Jan 8, 2006 - of instruction (Rivkin, Hanushek, and Kain (2005); Hanushek et al. (2005)). ...... References. Angrist, Joshua D., and Kevin Lang. 2004.
The Evolution of the Black-White Achievement Gap in Elementary and Middle Schools Eric A. Hanushek and Steven G. Rivkin *
Very Preliminary Please do not cite Paper prepared for American Economic Association Annual Meetings Boston, MA January 6-8, 2006 ABSTRACT Considerable recent attention has focused on the black-white achievement gap and its growth during the school years. Prior work has suggested that identifiable school characteristics have little to do with the changing gap. Our preliminary analysis, however, suggests that differences in the schools attended by blacks and whites combined with the added sensitivity of blacks to the racial composition of schools can completely explain the pattern of achievement gaps in late elementary school and middle school.
*
Stanford University, University of Texas at Dallas, and National Bureau of Economic Research; and Amherst College, University of Texas at Dallas, and National Bureau of Economic Research, respectively. Support for this work has been provided by the Packard Humanities Institute.
The Evolution of the Black-White Achievement Gap in Elementary and Middle Schools Eric A. Hanushek and Steven G. Rivkin
1. Introduction Evidence suggests that cognitive skills explain the bulk of racial gaps in school attainment and wages, making the reduction of such skill differences an important component in efforts to reduce race differences in economic and social outcomes.1 But, the longstanding skill gaps have remained quite impervious to substantial policy efforts to eliminate them. Earlier optimism about narrowing gaps (Jencks and Phillips (1998)) has dissipated with new evidence that the black-white achievement gap stayed constant, or maybe even grew, during the 1990s (National Center for Education Statistics (2005)). Most importantly, the causes of the existing large gaps have generally eluded researchers, adding to the policy confusion. This paper presents preliminary evidence on the role of schools and school policy in affecting black-white differences in achievement patterns through the schooling years. In recent work Fryer and Levitt (2004, 2005) document changes in achievement differences from preschool through 3rd grade but do not find strong evidence on the role of specific school (or other) factors. Murnane et al. (2005) identify somewhat different patterns of black-white achievement in early schooling, but contribute only modestly to the explanation of these.2 Identifying the contributions of schooling and other factors is a 1
Neal and Johnson (1996) and O'Neill (1990) provide evidence on wage differences, and Rivkin (1995) provides evidence on differences in educational attainment. 2 Murnane et al. (2005) employ a different sample of data for early childhood experiences developed by NICHD. After matching the samples to account for different sampling schemes, they find quite different patters in achievement. It is nonetheless difficult to sort out the effects on the results of their small samples,
difficult task, particularly in the context of race and location. Not only does the nonrandom allocation of students into neighborhoods schools and classrooms complicate the identification of causal effects of specific school and peer variables, but evidence strongly suggests that easily quantifiable factors explain only a portion of the variation in the quality of instruction (Rivkin, Hanushek, and Kain (2005); Hanushek et al. (2005)). In this paper we use both the Texas Schools Project (TSP) panel data and the Early Childhood Longitudinal Survey (ECLS) data used by Levitt and Fryer (analysis of ECLS is to be added and is not included in this draft) to extend the work on racial achievement differences up to the 8th grade. Our particular focus is estimating the importance of specific school and peer factors previously shown to be significant determinants of achievement. These include student mobility and racial composition, teacher experience, and the racial match between teachers and students.3 The higher mobility rates and share of teachers with little or no experience among blacks suggests that these factors contribute to the widening of the achievement gap as students age. The predominance of white teachers may also widen the gap, given evidence that race matches between teachers and students lead to higher achievement. Importantly, any effects of student/teacher race matching can widen within as well as between school differences. One issue that we examine in some detail is the possibility that changes in the racial achievement gap vary by initial achievement. Several hypotheses have been offered that suggest that the gap may grow more rapidly for initially high achieving blacks. On the one hand, blacks who excel in the early grades may face the strongest peer pressure against of their alternative tests, and of their more detailed measures of schooling. This divergence across samples motivates part of our work.
