Effects of High School Course-Taking on Test Scores, High ...

Draft version. Please do not cite without authors' permission.

Effects of High School Course-Taking on Test Scores, High School Graduation, and Postsecondary Entry*

Mark C. Long University of Washington

Daniel J. Evans School of Public Affairs Box 353055

Seattle, WA 98195-3055 206-543-3787 [email protected]

Dylan Conger

The George Washington University Trachtenberg School of Public Policy and Public Administration

805 21st Street NW, MPA 601G Washington, DC 20052

202-994-1456 [email protected]

Patrice Iatarola Florida State University

Department of Educational Leadership & Policy 113G Stone Building

Tallahassee, FL 32306-4452 850-644-8162 [email protected]

April 2, 2009

Running head: Effects of High School Course-Taking ______________________________________________________________________________*Prepared for the City University of New York Office of Policy Research's Higher Education Policy Seminar Series (April 9). Funding for this research was provided by the Florida Department of Education and the U.S. Department of Education, Institute of Education Sciences, Grant R305B070131. We are especially grateful to the Florida Department of Education for maintaining such a comprehensive and organized data system, and for making the data available to us for analysis. We also thank Danielle Fumia for superb research assistance. All authors contributed equally.

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Abstract

Many states have increased the number and rigor of courses that are required for graduation, yet the

literature on the effects of course-taking has not kept pace with these policy developments. Using

panel data from a census of public school students in the state of Florida, we examine the effects of

course-taking in various subjects on 10th grade test scores, high school graduation, and entry into

postsecondary institutions. We control for course-availability, 8th grade test scores, and other

student, school, and neighborhood characteristics. We use ordinary least squares, propensity score

matching, and instrumental variables in our effort to identify causal effects.

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1. Introduction

U.S. students fare poorly on international exams relative to students in other industrialized

nations and their high school graduation rates remain surprisingly low (NCES, 2005; Heckman &

LaFontaine, 2008). Many educators place blame on poor quality public school investments and

undemanding high school graduation requirements. In response, states have increased the number

and rigor of courses students are required to take in order to graduate. Yet, the research literature on

the effect of course-taking on achievement patterns in high school and college preparedness has not

kept pace with these policy developments. Much of the existing literature focuses strictly on math

and science courses, fails to control for other influences on achievement and course-taking, and

relies on now-dated samples of high school students. In addition, few studies closely examine the

relative performance returns to courses in different subjects and even fewer examine the

determinants of the variation in course-taking effects across subgroups of students and across high

schools with different characteristics. As a result, we know very little about which courses across the

high school curriculum improve student learning most, whether all students benefit equally from

their coursework, and the characteristics of the high schools that appear to produce the largest

course-taking effects.

Using panel data from several recent cohorts of 8th grade public school students in the state

of Florida, we examine the effects of course-taking in 9th and 10th grade on 10th grade test scores

and high school graduation. We further evaluate the link between high school course-taking and

entry into 2-year and 4-year postsecondary institutions. In estimating these effects, we control for

8th grade test scores, high school course-availability, and student, school, and neighborhood

characteristics. We also improve our estimates by using propensity score matching and instrumental

variables.

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2. Prior Research

The prior empirical work on course-taking effects includes studies that focus on the effects

of tracking students into different sections of the same subject according to their prior preparation,

and others that focus on the effect of the number, level (e.g. Advanced Placement), and subject (e.g.

Algebra I) of courses in a given area, irrespective of the assigned track. For simplicity, we combine

the literatures since both address the underlying effects of course-taking. Among those studies that

have controlled for prior achievement, the relationship between the number and level of courses a

student takes in a given subject or the overall intensity of the curriculum and her proficiency on tests

of achievement in that subject have been relatively strong (Gamoran, 1987; Byrk, Lee, & Smith,

1990; Cool & Keith, 1991; Stevenson et al., 1994; Rock & Pollack, 1995; NCES, 1997; Schneider et

al., 1998; Attewell & Domina, 2008). Most of this work has concentrated on mathematics and

science course-taking. For instance, using the National Educational Longitudinal Survey (NELS), a

panel study of 8th graders in 1988, NCES (1997) shows a strong correlation between the number of

science courses taken and gains in science proficiency from the 8th to the 12th grade. Using the High

School and Beyond (HSB) cohort of 10th graders in 1980, Gamoran (1987) examines the effect of

the number of courses and number of advanced courses on 10th to 12th grade gains on tests in math,

science, reading, vocabulary, writing, and civics. Gamoran finds relatively strong effects of the

number of courses, and particularly the number of advanced courses, on gains in all subject areas,

controlling for other student and school inputs. The influence of math courses is particularly strong

and is the only effect that holds when he examines the relationship between course-taking and

achievement separately for students who scored below average in math on the prior exam.

Schneider et al. (1998) are among the few to explore the link between course-taking and high

school graduation. Using the NELS, Schneider and her colleagues find that students who take more

advanced mathematics courses in their last two years of high school are more likely to complete high

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school. Other research has found a positive correlation between course-taking and achievement on

college admissions examinations, such as the Scholastic Achievement Test (SAT) or the ACT

(Sebring, 1987; Schneider, 2003; ACT, 2005; Attewell & Domina, 2008). And a few others find that

students who take more AP courses in high school—often, courses that may be used for college

credit—are more likely to attend college (e.g. Schneider et al., 1998; NCES, 2000). Indeed, taking

AP courses and receiving high grades in the course along with a pass on the AP exam is becoming

something of a prerequisite to gain admissions into several selective universities (Geiser & Santelices,

2004). In two of our previous papers using the Florida data, we also find that students who take

higher level math courses are less likely to require remediation in college (Long, Iatarola, & Conger,

2009) and that students who take Advanced Placement courses earn higher grades in college

(Conger & Long, 2009).

Collectively, the prior research suggests there may be a strong effect of course-taking on

high school achievement and college entry that varies by subject matter and by student, and that

appears to hold under controls for prior achievement. Yet we are uncertain as to the strength of

these relationships and the effects of course-taking on other educational outcomes because of the

following limitations of the existing work. First, the overwhelming majority of the research on

course-taking relies on two surveys of students conducted more than 17 years ago: the NELS and

the HSB. These surveys are limited as they are restricted to a single cohort of high school students

and have modest numbers of minority and low-income students. Since our data is a census of

Florida students, which includes a high number of minority and low-income students, we will be

able to answer more nuanced questions about these groups than is possible with the HSB and NELS

datasets. In addition, significant changes in high school curriculum and graduation requirements in

the past 20 years may have affected the relationship between high school courses and educational

outcomes. Given that most of the work has relied on national samples, little is known about course-

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taking patterns and effects within a single state, where minimum graduation requirements, course

classification systems, and state-level education policies are the same for all schools and students.

Second, most of the prior research has focused narrowly on the determinants and effects of math

and science course-taking, to the neglect of other potentially important subjects, such as English,

foreign-languages, and history as well as the tradeoffs between the various subjects. Third, most

research focuses on achievement gains among students who graduate from high school and, further,

on the effects of the last two years of high school coursework. Less attention has been paid to the

first two years of coursework, a potentially crucial time, or to the relationship between courses in

these early years and high school dropout or post secondary enrollment. Fourth, the prior literature

has not sufficiently examined how course-taking effects vary across high schools with different

characteristics and, thus, we know little about the schools that produce the largest benefits. Finally,

most prior studies rely on severely under-specified models that fail to address biases on estimated

coefficients due to unobservables or to non-linear effects of observables.

3. Model

Our basic model is the following:

(1) Yim = β0 + β 1Ci + β 2Ti + β 3Ai + β 4Di + β 5Ei + νim + εi,

where Yim is the outcome of interest, Ci is a vector of credits earned in specific courses (or in a single

course), Ti is the total number of credits earned, Ai is a vector of 8th grade test scores, Di is a vector

of demographic characteristics, Ei is a vector of educational need characteristics, and νim is 8th grade

campus fixed effects. This specification allows us to test whether the hypothesis that taking specific

courses raises or lowers academic achievement/attainment, controlling for total credits earned. That

is, we explicitly test whether a shift in the composition of courses affects outcomes.

