power,
the size of the predicted impact on GPA is in some cases meaningful. For instance, Model 4 predicts that if two otherwise identical students come from school districts
in which 20 percent and 50 percent of the adult population held four-year or higher
college degrees respectively, the latter student will obtain a university GPA of (0.5-
0.2) * (0.3804) or about 0.11 grade point higher.
An alternative approach to improving predictions of student performance is to
condition the model not on specific traits of the high school, but on the fixed effects for the schools themselves. When we ran the fixed effect model the R2 on Model 2
in Table 3 rose from 0.2962 to 0.3984.25 Thus adding separate intercepts for each
school can account for roughly another 9-10 percent of the variation in undergradu-
ate GPAs.
VI. Conclusion
Existing research on the determinants of school quality tends to focus
on models of test scores or earnings. Very little attention has been given to the impac 23. As before, we reestimated this model after removing schools attended by fewer than 3 students, in a
bid to minimize the possibility that what we are identifying is not school effects so much as individua effects. We obtained the same p-value for the hypothesis in (6).
24. Of course, it would be wrong to conclude from this comparison that the variables in the simple model
in Column 1 “explain” 28/3 = 9.3 times as much of the variation in GPAs as do the additional regressor added in Column 4. This interpretation is incorrect because the change in R2 depends on which set of
regressors-the new regressors in Column 4 or the regressors in Column 1, are added first. Our goal here
is simply to estimate how much additional variation in GPA can be explained by personal, school and demographic factors, given that administrators are already “controlling” for high school GPA and SAT scores in the admissions process.
25. When we repeated this exercise on the subsample of schools for which we had three or more students,
in order to ensure that the school fixed effects were identifying a school effect rather than an individual
effect, the R2 rose from 0.2963 to 0.3856.
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288 The Journal of Human Resources
of schools on educational achievement. Betts (1996b) finds only 14 published artic dealing with the link between school resources and educational attainment. In m cases, the only way in which attainment has been measured is in terms of year education completed.
This paper has used a different measure of success in postsecondary educat the student’s GPA. This approach is useful given evidence that university GP linked to students’ subsequent earnings.
We find that personal background, including sex, ethnicity, and family inco is significantly linked to university GPA. We also find that the socioeconomic en ronment of the school matters. We tested that three measures of school resou the teacher-pupil ratio, the average experience of teachers, and the proportio teachers with advanced degrees, influenced students’ subsequent performance in versity. For the teacher-pupil and teacher education variables, we could find no e dence of a positive and significant link with university GPA. We in fact fou significant and negative link between GPA and the proportion of high school teac with advanced degrees. Although surprising at first, these findings are in accorda with much of the earlier literature on test scores. However, we did find a pos and significant link between teacher experience and the student’s GPA. We expre concerns that this apparent relationship might reflect selection of teachers with niority into job vacancies in the schools with the best prepared students, which typically in more affluent areas. But two sets of robustness tests suggest that sort of reverse causation is not at work.
We have also tested whether college administrators’ use of high school GPA and
SAT scores to predict success in university is valid. High school GPA and SAT
scores are indeed strongly linked to university GPAs. However, we also find strong
evidence that GPA predictions could be improved by including measures of the stu-
dent’s personal background, the socioeconomic environment of the school, and some
measures of school resources. For instance, women tend to obtain higher GPAs than
men.26 Similarly, students who attended a school in which a high proportion of stu-
dents’ families received AFDC, or a school in an area where only a small proportion
of adults hold college degrees, obtain significantly lower GPAs in university than
other students. However, the gains in predictive power we obtained are fairly modest.
Addition of controls for personal background, school resources and the school’s
socioeconomic environment explained an additional 3 percent of the variation in
university GPAs beyond the simple model. An alternative method for improving
forecasts of university GPA would be to model GPA with separate intercepts for
each high school. Such a fixed effect model can explain about 10 percent of the
variation in university GPA beyond the simple model.
These results should be of interest to two policy communities. First, for university
administrators, our results suggest that although high school grades and test scores
are good predictors of university GPA, more complex models that condition on per-
sonal background and school and neighborhood traits can significantly improve pre-
dictions of student’s university GPA. Even after controlling for high school grades
26. However, we caution the reader that omitted variable bias may be responsible for some of the observed
variations across gender and ethnicity.
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Betts and Morell 289
and test scores, students from certain underrepresented groups, and from scho located in economically disadvantaged areas, are likely to obtain lower grades university.
We wish to stress, though, that GPA is only one measure of adult success. Our
data provide no evidence on how much two different students would gain in earnings
from attending university. Although a student from a disadvantaged area may indeed
obtain a lower GPA at university than an otherwise identical student from an affluent
area, the gain in earnings from attending university could be larger for the student
from the economically disadvantaged area.
Second, our results should be of interest to public school administrators and to
those studying the economics of education. The research provides evidence that
schools with more highly experienced teachers produce graduates who perform sig-
nificantly better at university. But the effects are moderate in size: an extra ten years
of teaching experience among teachers at the student’s school is associated with a
university GPA which is approximately 0.1 point higher. Our results for the other
two measures of school inputs conform more closely to the test-score literature,
which has typically found little evidence that greater school resources improve stu-
dent performance. Overall, our estimates suggest that in California, variations in
family background and in the socioeconomic environment of the school play far
more crucial roles in determining student outcomes in university than do variations
in school resources.