2
academic success. Alternatively, higher achieving blacks may fall further from the center of their school’s achievement distribution and be less likely to participate in an academic program that facilitates continued excellence. Importantly, we consider the effects of test measurement error and regression to the mean on the pattern of racial achievement differences. Another important issue is the possibility that the structure of the test used by the state of Texas may lead to substantial divergence between trends in knowledge differences and trends in the observed achievement gap. Specifically, consider the possibility that the test fails to capture much of the variation in higher order skills and that a higher share of instruction for blacks compared to whites focuses on tested skills during the school year. In such a case analysis, using a test emphasizing basic skills will tend to bias downward estimates of changes in the mean racial achievement gap. By focusing on students at different initial skill levels we can learn more about the importance of test degree of difficulty.4 Our preliminary results differ noticeably from the other recent analyses of the black-white achievement gap. We find that identifiable school factors – school mobility rates, teacher experience, and racial composition of students and teachers – completely explain the growth in the achievement gap between grades 3 and 8. Black students go to schools that differ noticeably along these dimensions from those attended by white, and blacks are differentially sensitive to racial composition effects, leading to the overall
3
Hanushek, Kain, and Rivkin (2004a) investigate the effects of student mobility; Rivkin, Hanushek, and Kain (2005) investigate the effects of teacher experience; and Dee (2004a, 2004b) and Hanushek et al. (2005) examine the effects of student/teacher race matching. 4 Fryer and Levitt (2005) consider a related hypothesis through comparing performances of blacks and whites on alternative cognitive tests and suggest that blacks may indeed be doing more poorly on tests of higher order skills.
3
importance of these in explaining the observed racial achievement gap and its pattern through elementary and middle schooling. The next section describes the TSP micro-data sample used in this analysis. Section 3 develops the empirical framework, and Section 4 presents the preliminary results. The final section summarizes the findings and discusses directions for further research.
2. UTD Texas Schools Data The cornerstone of the analysis of racial composition effects on achievement is a unique stacked panel data set of school operations constructed by the UTD Texas Schools Project. The data we employ track the universe of four successive cohorts of Texas public elementary students as they progress through school. For each cohort there are over 200,000 students in over 3,000 public schools. Unlike many data sets that sample only small numbers from each school, these data enable us to create quite accurate measures of peer group characteristics. We use data on four cohorts for grades three through eight. The most recent cohort attended 8th grade in 2002, while the earliest cohort attended 8th grade in 1999. The student data contain a limited number of student, family, and program characteristics including race, ethnicity, gender, and eligibility for a free or reduced price lunch (the measure of economic disadvantage). The panel feature of the data, however, is exploited to account implicitly for a more extensive set of background characteristics through the use of a value added framework that controls for prior achievement. Importantly, students who switch schools can be followed as long as they remain in a Texas public school.
Beginning in 1993, the Texas Assessment of Academic Skills (TAAS) was administered each spring to eligible students enrolled in grades three through eight. The 4
tests, labeled criteria referenced tests, evaluate student mastery of grade-specific subject matter. This paper presents results for mathematics. Each math test contains approximately 50 questions. Because the number of questions and average percent right varies across time and grades, we transform all test results into standardized scores with a mean of zero and variance equal to one, which transforms the outcome into a measure of relative position in the achievement distribution. Importantly, the student database can be linked to information on teachers and schools. The school data contain detailed information on individual teachers including grade and subject taught, class size, years of experience, highest degree earned, race, gender, and student population served. While individual student-teacher matches are not possible, students and teachers can be uniquely related to a grade on each campus. Each student is assigned the average class size and the distribution of teacher characteristics for teachers in regular classrooms for the appropriate grade, school, and year.