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One should be concerned with the possibility of a selection effect: that is, the possibility that

those students who choose to take particular courses would have higher values of Y even if they had

not taken the course. The variables A, D, E, and ν are included in the specification in an attempt to

minimize the possibility of omitted variable bias. Student's ability, demographics, educational needs,

and 8th grade campus (and it's associated neighborhood) are likely to both influence the student's

course-taking and the student's educational outcomes. Even with these controls, there may be two

remaining sources of bias..

The first is the possibility that the linear specification may not adequately control for these

observable characteristics, and that we may be using students with low probability of taking

particular courses to identify the effects for students who did take the courses. We address this

possibility using propensity score matching. We first estimate Equation (2) using a probit

specification for our binary course-taking measures:

(2) Probability(Ci=1) = Φ(γ0 + γ 1Ti + γ 2Ai + γ 3Di + γ 4Ei + εi).

We estimate this specification for each 8th grade campus then predict the propensity to take the

course for each student based on the results for that student's 8th grade campus.1 We then

construct a sample by matching each "treated" student (i.e., a student who took the course) to an

"untreated" student who had a similar propensity to take the course but who did not take the

course.2 We impose a common support restriction by dropping treated students whose propensity

to take the course was greater than any untreated student, and dropping untreated students whose

propensity to take the course was less than any treated student. The average effect of the treatment

on the treated is given by Equation (3) and is based on a difference of mean outcomes for the

treated and untreated matched samples: 1 If everyone in the 8th grade campus took the course, we set the predicted propensity to one, and if no one took the course, we set the predicted propensity to zero. 2 In subsequent drafts of this paper, we will replace nearest neighbor matching with kernel matching. This nearest neighbor matching is done with replacement.

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(3) Estimated treatment effect = mean(YTreated Students) - mean(YMatched Untreated Students).

Standard errors for this estimated treatment effect are estimated by computing the standard error

across 50 estimates derived from 50 bootstrapped samples.3

We estimate the treatment effect using students from the entire state of Florida, and then

repeat the estimation for each high school in the state. By estimating the effects for each high

school, we can examine the variation in effects across the high schools, and determine the school-

level predictors of the variation with the following regression:

(4) Estimated treatment effecth = δ0 + δ1Sh + εh,

where Sh is a vector of characteristics of high school h. Since the dependent variable in Equation (4)

is an estimated value with a non-constant level of variance, each high school level observation must

be weighted appropriately when estimating Equation (4). The technique for producing these

weights is described in Hanushek (1974) and Lewis and Linzer (2005).4

Returning to the first-stage individual-level regression, our second possible source of bias is

due to unobserved characteristics that influence a student's course-taking and academic outcomes,

and thereby bias the estimation of the treatment effect (for both the regression and propensity score

matching techniques). Since experiments are not available to estimate causal course-taking effects,

we need an instrumental variable to identify the effects non-experimentally. Of course, as in most

settings, finding a suitable instrument is challenging. We use the share of a high school's teachers

that are certified in various subjects to instrument for the likelihood that a student takes a course in a

3 In subsequent drafts of this paper, we will increase the number of bootstrapped samples to more accurately estimated the standard errors. 4 The authors would like to thank Drew Linzer for sharing their code for producing these weights. An alternative approach to the one described above would be to combine Equations 1 and 4 using a multilevel model (e.g. random effects, hierarchical linear modeling) to estimate the coefficients. The downside of using a multilevel model would be that we would need to sacrifice the propensity score estimation technique in the first-stage estimation. Since there may be substantial gains in using propensity score estimation over a linear first-stage model, and since our primary interest is the first-stage results, we prefer the two-stage process that we are using. We have also sufficiently corrected the standard errors in the second stage model so the results should be similar to what we would have gotten had we combined to the two levels.

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particular subject. For this specification, we include high school fixed effects. Thus, the

instrumental variable identifies how changes in the composition of a high school's teaching staff

changes their students' course-taking patterns. For this IV strategy to work, requires two

assumptions: 1) that the composition of the teaching staff does not directly affect student outcomes

except through the effect on students' course-taking, and 2) that parents do not change their selected

high school for their child in response to changes in the composition of the teachers. Neither of

these assumptions is likely to hold perfectly. Thus, the utility of this modeling strategy rests on the

extent to which there is residual correlation in teacher composition and student outcomes (net of the

effect via course-taking) and the extent of omitted variable bias in the estimates given in Equations

(1) and (3).

The IV approach is as follows. First, estimate Equation (5):

(5) Ci = ρ0 + ρ1Vh + ρ2Ti + ρ3Ai + ρ4Di + ρ5Ei + ηih + τi + εi,

where Vh is a vector denoting the share of a high school's teachers credentialed in math, English,

science, social studies, and foreign language, ηim is high school fixed effects, and τi is year fixed

effects. Second predict the likelihood of the student taking each course; modify Equation (1) by

replacing Ci with a vector of predicted course-taking variables, replacing the middle school fixed

effects with high school fixed effects, and adding time fixed effects; and then re-estimate Equation

(1).5

4. Description of Data

Our data have been provided by the Florida Department of Education (FDOE). For this

draft version of the paper, we rely on one cohort of students (later versions will include later

5 While we have described this as a two-stage procedure, we actually perform the estimation in one step (using "ivregress" in Stata) so as to produce the correct standard errors.

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cohorts). To construct our analytic cohort, we begin with all students who were enrolled in the 8th

grade in 1998-99, along with students who entered the cohort in subsequent years and grades and

who would be on track to graduate in 2003-04 assuming normal progression (those students first

observed in the 9th grade in 1999-2000, 10th grade in 2000-01, and so on). For our analyses of the

effects of course-taking through the 10th grade, we use data on the 128,611 students who were

observed in the 9th and 10th grades. For our analyses of completed high school course-taking, we use

data on the 106,709 students who were observed in at least three high school grades and who

received a high school diploma or general equivalency degree (GED) within four years of entering

school. Restricting the sample to students who are observed in at least three grades minimizes the

measurement error that would be attributed to making assumptions about the high school course-

taking patterns of students that we do not observe for their entire high school careers. It also

prevents us from confounding the effects of high school dropout and limited high school course-

taking.

The Florida data contains detailed records of students’ high school course-taking. For each

student, the data record the course code and name as well as the term in which the course was taken

and the number of credits the student earned in the course. All schools in the state adhere to a

common course code with the FDOE maintaining a course code directory of authorized courses

along with course descriptions that allow us to determine the subject of each course. The FDOE

also provides a classification scheme that identifies whether a course is at level one, two, or three,

where the higher number indicates greater difficulty. For instance, in the subject of Algebra, "Pre-

Algebra" is a Level 1 course, "Algebra 1" is a Level 2 course, and "Honors Algebra 1" is a Level 3

course. Only very basic or remedial courses are identified as Level 1; for instance "Consumer

Mathematics" and "English Skills 1" are Level 1 courses. For our models, we use various measures

of course-taking, including total credits earned, the number of credits earned by subject, the highest

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math course taken (1= no math course to 13 = calculus), whether the student completed Algebra 1,

whether the student completed a Level 3 math course, and whether the student took an Advanced

Placement (AP) or International Baccalaureate (IB) course prior to graduation.