Appendix
Merging the Datas
Merging the school-level data with the individual student data proceeded in several
steps. First, the California Department of Education datas, for which high school
names, city, zip code and the California “CDS” code were available, were merged
with each other using the CDS school-level codes. Second, the ETS data containing
SAT scores and ETS school codes was merged with the California data by matching
for the CDS school district code and the school name, which were available in both
datas. Next, the Census of Population data by school district were merged using
the CDS district-level codes. Finally, the resulting data containing information on
individual high schools and the demographic traits of the populations in the corre-
sponding school districts was merged with the data on UCSD undergraduates, using
the ETS school codes. This process did not provide a match for every UCSD student
who had attended a public school, because of missing data in the “bridging” data
which contained both ETS codes and CDS codes. Consequently, in cases where we
had initially failed to match the high school attended by a UCSD freshman to the
California Department of Education data, we manually matched schools using infor-
mation on the school’s name, and the city and county in which they were located.
These pieces of information were available both from the UCSD Registrar’s data
and the California Department of Education data. We achieved matches for 98.6
percent of the schools and 99.7 percent of the freshmen who had attended California
public high schools.
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290 The Journal of Human Resources
Table Al
Means and Standard Deviations of Variables Used in Tables 1 to 4
Variable Number Mean Standard
University GPA 5,623 3.033 0.516
High school GPA 5,602 3.875 0.338
SAT math 5,491 618.880 84.621
SAT verbal 5,491 514.163 89.876
Male 5,623 0.487 0.500
Black 5,623 0.023 0.151
Hispanic 5,623 0.103 0.304
Asian 5,623 0.338 0.473
Other race 5,623 0.025 0.156
Foreign 5,623 0.095 0.293
Income 25-49.999K 5,623 0.190 0.392
Income 50-74.999K 5,623 0.198 0.398
Income 75-99.999K 5,623 0.147 0.354
Income 100-199.999K 5,623 0.138 0.345
Income 200K-higher 5,623 0.020 0.141
Last year enroll 2 5,623 0.057 0.232
Last year enroll = 3 5,623 0.327 0.469
Last year enroll 4 5,623 0.433 0.496
Last year enroll = 5 5,623 0.123 0.328
Engineering 5,623 0.226 0.419
Science 5,623 0.243 0.429
Arts 5,623 0.018 0.133
Humanities 5,623 0.030 0.170
Social science 5,623 0.156 0.363
Proportion on AFDC 5,623 0.098 0.095
Median household income 5,623 41.938 12.318
Proportion with bachelor’s degree 5,623 0.279 0.123
Teacher-pupil ratio 5,623 0.041 0.004
Proportion teachers graduate degree 5,623 0.559 0.128
Average teacher experience 5,623 17.963 2.560
Average teacher experience in district 5,623 15.312 3.044
Average teacher experience outside 5,623 2.651 1.557
district
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Betts and Morell 291
Table A2
Repetition of GPA Models from Table 1 with Principal Components from a
Factor Analysis of Demographic Background as Additional Controls
Variables 1 2 3 4
Teacher-pupil Ratio -1.6900 -2.0016
(-0.86) (-1.00)
Average teacher experience 0.0067 0.0096
(2.34) (3.21)
Proportion teachers graduate -0.1567 -0.2194
Degree (-2.86) (-3.81)
R-squared 0.1573 0.1580 0.1584 0.1603
Adjusted R-squared 0.1573 0.1527 0.1531 0.1546
Note: Sample size is 5,537. T-statistics appear in parentheses. Other regressors no as listed in Table 1, Models 3 through 5, and the first 14 principal components from 24 variables and their squares, each of which is meant to serve as a proxy for th of the school. These 24 variables included the AFDC (1994) variable, median hou in the school district, and the proportion of the adult population in the district wi higher (1990), which correspond to the three variables that we have already used in We also added the following district-level variables derived from the 1990 Census: t population over 20 with high school diplomas, the proportion with some college median gross rent, and the proportions of the population which are “urban-inside u farm,” and “ruralnonfarm,” with “urban-outside urbanized area” as the excluded variables refer to 1990. We also included the following characteristics of the studen high school: the proportion of students in the attendance area receiving free or proportion of the student body which was in the category of Limited English Prof indicating the proportion of the student body which was black, Asian, Hispanic, proportion of the graduates from the high school who had completed all courses re the University of California or the California State University systems, the high-sch age scores on the verbal and math components of the SAT, the number of stude exams as a proportion of Grade 12 enrollment, and the proportions of the Grade 10 5 or 6 on the reading, writing and math components of the California Learning As (Information provided to us by the California Department of Education states that from 1 to 6, with 1, the lowest level, showing little or no evidence of understandin 6, the highest level, indicating exemplary student work.) All of these latter vari 93 school year, except for the meal assistance variable, which refers to the 1994 References
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