3. Empirical Framework Because the acquisition of knowledge is a cumulative process, achievement today is influenced not just by current family, school, and peer interactions but also by those of the past that establish the base for any current learning. Data limitations make it virtually impossible to control for all factors that contribute to current achievement. In order to isolate the causal effects of specific variables we use a fixed effect in gains approach designed to isolate variation in contemporaneous student, school and peer characteristics not correlated with confounding factors. Equation (1) describes the gain in achievement (∆A) for student i in grade g and
5
school s in year y, (1)
∆A igsy = X igsy β + S gsy δ + P( − i ) gsy λ + eigsy
where P is peer influence measured by average characteristics of schoolmates (individual i is omitted from the calculation) including proportion black and proportion new to the school and X and S are relevant family background and school inputs, respectively, including race, subsidized lunch receipt, special education program participation, and mobility dummies, teacher experience and race, and other school and teacher characteristics. Some parameters such as the effect of teacher race may also vary by student race. Finally, indicators for structural moves that account for any effects of transitions to junior high school and a complete set of grade by year dummy variables are also included. The gains model explicitly accounts for prior influences by focusing on the annual achievement change. This form of the value added model does impose the unrealistic assumption that there is no depreciation in human capital, i.e. that the parameter on the prior test score equals one. However, Rivkin (2005) shows that this does not bias the estimates as long as the variables of interested are not serially correlated conditional on the other regressors. In order to mitigate specification errors resulting from both omitted variables and the form of the gains model, we include a full set of school by grade and school by year fixed effects in some specifications. The remaining variation in school and peer characteristics has therefore been purged of campus by year specific influences such as neighborhood change and campus by grade specific influences such as curriculum or systematic achievement patterns. Remaining variation is produced by movements in teachers and students or changes in school policy that are not systematically related to
6
other determinants of learning. Because neighborhood and school changes may directly affect achievement and because changes may have systematically lower achievement than stayers, it is necessary to account for both mobility and initial achievement in order that the remaining variation in the school characteristics is unrelated to confounding factors. The initial empirical analysis follows Fryer and Levitt (2004, 2005) by estimating a baseline model with few controls and then adding student, school, and peer variables. An important difference is the focus on specific school factors found to be systematically related to achievement. These include both student turnover and the share of teachers with little or no experience.5 In addition, the inclusion of school by grade and school by year fixed effects in a value added framework should provide superior controls for potentially confounding influences. In addition to the analysis of the determinants of mean achievement differences we also investigate the possibility that changes in the racial achievement gap vary by a student’s initial location in the skill distribution. By dividing the 3rd grade achievement distribution into a number of equal sized intervals, systematic variation by initial achievement in the change in the achievement gap between 3rd and 8th grades can be identified. Differences can be compared with race differences in family, student and school characteristics. Because test scores measure actual knowledge with error, both true knowledge and the error draw determine division by initial achievement. If errors are uncorrelated over time, those initially placed in high achievement categories will tend to draw less positive errors in the subsequent year, while those placed in the lower categories will tend to draw
5
Hanushek, et al (2004) provides evidence on student turnover, and Rivkin, et al (2005) provides evidence on the effects of early experience.
7
more positive errors in the subsequent year. Therefore regression to the mean will account for a portion of the observed difference in test score changes across categories. Mean regression also complicates black-white comparisons because of differences in the actual initial skill distribution. This can easily be seen by a comparison the proportion of observations erroneously classified in different categories at any point in time. Considerate the trivariate skill distributions shown in the top panel of Table 1 for blacks and whites, where the distribution for blacks is more concentrated in the lower categories than the distribution for whites. If measurement error is randomly distributed with no differences by race, there are no race differences in the probabilities of being observed in test score category j with true skill in category i (ie. Pij does not depend on race). In this simple case, the bottom panel of Table 1 describes the distribution of true and erroneous observations by race and observed skill category. More whites than blacks have been misclassified into the lowest observed skill category, while the opposite is true for the highest observed skill category. As a result purely of a regression to the mean phenomenon, the expected achievement gain in the next period is higher for whites than for blacks at the low end of the observed skill distribution and probably at the high end if the errors leading to the misclassification are uncorrelated over time. The type of pattern shown in Table 1 invalidates the categorization of students on the basis of tests in which the average error for blacks differs systematically from the average error for whites within categories. Therefore we use a test in a different subject to categorize students by initial mathematics skill level based on the assumptions of positive correlations across subjects in true skill and no correlation in the test measurement errors across subjects. This scheme severs the link between initial category and expected
8
Table 1. Simulated Observed and Actual Test Score Distributions for Blacks and Whites Initial Actual Skill Distributions Blacks Whites Observed Test distribution Blacks Low Middle High Whites Low Middle High
Low 0.4 0.2
Middle 0.4 0.5
High 0.2 0.3
0.4*PLL + (0.4*PML + 0.2*PHL) 0.4*PMM + (0.4*PLM + 0.2*PHM) 0.2*PHH + (0.4*PLH + 0.4*PMH) 0.2*PLL + (0.5*PML + 0.3*PHL) 0.5*PMM + (0.2*PLM + 0.3*PHM) 0.3*PHH + (0.2*PLH + 0.5*PMH)
difference in the error realizations for the initial and subsequent periods.