Table 1 provides descriptive statistics on our two samples of students. Consistent with at least

some estimates (see Laird, Lew, DeBell, and Chapman, 2006), only 73% of the students in our

cohort (who were observed in both 9th and 10th grade) graduate from high school on time. A fairly

large percentage (59% of all students observed in both 9th and 10th grade and 71% of on-time high

school graduates) pursue a higher degree, with a slightly higher share going on to a 4-year versus a 2-

year institution. The 10th grade achievement scores are standardized with a mean of zero and a

standard deviation of one.6 The middle of the table provides the distribution on our course-taking

measures with the average student earning approximately 10 credits by the 10th grade and 26 credits

by graduation. By the 10th grade, the mean student has completed a Level 1 course or a Level 2

course other than Algebra 1 (the value of 5 on our highest math course measure) but not yet Algebra

1 (the value of 6). By the 12th grade, the mean graduate has completed Geometry (the value of 7)

but not Algebra 2 (the value of 8). Forty-three percent of the graduates complete a Level 3 course

upon graduation. In both samples, students average slightly higher credits in English than math and

science, reflecting Florida's high school graduation requirements (4 credits required in English, 3

credits in math, and 3 credits in Science). The majority of the credits are earned in high school level

courses- Level 2 and 3—with few students requiring remediation at the high school level.

At the bottom of the panel, we provide descriptive statistics on the model covariates, which

include 8th grade Florida Comprehensive Assessment Test (FCAT) scores in reading and math along

6 Since these scores are standardized among all test-takers, the means for all test-takers equal 0.00. However, the mean 10th grade test score is 0.09 for both reading and math among our sample of students observed in both 9th and 10th grades. This suggests that our sample has somewhat higher achievement than the full sample of 10th graders. This result is not surprising as our sample consists of students with more stability than the full sample, which includes students who move into and out of Florida's public schools.

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with student socio-demographic and educational characteristics. Approximately 31% of the 9th and

10th grade sample and 26% of the graduate sample is missing data on one or more right-hand side

variables.7 To improve efficiency and to avoid sampling bias, we impute the missing values using

multiple imputation by chained equations (Rubin, 1987; Royston, 2004) creating five multiply-

imputed datasets.8 The estimated effects resulting from the five imputed datasets are averaged and

standard errors are adjusted to account for uncertainty caused by imputation.

Finally, the 8th grade campus fixed effects and the student's main high school were

determined using only "regular" campuses, excluding juvenile justice facilities and other alternative

institutions. If the student attended multiple "regular" campuses, we select the campus with the

most terms of enrollment (or select randomly amongst the campuses tied for most terms of

enrollment). Students who were never enrolled in a "regular" 8th grade campus were assigned into

one group for the purpose of computing the 8th grade fixed effect.

5. Results

5a. Effects of 9th and 10th grade course-taking

OLS Results

Table 2 presents the OLS and Probit results for the effects of 9th and 10th grade course-

taking. Controlling for total credits earned through the 10th grade, increasing the highest math

course taken by one level raises the likelihood of graduation from high school by 3.3 percentage

points, raises the likelihood of attending a four-year college by 6.0 percentage points, and raises 10th

grade math and reading FCAT scores by 0.10 and 0.06 standard deviations. Since it is somewhat

challenging to interpret the meaning of "the highest math course taken by one level", in the second

7 8th grade test scores are missing for roughly one-fifth of the students in both samples. 8 For a relatively small amount of missing information in the data there is little efficiency gains to be made with more than five imputations of the data (Rubin, 1987).

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panel we use a discrete measure: "Completed Algebra 1 or higher by 10th grade". These results are

comparable; completing Algebra 1 or higher raises the likelihood of graduation from high school by

10.0 percentage points, raises the likelihood of attending a four-year college by 9.7 percentage points,

and raises 10th grade math and reading FCAT scores by 0.20 and 0.11 standard deviations. Note

that Florida requires students to complete Algebra 1 or an equivalent course in order to earn a diploma.

Thus, the fact that completion of Algebra 1 is not perfectly correlated with graduation suggests that

these alternative pathways to graduation are taken by many students.

In the next panel, we consider the relative effects of credits in various subjects. Since we are

controlling for total credits earned we can interpret the effects on each subject as the effect of

replacing a credit in a "non-listed" subject (e.g., art, physical education, home economics, etc.) with a

credit in that particular subject. For example, if one were to replace a "non-listed" credit with a

credit in math earned by the end of the 10th grade, the student's likelihood of earning an on-time

high school diploma would increase by 3.6 percentage points. For the most part, the listed subjects

have positive effects on these outcomes but there are some notable differences in the magnitudes of

these effects.

First, the largest effects are found for credits in foreign languages, which raise the likelihood

of graduation from high school by 8.3 percentage points, raises the likelihood of attending a four-

year college by 10.6 percentage points, and raises 10th grade math and reading FCAT scores by 0.10

and 0.08 standard deviations.

Second, credits earned in English and social studies are negatively related to receiving a high

school diploma and credits earned in English are negatively related to attending a four-year college

relative to credits earned in non-listed subjects. On the other hand, relative to credits in non-listed

subjects, credits earned in English and social studies raise the likelihood of attending a two-year

college and raise 10th grade FCAT math and reading scores. In fact, more credits in English are

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positively correlated with 10th grade math scores, yet more credits in math is uncorrelated with 10th

grade reading scores. Thus, except for 10th grade reading scores, math credits may lead to greater

returns than English credits.

Third, controlling for credits in the five listed subjects, a student who earns more credits in

the non-listed subjects (which tend to be in non-academic subjects9) are slightly more likely to

graduate high school, but less likely to attend a postsecondary institution and earn slightly lower 10th

grade FCAT scores. That is, amassing credits in non-academic subjects may help the student attain

the credits needed to complete high school, but these non-academic subjects have negative effects

on subsequent academic outcomes.

The bottom-panel of Table 2 repeats the analysis in the third-panel, but focuses on credits in

Level-2 or Level-3 courses only (thus not including credits in remedial courses). The results are

largely the same as those in the third-panel.

Propensity Score Matching Results: Discrete Treatment

Table 3 repeats the analysis for the effect of completing Algebra 1 or higher by 10th grade

using propensity score matching (PSM). Essentially, this method creates a subsample consisting of

all students who completed Algebra 1 or higher, and matches these students to "non-treated"

students who had similar probabilities of completing Algebra 1 or higher, based on their 8th grade

test scores, 8th grade campuses, and other individual characteristics. We then compute the

difference in the means of the outcomes for the "treated" and "untreated" students.

The PSM results show strikingly larger effects. Completing Algebra 1 or higher by 10th

grade is associated with a 27.3 percentage point increase in the likelihood of receiving an on-time

9 The definition of what should be counted as an "academic" subject varies. " The No Child Left Behind Act of 2001 defines "core academic subjects" as: English, reading or language arts, mathematics, science, foreign languages, civics and government, economics, arts, history, geography." (http://ritter.tea.state.tx.us/nclb/hottopics/def.core.acad.subj.html). With the exception of "arts", these subjects are covered in our five listed subjects.

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high school diploma, a 28.0 percentage point increase in the likelihood of attending a four-year

college, and raises 10th grade math and reading FCAT scores by 1.05 and 0.97 standard deviations.

There are two possible explanations for the higher magnitudes of the estimates. First, is the

possibility that the linear specification was inadequate as it included students with low probabilities

of taking higher-level math courses in the counterfactual. Thus, the semi-parametric PSM estimate

with the "common support" requirement produces more accurate estimates of the treatment effect.

The other possibility is that the propensity score matching process has not successfully matched the

treated and untreated students on their covariates. We have not yet tested whether our first-stage

probit predicting the likelihood of completing Algebra 1 or higher satisfies the "balancing property"

(i.e., that the means of the covariates in the treated and untreated samples are roughly equivalent).

We will test the balancing of the samples in the next draft of the paper.

Propensity Score Matching Results: Continuous Treatment

Since the discrete propensity score matching results produced such interesting results, we are

now exploring using a propensity score matching technique to evaluate the effects of a one unit

increase in credits in each subject, controlling for credits taken in other subjects. The goal is

produce propensity score matching results that correspond to the results shown in the third panel of

Table 2. This section of the paper describes very preliminary results using a 5% sample of all

Florida students which does not yet incorporate 8th grade campus fixed effects.

Hirano and Imbens (2004) introduce the methodology and theory behind propensity score

matching with continuous (as opposed to binary) treatments. To estimate the "dose-response" and

"treatment effect" functions, we first estimate the conditional distribution of the treatment variable

(the number of credits taken in a particular subject) given the covariates. The treatment ("dose") is

the number of credits earned in one of the following subjects: math, english, social studies, science,

or foreign language. Here the covariates included standardized math and reading test scores in 8th

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grade, demographic variables (race, free or reduced price lunch recipient, sex, age), educational

demographic variables (lep and exceptional), and total credits earned by 10th grade. Additionally, we

also included credits earned in the other named subjects (math, English, social studies, science, and

foreign language, with the subject of interest omitted).

Bai and Mattei (2007) wrote a procedure for Stata (doseresponse.ado) which follows the

work of Hirano and Imbens (2004). We employe this program to estimate the dose-response and

treatment effect functions. Following Hirano and Imbens (2004) and Bai and Mattei (2007), we

assume the treatment to be distributed normally given the covariates and estimate the generalized

propensity score (GPS). The procedure tests the normality of the distribution of the treatment

given covariates and the balancing property, which is done by dividing the treatment into quartiles.

We find that the balancing property is satisfied below the 0.01 level, while the normality assumption

is not statistically satisfied at the 0.05 level. Appendix Figures 1a-1e plot the distribution of the

treatment variables along with the normal distribution. These provide a visual indication of the

distribution of the treatment, although these distributions are not conditional on the covariates.

While the distributions are not normally distributed, they are not grossly non-normal (with the

exception of foreign languages).

We then estimated the dose-response function and the treatment effect function by

estimating the expected outcome given the GPS, the treatment, and the interaction of these variables.

The outcomes of interest were the standardized math and reading FCAT scores for 10th grade,

whether an individual graduated high school within 4 years, and whether an individual attended a (1)

4-year college within 5 years, (2) 2-year college within 5 years, and (3) any college within 5 years.

The average expected outcome is then estimated for each level of the treatment.

To calculate the treatment effect, we estimate the expected outcome at each level if the

number of credits was increased by one (1 additional year of credits) and subtract the expected

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outcome with the shift (i.e. the dose-response). Figures 1a-1e plot the dose-response and treatment

effect functions for each treatment (i.e. subject) and the outcome of graduating high school within

4-years ("hsd4") . The plot on the left-side of Figure 1a gives the predicted dose response function,

and can be interpreted as the expected probability of on-time graduation for an individual in a given

treatment level—i.e. with a given number of math credits taken by 10th grade. For example, an

individual with about 2 credits in math by 10th grade would have approximately 0.78 probability of

graduating high school in four years. That probability would increase to about 0.87 with 7.75 credits

in math. The plot on the right-side of Figure 1a gives the predicted treatment effect function, and

provides an estimate of what would happen if an individual in a given treatment level increased his

or her number of credits in math by 10th grade by 1. Thus, the treatment effect gives the change in

the expected outcome given a change in the treatment of 1 (roughly speaking, this is a plot of the

slope of the curve shown in the left-panels). For example, an individual with 1 credit in math by 10th

grade would see an approximately 7 percentage point increase in his or her expected probability of

graduating within four years if they increase the number of credits in math to 2 credits by 10th grade,

but increasing from 2 to 3 credits would lower the expected probability of graduating within four

years by nearly the same amount. In other words, if we look at the dose-response function on the

left, we can see that the probability of graduating would drop from approximately 0.78 to about 0.72

with an additional year of math before 10th grade for those at 2 credit treatment level. An individual

with 6 credits of math, however, would see about 3 percentage point increase in his or her

probability of graduating within 4 years if they took an additional year of math by 10th grade

increasing from a probability of about 0.81 to 0.84 again referring to the dose response function on

the left. The other figures can be interpreted similarly.

While these results are very preliminary, they suggest some interesting patterns. From Figure

1a, we see the marginal effect of math credits on high school graduation is mostly positive except for

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students with 2 math credits. At this point, we can only speculate on why the marginal effect is

negative at 2 credits of math. First, it could be the case that the sample of individuals with three

credits of math by 10th grade contain a disproportionate share of students who were retained in 9th

or 10th grade (and thus had three years to take courses in the 9th and 10th grade). Students who

were retained are likely to be more prone to not graduate high school within four years of high

school entry. A second hypthosesis is that moving from the second to third credit in math leads to

an imbalance in the credits earned that makes it more difficult to graduate. For example, an extra

math course could displace an English credit needed for high school graduation. (However, one

would expect the displacement effect to be greater still with an increase from three to four credits).

In Figure 1b, we see that the first two credits in English raise the likelihood of high school

graduation, while the third and fourth credits in English lower the likelihood of graduation. The

dose response function shown in Figure 1c for science credits mirrors Figure 1a for math credits;

additional credits in science raise the likelihood of high school graduation, except for the third credit.

Likewise, the dose response function shown in Figure 1d for social studies and Figure 1e for foreign

language mirrors Figure 1b for English credits; the first 1.5 credits in social studies and foreign

language raise the likelihood of high school graduation, while subsequent credits lower the likelihood

of high school graduation.

The next set of figures (2a-2e) repeat the analysis with 10th grade math FCAT scores as the

dependent variable. Unlike high school graduation, this outcome doesn't mechanically depend on

the composition of credits earned. Nonetheless, we still see the same patterns (in general), with

inflections in the effect at two credits. Thus, it appears that taking a balanced set of classes has effects

on both math acheivement and high school graduation. (In the next draft, we will attempt to

disentangle the issue of student retention on these outcomes).

18

Finally, note that Figures 2a-2e show positive effects of the first 1.5 credits in all subjects on

10th grade math FCAT scores. These results again appear to confirm that 10th grade math scores

do not simply depend on math course-taking.

Instrumental Variable Results

IV estimates are not yet computed, but will be included in the next draft of the paper.

5b. Effects of all high school course taking

OLS Results

Table 4 shows the effects of complete high school course-taking (not just courses through the

10th grade) on post-secondary entry for the sample of students who were observed in at least three

high school grades and who completed a high school diploma or GED within four years of high

school entry.10

There is a strong association of earning credits in advanced math and AP/IB classes and

attending any college or a four-year college, while credits earned in advanced math and AP/IB

classes are negatively associated with attending a two-year college. We view these results as more

likely to be reflecting selection on the part of the student than a causal effect of course-taking on

postsecondary entry. That is, students who take advanced math or AP/IB courses are likely doing

so with the understanding that these courses will improve their postsecondary enrollment prospects.

The fourth panel of Table 4 is potentially more interesting. There is a strong correlation

between taking science credits in high school and attending a 4-year institution. Among the five

listed subjects, additional credits in English have the lowest association with attending a four-year

institution (although the association is still positive). Each additional credit in the non-listed (mostly

non-academic) subjects lowers the likelihood of attending a four-year institution by 1.5 percentage

10 98.5% of this sample earned a high school diploma.

19

points. Thus, again, amassing credits in these non-listed subjects may increase the likelihood of the

student graduating high school, but appears to lessen the chance of the student attending a four-year

college.

5c. Variation in the Effects Across Students, by Race, Gender, and Poverty

We now explore whether the relationships between course-taking and outcomes vary across

demographic subgroups (white, Hispanic, black, poor, non-poor, female, and male). We repeat the

specification shown in the third panel for Table 2, but restrict the sample to one demographic

group at a time. We then compute the marginal effects and evaluate whether the marginal effects are

larger or smaller for "disadvantaged" groups (black, Hispanic, poor, and male) relative to their

reference group (whites, non-poor, or female students).11

The results are shown in Tables 5a and 5b. For the most part, the patterns of effects by

course type are maintained for various student subgroups. Where there are significant differences

between the effects by subgroup, the effects are slightly more favorable for disadvantaged students.

Ignoring the 4-year and 2-year college results, there are 29 significant positive differences, 17

significant negative differences, and 58 insignificant differences.