4. Preliminary Results This section begins with a description of changes in the black-white mathematics achievement gap between 3rd and 8th grade and then analyzes the determinants of changes in the gap. In the descriptive section we examine the effects of sample attrition and grade retention, decompose changes into within and between school components, and then investigate differences by initial (3rd grade) place in the skill distribution. The empirical analysis focuses on the effects on outcomes of teacher experience, student mobility, and racial composition, all factors that differ significantly by race. Elementary and Middle School Racial Achievement gap Table 2 reports the black-white achievement gap for grades 3,5, and 8 for the sample as a whole and for the subset of students with no missing test observations for grades 3 through 8. Grades 3, 5, and 8 are reported, because movement from elementary to junior high or middle school produces a great deal of temporary test volatility in grades 6 and 7 that disappears within a year following the transition. The table also reports the within school black-white gaps constructed by removing school fixed effects. A comparison of the gaps produced by the repeated cross sections (top panel) and sample of students with a complete set of test observations who progress with their class (bottom panel) highlights the importance of grade retention, special program assignment, and other factors that determine test taking patterns. As Appendix Table A1 shows, grade retention and special education classification rates for blacks exceed those for whites in all grades, and the gaps are higher in grades 5 and 8. Because test taking rates are far lower for
9
Table 2. Black-white Math Test Score gap (average black score minus average white score) grade
entire sample overall gap within school gap
3
5
8
-0.70 -0.64
-0.72 -0.63
-0.75 -0.61
-0.64 -0.56
-0.70 -0.58
sample of students with complete set of observations overall gap -0.58 within school gap -0.56
children classified as special needs, a much larger share of black 3rd grade test takers will either lack a test observation or no longer attend school with their original cohort by the end of 8th grade. As the probability of grade retention or special education classification is higher for those in the lower portion of the achievement distribution, this means that blacks in the complete cohort sample will tend be a more select group than whites in the complete cohort sample. Across grades, the sample of blacks will tend to have been in school longer on average than whites because of grade retention, and this works to narrow the black-white gap when taken as a snapshot at a given grade level. The lower 3rd grade test score gap and larger increase in the gap between 3rd and 8th grade observed for the complete cohort sample both result from these differences in grade retention and special education classification. In the complete panel sample, the gap rises from 0.58 standard deviations at the end of 3rd grade to 0.64 in 5th grade and to 0.70 in 8th grade. This means that changes between grades 3 and 8 account for roughly one sixth of the 8th grade gap. If grades K through 3 were to contribute a similar differential, the elementary school years would account for roughly one fourth of the 8th grade achievement differential. The bottom row reveals that the within school achievement gap remains roughly constant between grades 3 and 8, meaning that the bulk of the gap increase occurs between schools. Although family, neighborhood, or other nonschool factors could affect between school differences, the pattern in Table 2 is consistent with the possibility that school quality accounts for much of the rise in the elementary school racial achievement gap. Prior to considering the sources of the mean achievement gap increase in greater