There are some interesting patterns in these results that deserve attention. First, additional

credits in English have a more positive effect on 10th grade math and reading scores for blacks,

Hispanics, poor students, and males. But, additional credits in English significantly lowers the

chances of black, Hispanic, and poor students from receiving a high school diploma, while having

insignificant effects on the likelihood of enrollment for whites and non-poor students. This result

11 For the dichotomous dependent variables a difference in the marginal effect between two demographic groups could come as a result of either a difference in the effect of the course on the outcome or from the demographic groups having different base likelihoods. For example, the marginal effect of taking an additional math course on a high school diploma is dHSD/dMath = φ(X'β)*βMath. Thus, if the demographic groups have different values of φ(X'β), they would have different marginal effects even with the same value of βMath.

20

suggests that there could be a tension between meeting the Adequate Year Progress requirements of

No Child Left Behind and promoting graduation for these subgroups.

Other results are noteworthy. Additional credits in social studies tend to have positive

effects on disadvantaged students, with significant positive differences for blacks on 10th grade

reading, Hispanics on HS diploma, poor students on 10th grade reading and math and

PSE entry, and males on 10th grade reading. Additional credits in science have larger positive

effects on 10th grade math scores for females than for males. Finally, and not surprisingly,

additional credits in foreign languages have significantly smaller effects for Hispanics than for whites.

5d. Variation in the Effects Across High Schools, by School Characteristics

To get a sense of how these effects of course-taking vary across high schools, we

recomputed the propensity score estimates for the effect of completing Algebra 1 or higher that are

shown in Table 3 for each of 333 high schools in the state of Florida. These estimates differ from

those in Table 3 in that the nearest neighbor matching is computed within high schools, rather than

within the entire state of Florida. (The first-stage propensity score estimates are computed within

each 8th grade campus, as was done previously).

Figure 3 plots the distribution of the effect size estimates across the 333 high schools. The

peaks of the density estimates roughly correspond to the state-wide estimates shown in Table 3 (i.e.,

roughly 0.25 for high school diploma and attending a four-year college, and 1.1 for 1.0 for math and

reading FCAT scores). Each of the distribution is uni-peaked -- yet there is a large degree of

variation in the effects. At the high school-level, the effects of competing Algebra 1 or higher are

generally positive for each of the outcomes. However, the effects of competing Algebra 1 or higher

are negative for attending a two-year college for a sizable share of high schools (and positive and

large for another group of high schools). This variation in the magnitude of the effects motivates

21

our investigation of the relationship between school characteristics and the school-level effect

magnitudes.

Before turning to regression estimates, Figure 4 shows the bivariate relationships between

school characteristics and the effect of completing Algebra 1 or higher by 10th grade on attending a

four-year college. The effects tend to be higher in schools with more enrollment, fewer poor

students, yet lower resources (i.e., lower expenditures per pupil, fewer teachers per pupil, lower share

of teachers with advanced degrees, and non-magnet schools). In the regressions that follow, we

then test whether these bivariate associations are maintained when controlling for the other school

characteristics.

Table 6 shows the regression results. In general (but depending on the outcome evaluated),

the bivariate results are maintained. Most interestingly, the positive effects of taking more advanced

math on attending a four-year college are muted in schools with more poor students (i.e., schools

with a higher share of their students receiving free or reduced-price lunch). Whereas, the effect of

taking more advanced math on attending a two-year college (which is negative for some schools)

tends to be more positive if the school has more poor students. These differential effects could be

due to differences in the quality of the advanced courses in high- and low-poverty schools or to

other resource differentials proxied by the poverty of the students in the school, such as the college

guidance counselors. Another interpretation is that the financial limitations of students influences

the direction of the effects of advanced course-taking; in other words, the share of poor students in

the school proxies for traits of the students themselves that we have not sufficiently held constant

with student poverty level.

Similar interpretations may apply to the somewhat counterintuitive effects of school

resources. The effects of advanced course-taking on most of these outcomes tend to be lower in

schools with high resources. For instance, the effect of advanced courses tends to be lower in

22

schools with higher teacher-pupil ratios. There may be ceiling effects such that students in these

schools are likely to have parents with higher incomes and are already quite likely to attend college.

Thus, the effects of course-taking on these advantaged students is lower.

We previously found strong effects of magnet school attendance on the likelihood that the

student would take Level-3 courses and AP/IB courses (Conger, Long, & Iatarola, 2009). It is

possible that these magnet schools are pushing students into courses where they are not fully

prepared, and this lessens the effect of the course on their subsequent outcomes. On the other hand,

in Long, Iatarola, and Conger (2009) we found sizable effects of highest math course taken on

reducing the need for college math remediation even for students with lower math scores.

Nonetheless, as shown in Table 6, we find that schools with more prepared students (i.e., with

higher 8th grade math FCAT scores) show larger effects of advanced math course-taking on 10th

grade FCAT scores and the likelihood of going to a four-year college. Thus, the cumulative

evidence seems to show that the course-taking effects are larger when students are more prepared,

and in schools that are less likely to push students with less preparation into the advanced courses.

6. Conclusions

This paper aims to fully investigate the effects of high school course-taking on student

achievement and attainment. This first draft provides an overview of the scope of the analysis: we

use several measures of course-taking, examine outcomes at the secondary and post-secondary level,

explore variation in the effects of course-taking across subgroups of students and the schools they

attend, and address specification errors common to most prior studies.

The preliminary analyses presented here offer several findings that will be investigated

further. First, and perhaps unsurprisingly, obtaining more credits and higher-level credits in high

school associates with higher levels of achievement and attainment. Second, and more interestingly,

23

the type of credits earned matters: a) foreign-language courses are more positively correlated with

outcomes than any other type of course; b) except for 10th grade reading scores, math credits may

lead to greater educational performance returns than English credits; c) amassing credits in non-

academic subjects may help the student attain the credits needed to complete high school (in fact,

helps even more than taking English credits), but these non-academic subjects may have negative

effects on subsequent academic outcomes; and d) there is a strong positive association between

taking science courses and attending a 4-year post-secondary institution. Third, most of the

relationships between course-taking and outcomes hold across demographic groups, and where

there are significant differences the differences tend to favor disadvantaged students (blacks,

Hispanics, males, and poor students). Finally, the effects of courses matter differently according to

the characteristics of the high school students attend. In general, we find that the effects of

advanced courses are smaller in schools with somewhat greater resources, including fewer poor

students, fewer students overall, and higher teacher-pupil ratios.

We caution the reader that these analyses are very preliminary. However, they suggest some

important areas to pursue further including the tradeoff between credits in different subjects and the

differential effects of these tradeoffs for different kinds of schools. Stay tuned.

24

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26

Table 1: Descriptive Statistics

Mean SD Mean SD

Outcome Variables Receive a High School Diploma Within Four Years of HS Entry 0.73Attended Any 4‐Year College Within Five Years of HS Entry 0.31 0.39Attended Any 2‐Year College (But No 4‐Year College) Within Five Years of HS Entry 0.29 0.32Attended Any College Within Five Years of HS Entry 0.59 0.7110th Grade Math FCAT Score 0.09 1.0410th Grade Reading FCAT Score 0.09 1.02

Course‐taking Variables Total Credits Earned 9.82 4.58 26.23 4.89Highest Math Level (1‐13, with 13 = Calculus) 5.38 2.05 7.80 2.42Completed Algebra 1 0.72Completed Level 3 Math Course 0.43Credits Earned in Math 1.51 0.79 3.75 1.08Credits Earned in English 1.54 0.87 4.41 1.40Credits Earned in Science 1.27 0.63 3.39 1.03Credits Earned in Social Studies 0.95 0.71 3.65 1.19Credits Earned in Foreign Language 0.53 0.68 1.71 1.15Level 2 or 3 Credits Earned in Math 1.27 0.74 3.40 1.16Level 2 or 3 Credits Earned in English 1.39 0.76 4.10 1.29Level 2 or 3 Credits Earned in Science 1.22 0.65 3.31 1.11Level 2 or 3 Credits Earned in Social Studies 0.95 0.70 3.56 1.16Level 2 or 3 Credits Earned in Foreign Language 0.54 0.69 1.70 1.15Credit Earned in Any Advanced Placement or International Baccalaureate Course 0.28