10
detail, we examine differences in the rate of increase along the initial achievement distribution. This view is particularly important, because the distributions of achievement for whites and blacks – as expected from the means – are quite different. Figure 1 reports the 3rd grade reading achievement distribution for 16 groups based on the TAAS tests.6 The white students are heavily weighted in the top achievement categories, while blacks are more evenly spread across categories. Table 3 provides the distribution of black-white math gaps (in standard deviations) for each of the categories of 3rd grade reading scores. In third grade, the math gaps are noticeably greater in the low reading groups compared to the high reading groups. But, as the top panel of the table clearly reveals, the changes in the gap as students are followed through grade increase when moving up the 3rd grade reading distribution. Figure 2 plots the change in grade 3 to 8 black-white gaps by 3rd grade achievement (hashed bars). Increases in the black-white gap between 3rd and 8th grade do not exceed 0.1 standard deviations in the bottom seven initial achievement categories, while they exceed 0.15 standard deviations in the top seven categories and 0.25 in the top 2. Thus substantial increases in the achievement gap for students at the upper end of the initial skill distribution emerge despite the focus of the Texas tests on lower order skills. The result is a noticeable leveling of the distribution of gaps in 8th grade as compared to 3rd grade. As is the case for the sample as a whole, the bulk of the increases in virtually all categories occurs between schools. The bottom panel in Table 3 and the solid bars in Figure 2 show the change in gaps within schools. The average within-school gap does increase in the top achievement categories by roughly 0.1 standard deviations, consistent
This figure and the following discussion relies on the sample of students with complete test data for grades 3-8. 6
11
Figure 1. Achievement Distributions for Blacks and Whites 30%
% students (by race)
25%
20%
15%
10%
5%
0% 1
2
3
4
5
6
7
8
9
10
11
Achievement category (1=lowest) whites
blacks
12
13
14
15
16
Table 3. Black-white Math Test Score Gap by 3rd Grade Reading Test Score Category (students with complete observations) test score group (by grade 3 reading scores)a lowest
overall gap 3rd grade 5th grade 8th grade within school gap 3rd grade 5th grade 8th grade whites (1000s) blacks (1000s)
highest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
-0.51
-0.49
-0.43
-0.40
-0.36
-0.41
-0.35
-0.32
-0.30
-0.30
-0.26
-0.24
-0.21
-0.21
-0.18
-0.15
-0.61
-0.61
-0.49
-0.52
-0.47
-0.49
-0.46
-0.45
-0.41
-0.41
-0.38
-0.36
-0.36
-0.37
-0.31
-0.34
-0.58
-0.56
-0.48
-0.48
-0.45
-0.51
-0.44
-0.49
-0.42
-0.47
-0.44
-0.43
-0.42
-0.45
-0.44
-0.44
-0.37
-0.45
-0.41
-0.40
-0.36
-0.38
-0.34
-0.33
-0.34
-0.31
-0.29
-0.28
-0.25
-0.24
-0.21
-0.21
-0.50
-0.60
-0.44
-0.46
-0.38
-0.43
-0.42
-0.41
-0.39
-0.38
-0.35
-0.33
-0.32
-0.30
-0.25
-0.28
-0.47
-0.47
-0.38
-0.38
-0.38
-0.38
-0.38
-0.40
-0.35
-0.37
-0.38
-0.31
-0.35
-0.35
-0.33
-0.31
8.9
12.5
11.1
16.4
25.5
22.0
36.9
64.7
50.2
62.0
126.5
186.0
176.3
308.4
496.0
371.2
8.7
11.3
8.8
13.4
18.3
15.1
21.4
35.0
24.7
27.1
47.6
58.8
43.2
59.9
69.1
36.7
Note: a. Reading scores range from -2.1 std. dev. to 1.2 std. dev. and are divided into intervals roughly .2 std. dev. in width.
Figure 2. Change in Black-White Achievement Gaps Between Grades 3-8 by Initial Achievement Level (students with complete observations) 0.10
Change in gap (s.d.)
0.00 1
2
3
4
5
6
7
8
9
10
11
12
-0.10
-0.20
-0.30
-0.40 Achievement category (1=lowest) overall change
within school change
13
14
15
16
with the possibility that teachers or peers provide less support to blacks than to similarly high achieving white schoolmates. Nonetheless, the overall picture indicates that differences among schools rather than divergent experiences within schools are the largest contributors to the achievement gap increase across the skill distribution. Determinants of growth in the racial achievement gap Table 4 reports estimates of the effects of student, school, and peer characteristics on annual achievement gain for a number of specifications. Only black and white non-Hispanic students with non-missing test scores for grades three through eight are included in the sample. There are a total of 1,726,908 observations of gains in grades four through eight. All specifications also include indicators for a transition to junior high, grade-by-year dummy variables, proportion of teachers who are Hispanic and that proportion interacted with the black dummy variable.7 Robust standard errors clustered by school are also reported in the tables. The first two columns provide baseline specification that include just indicators for a structural move and year-by-grade in addition to the race dummy and the addition of special education and economic disadvantage indicators.8 The remaining columns add a progressively larger set of explanatory factors, while the last column restricts attention just to within school and grade comparisons (by adding school-by-grade and school-by-year fixed effects). The baseline story from the first two columns is that blacks on average tend to lose 0.015-0.022 s.d. annually compared to whites – i.e., the achievement gap grows as seen in
7 8
Coefficients on the proportion of teachers who are Hispanic variables were all small and insignificant. Note that special education placement is a choice by schools and thus is not a pure background correction.
12
Table 4. Estimated Effects of School and Student Characteristics on Achievement (robust std errors controlling for grouping by school in parenthesis; 1,726,908 observations)* campus by year fixed effects
no
no
no
no
no
no
yes
campus by grade fixed effects
no
no
no
no
no
no
yes
black special education subsidized lunch
-0.022
-0.015
-0.008
-0.007
0.013
0.014
0.012
(0.003)
(0.003)
(0.003)
(0.003)
(0.005)
(0.005)
(0.002)
0.0055
0.0055
0.0054
0.0048
0.0048
0.0058
(0.0026)
(0.0026)
(0.0026)
(0.0026)
(0.0026)
(0.0024)
-0.016
-0.014
-0.014
-0.013
-0.013
-0.018
(0.002)
(0.002)
(0.002)
(0.002)
(0.002)
(0.001)
student moved to new school
-0.003
-0.003
-0.003
-0.003
-0.037
within district
(0.005)
(0.005)
(0.005)
(0.005)
(0.004)
student moved to new district proportion students new to school
-0.03
-0.03
-0.03
-0.03
0.00
(0.004)
(0.004)
(0.004)
(0.004)
(0.003)
-0.15
-0.14
-0.13
-0.13
-0.15
(0.02)
(0.02)
(0.02)
(0.02)
(0.03)
proportion students black proportion students black*student black proportion 0 years proportion 1 year proportion 2 years proportion of teachers black prop of tea black*student black
0.003
0.013
-0.028
(0.012)
(0.013)
(0.047)
-0.058
-0.069
-0.062
(0.017)
(0.017)
(0.014)
-0.042
-0.040
-0.040
-0.063
(0.008)
(0.008)
(0.008)
(0.010)
-0.017
-0.016
-0.016
-0.033
(0.008)
(0.008)
(0.008)
(0.010)
-0.004
-0.004
-0.004
-0.016
(0.008)
(0.008)
(0.008)
(0.010)
-0.022
-0.009
(0.012)
(0.016)
0.024
0.024
(0.015)
(0.010)
the previous aggregates.9 The estimate of the achievement disadvantage for blacks declines monotonically as student mobility and teacher experience are considered – exactly consistent with prior work that suggested these factors differentially affected blacks (Hanushek, Kain, and Rivkin (2004a), Hanushek, Kain, and Rivkin (2004b)).10 Interestingly, once the racial composition of the school and the racial matching of students and teachers is considered, black students tend to show larger achievement gains than white students. It is important to note that these race-related factors are allowed to have differential effects based on the race of the student, a natural specification that is consistent with our prior investigations of racial factors.11 These findings are especially noteworthy because many prior researchers have concluded that school factors are unlikely to be an important explanation of the achievement gap and of changes in the gaps within schools. These statistically significant differences even remain when comparisons are made just within school and grade (last column). Concerns that confounding factors could bias coefficients leads to the inclusion of school- by-grade and school-by-year fixed effects, but the clearest impact of these is to elevate the importance of having teachers in their first few years of teaching – a school characteristic that tends to be wrapped up in characteristics of schools and their student bodies (Greenberg and McCall (1974), Murnane (1981), Lankford, Loeb, and Wyckoff (2002), Hanushek, Kain, and Rivkin (2004b)). Overall, it appears that teacher experience and student turnover are important The impact of subsidized lunch status and special education are always statistically significant, and their magnitude is unaffected by inclusion of the detailed student and school information across specifications. 10 Of course the ordering of this table is arbitrary, meaning that changes in the coefficient on the black dummy do not reflect the relative importance of specific variables. We provide an ordering that matches the varying complexity of different specifications that have previously appeared.