Control Variables 8th Grade Math FCAT Score 0.15 0.99 0.35 0.868th Grade Reading FCAT Score 0.15 0.99 0.35 0.87Student is White 0.58 0.60Student is Black 0.22 0.19Student is Hispanic 0.17 0.17Student is Asian American 0.02 0.02Student is Male 0.50 0.47Student's Age (as of July 1st, 2003) 18.50 0.53 18.41 0.47Student Received Free‐ or Reduced‐Price Lunch in 8th Grade or High School 0.44 0.38Student Classified as Limited English Proficient in 8th Grade or High School 0.14 0.13Student Classified as Having a Disability in 8th Grade or High School 0.15 0.11

Number of Observations 128,611 106,709

(Measured through the 10th grade for the first two columns)

Students observed in both 9th and 10th

Grade

Students observed in at least three of the four HS grades and who received a HS

diploma or GED within 4 years of HS entry

27

Table 2: Effects of 10th Grade Course Taking, as Estimated by OLS or Probit Regressions

Highest Math Level by 10th Grade 0.033 (0.001) 0.060 (0.001) ‐0.005 (0.001) 0.059 (0.001) 0.103 (0.001) 0.062 (0.002)

Total Credits Earned by 10th Grade 0.012 (0.000) ‐0.005 (0.000) ‐0.002 (0.000) ‐0.003 (0.000) ‐0.011 (0.001) ‐0.007 (0.001)

Completed Algebra 1 or Higher by 10th Grade 0.102 (0.004) 0.097 (0.004) 0.067 (0.004) 0.138 (0.004) 0.197 (0.005) 0.113 (0.007)

Total Credits Earned by 10th Grade 0.012 (0.000) 0.000 (0.000) ns ‐0.004 (0.000) 0.000 (0.000) ns ‐0.007 (0.001) ‐0.004 (0.001)

Credits Earned in Math by 10th Grade 0.036 (0.002) 0.007 (0.003) 0.011 (0.002) 0.018 (0.003) 0.054 (0.004) ‐0.004 (0.004) ns

Credits Earned in English by 10th Grade ‐0.035 (0.002) ‐0.014 (0.002) 0.025 (0.002) ‐0.009 (0.002) 0.048 (0.003) 0.048 (0.003)

Credits Earned in Science by 10th Grade 0.040 (0.003) 0.027 (0.003) 0.024 (0.003) 0.034 (0.004) 0.022 (0.004) 0.035 (0.004)

Credits Earned in Social Studies by 10th Grade ‐0.015 (0.003) 0.020 (0.003) 0.008 (0.002) 0.013 (0.003) 0.048 (0.004) 0.070 (0.004)

Credits Earned in Foreign Language by 10th Grade 0.083 (0.003) 0.106 (0.002) ‐0.023 (0.002) 0.125 (0.003) 0.100 (0.003) 0.077 (0.003)


Level 2 or 3 Credits Earned in Math by 10th Grade 0.036 (0.003) 0.028 (0.003) 0.036 (0.002) 0.041 (0.003) 0.095 (0.003) 0.037 (0.005)

Level 2 or 3 Credits Earned in English by 10th Grade ‐0.033 (0.003) ‐0.012 (0.003) 0.031 (0.002) ‐0.010 (0.003) 0.008 (0.003) 0.030 (0.004)

Level 2 or 3 Credits Earned in Science by 10th Grade 0.017 (0.003) 0.024 (0.003) 0.029 (0.003) 0.026 (0.004) 0.076 (0.005) 0.074 (0.005)

Level 2 or 3 Credits Earned in Social Studies by 10th Grade ‐0.019 (0.003) 0.020 (0.003) ‐0.006 (0.003) 0.003 (0.003) ns 0.026 (0.004) 0.051 (0.004)

Level 2 or 3 Credits Earned in Foreign Language by 10th Grade 0.084 (0.003) 0.105 (0.002) ‐0.028 (0.002) 0.123 (0.003) 0.086 (0.003) 0.068 (0.003)


Notes: 1) Each panel shows the results from a separate regression. Each regression controls for 8th grade test scores, demographic characteristics, educational needs, and 8th grade fixed effects. 2) Results for the indicator variables show the marginal effect computed at the mean of the independet variables. 3) Robust standard errors are shown in parentheses. 4) All results are significant, except where noted by "ns" for "not significant" or "ms" for "marginally significant" (i.e., 10% level).

Attended Any 2‐Year College (But No 4‐Year College)

Within Five Years of HS Entry

Attended Any 4‐Year College Within Five Years of HS Entry

Receive a High School Diploma Within Four Years of

HS Entry

Attended Any College Within Five Years of HS Entry

10th Grade Math FCAT Score 10th Grade Reading FCAT Score

28

Table 3: Effects of Completing Algebra 1 or Higher by 10th Grade, as Estimated by Propensity Score Matching

Effect 0.273 (0.037) 0.280 (0.028) 0.056 (0.035) 0.336 (0.038) 1.053 (0.076) 0.969 (0.081)

Notes: 1) Each panel shows the effect size from a separate propensity score estimation. Each student "treated" student (i.e. who took Algebra 1 by 10th grade) is matched with their nearest "untreated" neighbor (i.e. the student who has the most similar propensity to take Algebra 1, but who did not do so). Propensity scores are based on a first‐stage probit regression run for each 8th grade campus, which controlled for 8th grade test scores, demographic characteristics, and educational needs. 2) Standard errors are computed by the standard error across 100 random subsamples of the state of Florida. 3) All effects shown are significant, except where noted by "ns" for "not significant" or "ms" for "marginally significant" (i.e., 10% level).

Receive a High School Diploma

Within Four Years of HS Entry


Attended Any 2‐Year College (But No 4‐Year College) Within Five Years of HS Entry

Attended Any College Within Five Years of

HS Entry

10th Grade Math FCAT Score

10th Grade Reading FCAT Score

29

Table 4: Effects of High School Course Taking, as Estimated by OLS or Probit Regressions

Highest Math Level 0.114 (0.001) ‐0.018 (0.001) 0.080 (0.001)Total Credits Earned 0.010 (0.000) 0.003 (0.000) 0.008 (0.000)

Completed Level 3 Math 0.426 (0.004) ‐0.120 (0.003) 0.275 (0.004)Total Credits Earned 0.014 (0.000) 0.003 (0.000) 0.013 (0.000)

Credit Earned in AP or IB Course 0.457 (0.004) ‐0.189 (0.004) 0.247 (0.004)Total Credits Earned 0.017 (0.000) 0.003 (0.000) 0.015 (0.000)

Credits Earned in Math 0.053 (0.002) ‐0.020 (0.002) 0.027 (0.002)Credits Earned in English 0.016 (0.002) 0.023 (0.001) 0.016 (0.001)Credits Earned in Science 0.089 (0.002) ‐0.028 (0.002) 0.048 (0.002)Credits Earned in Social Studies 0.065 (0.002) 0.011 (0.002) 0.054 (0.002)Credits Earned in Foreign Language 0.130 (0.002) ‐0.006 (0.001) 0.108 (0.002)Total Credits Earned ‐0.015 (0.001) 0.002 (0.000) ‐0.008 (0.001)

Level 2 or 3 Credits Earned in Math 0.059 (0.002) 0.016 (0.002) 0.050 (0.002)Level 2 or 3 Credits Earned in English 0.012 (0.002) 0.021 (0.001) 0.012 (0.002)Level 2 or 3 Credits Earned in Science 0.072 (0.002) ‐0.019 (0.002) 0.039 (0.002)Level 2 or 3 Credits Earned in Social Studies 0.023 (0.002) 0.009 (0.002) 0.016 (0.002)Level 2 or 3 Credits Earned in Foreign Language 0.128 (0.002) ‐0.015 (0.001) 0.103 (0.002)Total Credits Earned ‐0.008 (0.001) ‐0.002 (0.000) ‐0.004 (0.000)

Notes: 1) Each panel shows the results from a separate regression. Each regression controls for 8th grade test scores, demographic characteristics, educational needs, and 8th grade fixed effects. 2) Results show the marginal effect computed at the mean of the independet variables. 3) Robust standard errors are shown in parentheses. 4) All results are significant, except where noted by "ns" for "not significant" or "ms" for "marginally significant" (i.e., 10% level).