9
13
determinants of achievement. Moreover, racial composition – perhaps the clearest focus of policy toward racial gaps because of Brown v. Board of Education – has a clear impact on black performance and thus on the achievement gaps.12 The significance of the teacher experience and student turnover variables suggests that differences in both peer and teacher composition could account for much of the growth in the racial achievement gap. Appendix Table A2 shows that the average black student experiences attends school with much higher student turnover (23 versus 18 percent of students are new to a school) and has a 2.6 percent higher probability of having a teacher with no experience. In addition, the average black has far higher percentages of black schoolmates and teachers: The average black student has 28 percent more black classmates and 22 percent more black teachers than the average white student. The results in Table 4 combined with the distribution of school and peer factors in Table A2 permit us to decompose the overall growth in the math achievement gap. Most attention to black-white differences focuses on socio-economic background differences. Within our sample, these background differences measured by differential free and reduced lunch status account for a 0.008 s.d. annual widening in the black-white gap between grades 3 and 8. Teacher experience differences – another focus of considerable prior attention – account for only a 0.002 s.d. expansion of the gap. On the other hand, the differential racial compositions of schools for blacks and whites combined with the more pronounced impact on blacks accounts for a 0.03 s.d. annual increase in the black-white gap. This racial impact is, however, offset by 0.006 s.d. improvement in the gap because of
In Hanushek, Kain, and Rivkin (2002) we find that racial composition adversely affects blacks but has not impact on whites. 12 The differential effect of racial composition is also consistent with the findings of Angrist and Lang (2004) and Guryan (2004). 11
14
the higher propensity of matching black teachers with black students. These school factors more than completely account for the changes in the black-white achievement gap during elementary and middle school. An important question is whether they can also explain the larger differences observed for students at the higher end of the initial skill distribution. Either variable effects or racial differences in the characteristics could be larger at the upper end of the initial skill distribution. At this point we have not investigated the possibility of varying effects, but we have examined the variable distributions by initial reading test score group. Appendix Table A3 provides little or no evidence of systematic differences by initial skill grouping in the racial difference in teacher experience, student turnover, student racial composition, or other school or peer characteristics.13 In addition, neither the difference in peer average 3rd grade mathematics achievement nor the difference in the share of peers in one of the top four reading groups (not shown) rises along with initial reading score. Thus it does not appear that the pattern of differences in school or peer characteristics accounts for the higher growth in the achievement gap at the higher end of the initial reading test distribution.
5. Tentative Conclusions This paper documents the important contribution of specific characteristics of teachers and peers to the racial gap in mathematics achievement. These results differ from those reported in Fryer and Levitt (2005) and Murnane et al. (2005) for the early elementary grades. Understanding the sources of the differential findings is a main issue
15
for future work. On the one hand, Texas may differ from the nation as whole, or achievement determinants in the early grades may differ from those in the higher elementary and middle school grades. On the other hand, early teacher experience, student turnover, and particularly racial composition – factors not considered by Fryer and Levitt or by Murnane et al. (2005) – may also exert significant effects in the early grades.14 Gaining a better understanding of the more rapid widening expansion of the black-white achievement gap for students higher up the initial skill distribution is the second main objective for future work. We will begin by examining the ECLS data for a similar pattern and then explore the possibility that variables included in this analysis have larger effects for students at higher initial skills. Finally, we will explore the possibility that other factors including curriculum contribute to this pattern.
Perhaps the most interesting pattern of racial differences shown in Table A3 is that whiles tend to be placed in special education at a higher rate than blacks within each achievement category. This higher placement is obscured by the very different achievement distributions shown in Figure 1. 14 Murnane et al. (2005) do consider the impact of teachers in their first two years and find it to be consistently insignificant in explaining their various achievement measures. The difference in estimated impact may reflect the low power of their tests because of their relatively small samples. 13
16
Appendix Tables Table A1. Grade Progression and Test Taking Status by Race and Grade blacks
Has score Test Missing in special education absent during testing other Off grade sequence
whites
3 88.5%
5 85.3%
8 83.3%
3 93.5%
5 92.6%
8 90.2%
9.2% 1.2% 0.5% 0.6%
11.3% 0.7% 0.2% 2.5%
9.2% 1.1% 1.5% 4.9%
4.8% 1.1% 0.3% 0.2%
4.8% 0.9% 0.1% 1.6%
4.6% 1.1% 1.0% 3.1%
Table A2. Descriptive Characteristics for Sample with Complete Set of Observations, by Race (observation is student by year) Blacks
Whites
Difference (black - white)
proportion receiving special education
0.041
0.056
-0.015
proportion receiving subsidized lunch
0.606
0.158
0.448
proportion of who switched schools
0.169
0.093
0.073
proportion of schoolmates who are new to the school
0.230
0.183
0.047
proportion of schoolmates black
0.371
0.093
0.278
teacher experience proportion 0 yrs
0.096
0.070
0.026
proportion 1 yr
0.082
0.068
0.014
proportion 2 yrs
0.071
0.063
0.008
0.254
0.033
0.221
proportion of teachers black
Table A3. Racial Gap (black minus white) in Student and School characteristics by 3rd Grade Reading Test Category Reading test score group lowest
highest
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
special education
-0.28
-0.29
-0.27
-0.22
-0.19
-0.17
-0.11
-0.12
-0.09
-0.08
-0.06
-0.04
-0.03
-0.02
-0.02
-0.01
subsidized lunch
0.37
0.45
0.41
0.39
0.40
0.40
0.38
0.41
0.42
0.41
0.42
0.42
0.41
0.40
0.40
0.40
student switched schools
0.09
0.08
0.05
0.05
0.06
0.05
0.05
0.05
0.05
0.05
0.06
0.05
0.06
0.06
0.06
0.06
proportion students new to school
0.049
0.039
0.032
0.030
0.038
0.036
0.036
0.035
0.033
0.035
0.036
0.036
0.038
0.038
0.041
0.042
proportion students black
0.35
0.32
0.29
0.30
0.30
0.30
0.29
0.28
0.28
0.28
0.28
0.28
0.28
0.28
0.29
0.30
0.047
0.029
0.027
0.025
0.025
0.023
0.021
0.026
0.021
0.021
0.023
0.023
0.022
0.025
0.024
0.028
prop 1 year
0.013
0.019
0.013
0.009
0.008
0.012
0.012
0.012
0.012
0.011
0.012
0.015
0.013
0.014
0.015
0.015
prop 2 years
0.012
0.011
0.011
0.007
0.006
0.008
0.008
0.003
0.004
0.006
0.007
0.007
0.008
0.009
0.007
0.009
prop teachers 0.28 0.23 0.21 0.22 0.22 0.21 0.21 0.21 0.20 0.20 0.20 0.21 black TAAS reading test scores vary from -2.1 std dev to 1.2 std dev, and intervals are roughly .2 std dev in width.
0.21
0.21
0.23
0.25
teacher experience prop 0 years
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