Attended Any 2‐Year College (But No 4‐Year College) Within Five Years of HS Entry

Attended Any College Within Five Years of

HS Entry

30

Table 5a: Effects of 10th Grade Course Taking, by Demographic Subgroup

Student Subgroup Credits Earned by 10th Grade

(Non‐Hispanic) White In Math 0.034 (0.003) 0.016 (0.004) 0.006 (0.003) 0.015 (0.004) 0.060 (0.005) 0.002 (0.005)In English ‐0.013 (0.002) ‐0.006 (0.003) 0.025 (0.003) ‐0.007 (0.003) 0.029 (0.004) 0.033 (0.004)In Science 0.033 (0.004) 0.024 (0.005) 0.022 (0.004) 0.019 (0.005) 0.024 (0.006) 0.031 (0.007)In Social Studies ‐0.017 (0.003) 0.015 (0.004) 0.012 (0.003) 0.009 (0.004) 0.040 (0.006) 0.064 (0.006)In Foreign Languages 0.087 (0.003) 0.111 (0.003) ‐0.029 (0.003) 0.135 (0.004) 0.097 (0.003) 0.076 (0.004)Total Credits Earned 0.007 (0.001) ‐0.009 (0.001) ‐0.010 (0.001) ‐0.006 (0.001) ‐0.019 (0.001) ‐0.013 (0.002)

(Non‐Hispanic) Black In Math 0.045 (0.005) 0.002 (0.004) ‐ 0.017 (0.004) + 0.022 (0.006) 0.039 (0.006) ‐ ‐0.018 (0.007) ‐In English ‐0.070 (0.004) ‐ ‐0.022 (0.004) ‐ 0.025 (0.003) ‐0.010 (0.005) 0.078 (0.006) + 0.071 (0.006) +In Science 0.053 (0.007) + 0.026 (0.005) 0.025 (0.005) 0.053 (0.007) + 0.007 (0.008) 0.032 (0.008)In Social Studies ‐0.029 (0.006) 0.016 (0.004) 0.004 (0.005) 0.015 (0.006) 0.063 (0.007) + 0.082 (0.007)In Foreign Languages 0.120 (0.008) + 0.077 (0.004) ‐ ‐0.014 (0.005) + 0.123 (0.007) 0.096 (0.008) 0.079 (0.007)Total Credits Earned 0.012 (0.001) + ‐0.004 (0.001) + ‐0.007 (0.001) + ‐0.009 (0.001) ‐0.023 (0.001) ‐0.017 (0.002)

Hispanic In Math 0.038 (0.006) ‐0.003 (0.007) ‐ 0.011 (0.005) 0.004 (0.005) 0.053 (0.008) ‐0.002 (0.009)In English ‐0.055 (0.005) ‐ ‐0.023 (0.006) ‐ 0.016 (0.003) ‐0.020 (0.004) ‐ 0.050 (0.008) + 0.051 (0.008)In Science 0.046 (0.007) 0.031 (0.008) 0.022 (0.005) 0.030 (0.006) 0.047 (0.011) 0.058 (0.011) +In Social Studies 0.012 (0.007) + 0.039 (0.007) + 0.003 (0.005) 0.019 (0.006) 0.050 (0.009) 0.068 (0.009)In Foreign Languages 0.036 (0.006) ‐ 0.065 (0.006) ‐ 0.002 (0.004) + 0.057 (0.005) ‐ 0.074 (0.007) ‐ 0.047 (0.008) ‐Total Credits Earned 0.007 (0.001) ‐0.008 (0.002) ‐0.006 (0.001) + ‐0.003 (0.001) + ‐0.023 (0.002) ‐0.016 (0.002)

Notes: 1) Each panel shows the results from a separate regression applied only to members of that demographic subgroup. Each regression controls for 8th grade test scores, demographic characteristics, educational needs, and 8th grade fixed effects. 2) Results for the indicator variables show the marginal effect computed at the mean of the independet variables. 3) Robust standard errors are shown in parentheses. 4) + / ‐ indicates significantly larger/smaller marginal effect (at the 5% level) than the reference group (i.e., white, non‐poor, or female).




Attended Any 2‐Year College (But No 4‐Year College) Within Five Years of HS

Entry




31

Table 5b: Effects of 10th Grade Course Taking, by Demographic Subgroup

Student Subgroup Credits Earned by 10th Grade

Non‐Poor In Math 0.029 (0.003) 0.012 (0.005) 0.008 (0.004) 0.011 (0.004) 0.067 (0.005) 0.007 (0.004)In English ‐0.015 (0.002) ‐0.008 (0.004) 0.024 (0.003) ‐0.005 (0.003) 0.019 (0.004) 0.026 (0.005)In Science 0.027 (0.004) 0.029 (0.006) 0.026 (0.004) 0.027 (0.005) 0.037 (0.006) 0.046 (0.006)In Social Studies ‐0.012 (0.003) 0.019 (0.004) 0.008 (0.004) 0.007 (0.004) 0.039 (0.006) 0.060 (0.006)In Foreign Languages 0.068 (0.003) 0.135 (0.003) ‐0.036 (0.003) 0.108 (0.003) 0.092 (0.004) 0.070 (0.004)Total Credits Earned 0.005 (0.001) ‐0.010 (0.002) ‐0.009 (0.001) ‐0.005 (0.001) ‐0.019 (0.002) ‐0.014 (0.001)

Poor In Math 0.045 (0.004) + 0.004 (0.003) 0.014 (0.003) 0.022 (0.004) + 0.039 (0.005) ‐ ‐0.016 (0.006) ‐In English ‐0.057 (0.003) ‐ ‐0.016 (0.002) 0.019 (0.002) ‐0.012 (0.003) 0.075 (0.004) + 0.067 (0.004) +In Science 0.053 (0.005) + 0.022 (0.003) 0.018 (0.004) 0.037 (0.005) 0.012 (0.005) ‐ 0.028 (0.007) ‐In Social Studies ‐0.014 (0.004) 0.021 (0.003) 0.003 (0.003) 0.021 (0.004) + 0.056 (0.005) + 0.080 (0.007) +In Foreign Languages 0.093 (0.005) + 0.057 (0.003) ‐ 0.015 (0.003) + 0.114 (0.005) 0.088 (0.004) 0.074 (0.005)Total Credits Earned 0.011 (0.001) + ‐0.005 (0.001) + ‐0.007 (0.001) ‐0.009 (0.001) ‐ ‐0.022 (0.001) ‐0.016 (0.002)

Female In Math 0.033 (0.003) 0.001 (0.004) 0.012 (0.004) 0.014 (0.004) 0.058 (0.005) 0.000 (0.005)In English ‐0.035 (0.002) ‐0.017 (0.004) 0.024 (0.003) ‐0.012 (0.003) 0.036 (0.004) 0.036 (0.004)In Science 0.031 (0.004) 0.025 (0.005) 0.023 (0.004) 0.028 (0.005) 0.033 (0.006) 0.040 (0.007)In Social Studies ‐0.013 (0.003) 0.022 (0.004) 0.005 (0.004) 0.008 (0.004) 0.046 (0.005) 0.061 (0.005)In Foreign Languages 0.066 (0.003) 0.110 (0.003) ‐0.022 (0.003) 0.106 (0.004) 0.087 (0.004) 0.071 (0.004)Total Credits Earned 0.008 (0.001) ‐0.008 (0.002) ‐0.008 (0.001) ‐0.005 (0.001) ‐0.021 (0.001) ‐0.015 (0.001)

Male In Math 0.040 (0.003) 0.012 (0.003) 0.004 (0.003) 0.021 (0.004) 0.051 (0.005) ‐0.008 (0.006)In English ‐0.035 (0.003) ‐0.011 (0.003) 0.003 (0.003) ‐ ‐0.006 (0.003) 0.060 (0.004) + 0.058 (0.005) +In Science 0.050 (0.004) + 0.027 (0.004) 0.004 (0.004) ‐ 0.040 (0.005) 0.013 (0.005) ‐ 0.032 (0.006)In Social Studies ‐0.017 (0.004) 0.018 (0.003) 0.004 (0.003) 0.018 (0.004) 0.048 (0.007) 0.078 (0.007) +In Foreign Languages 0.101 (0.004) + 0.098 (0.003) ‐ 0.003 (0.003) + 0.142 (0.004) + 0.113 (0.004) + 0.083 (0.004) +Total Credits Earned 0.008 (0.001) ‐0.008 (0.001) 0.001 (0.001) + ‐0.010 (0.001) ‐ ‐0.021 (0.001) ‐0.015 (0.002)

Notes: 1) Each panel shows the results from a separate regression applied only to members of that demographic subgroup. Each regression controls for 8th grade test scores, demographic characteristics, educational needs, and 8th grade fixed effects. 2) Results for the indicator variables show the marginal effect computed at the mean of the independet variables. 3) Robust standard errors are shown in parentheses. 4) + / ‐ indicates significantly larger/smaller marginal effect (at the 5% level) than the reference group (i.e., white, non‐poor, or female).




Attended Any 2‐Year College (But No 4‐Year College) Within Five Years of HS

Entry




32

Table 6: Relationship Between School Characteristics and the High School's Estimated Effect of Completing Algebra 1 or Higher by 10th Grade, as Estimated by Propensity Score Matching

Total Enrollment (000s) ‐0.004 (0.000) 0.051 (0.000) *** ‐0.061 (0.000) *** ‐0.023 (0.000) ** ‐0.020 (0.000) ‐0.042 (0.000) **Teacher‐Pupil Ratio ‐0.326 (0.162) ** ‐0.249 (0.146) * ‐0.069 (0.203) ‐0.409 (0.229) * ‐0.856 (0.431) ** ‐0.677 (0.426)Expenditures Per Pupil ($000s) ‐0.022 (0.009) ** 0.014 (0.008) * ‐0.025 (0.009) *** ‐0.020 (0.010) ** ‐0.016 (0.022) ‐0.040 (0.021) *Percentage of Teachers with Advanced Degrees 0.001 (0.001) 0.000 (0.001) ‐0.002 (0.001) *** ‐0.002 (0.001) ** ‐0.003 (0.002) ‐0.003 (0.002)Magnet School ‐0.185 (0.047) *** ‐0.182 (0.044) *** 0.004 (0.041) ‐0.228 (0.047) *** ‐0.280 (0.114) ** ‐0.240 (0.112) **Mean 8th Grade Math FCAT Standardized Score 0.019 (0.040) 0.105 (0.033) *** 0.008 (0.034) 0.137 (0.038) *** 0.332 (0.086) *** 0.321 (0.085) ***Percentage of FRPL Students 0.032 (0.074) ‐0.137 (0.061) ** 0.116 (0.065) * 0.039 (0.070) 0.111 (0.159) 0.264 (0.157) *Constant 0.358 (0.057) *** 0.165 (0.050) *** 0.364 (0.052) *** 0.568 (0.057) *** 1.288 (0.133) *** 1.275 (0.128) ***

Observations 333 333 333 333 333 333Adjusted R‐Squared 0.100 0.351 0.221 0.194 0.122 0.099

Receive a High School Diploma Within Four Years of HS Entry


Attended Any 2‐Year College (But No 4‐Year College)

Within Five Years of HS Entry


10th Grade Math FCAT Score 10th Grade Reading FCAT Score

33

Figure 1a: Effect of Additional Credits in Math by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

Figure 1b: Effect of Additional Credits in English by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

.4.6

.81

E[h

d4(t)

]

0 2 4 6 8Treatment level

Dose Response Low bound

Upper bound

Confidence Bounds at .95 % levelDose r esponse function = Probability of a positive outcomeRegression command = logit

Dose Response Function

-.10

.1.2

.3

E[hd

4(t+

1)]-E

[hd4

(t)]


Treatment Effect Low bound

Upper bound

Confidence Bounds at .95 % levelDose response function = Probability of a positive outcomeRegression command = l ogit

Treatment Effect Function.4

.5.6

.7.8

E[h

d4(t)

]



Upper bound



-.2-.1

0.1

.2

E[hd

4(t+

1)]-E

[hd4

(t)]



Upper bound


Treatment Effect Function

34

Figure 1c: Effect of Additional Credits in Science by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

Figure 1d: Effect of Additional Credits in Social Studies by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

.4.5

.6.7

.8.9

E[h

d4(t)

]

0 2 4 6Treatment level


Upper bound



-.2-.1

0.1

.2.3

E[hd

4(t+

1)]-E

[hd4

(t)]



Upper bound


Treatment Effect Function.2

.4.6

.8

E[h

d4(t)

]



Upper bound



-.2-.1

0.1

.2

E[hd

4(t+

1)]-E

[hd4

(t)]



Upper bound



35

Figure 1e: Effect of Additional Credits in Foreign Language by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

Figure 2a: Effect of Additional Credits in Math by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

.2.4

.6.8

1

E[h

d4(t)

]



Upper bound



-.2-.1

0.1

.2

E[hd

4(t+

1)]-E

[hd4

(t)]



Upper bound


Treatment Effect Function-.5

0.5

E[m

10(t)

]



Upper bound

Confidence Bounds at .95 % levelDose response function = Linear prediction


-.4-.2

0.2

.4

E[m

10(t+

1)]-E

[m10

(t)]



Upper bound



36

Figure 2b: Effect of Additional Credits in English by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

Figure 2c: Effect of Additional Credits in Science by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

-1-.5

0.5

11.

5

E[m

10(t)

]



Upper bound



-.50

.51

E[m

10(t+

1)]-E

[m10

(t)]



Upper bound


Treatment Effect Function-1

-.50

.5

E[m

10(t)

]



Upper bound



-.50

.5

E[m

10(t+

1)]-E

[m10

(t)]



Upper bound



37

Figure 2d: Effect of Additional Credits in Social Studies by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

Figure 2e: Effect of Additional Credits in Foreign Language by the 10th Grade on the Likelihood of Graduating from High School in 4 Years (Estimated by Generalized Propensity Score Matching)

-.6-.4

-.20

.2.4

E[m

10(t)

]



Upper bound



-.50

.5

E[m

10(t+

1)]-E

[m10

(t)]



Upper bound


Treatment Effect Function-1

.5-1

-.50

.51

E[m

10(t)

]



Upper bound



-1-.5

0.5

1

E[m

10(t+

1)]-E

[m10

(t)]



Upper bound



38

Figure 3: Distribution of High School-Level Effects of Completing Algebra 1 (or Higher) by 10th Grade

01

23

Den

sity

-.5 0 .5 1Effect

kernel = epanechnikov, bandwidth = .04

Distribution of the Effectsof Algebra 1 (or Higher) by 10th Grade

on HS DiplomaAcross High Schools

0.5

11.

5D

ensi

ty

0 .5 1 1.5 2Effect



on 10th Grade Math FCAT ScoreAcross High Schools

0.5

11.

5D

ensi

ty

-.5 0 .5 1 1.5 2Effect


Distribution of the Effectsof Algebra 1 (or Higher) by 10th Gradeon 10th Grade Reading FCAT Score

Across High Schools

01

23

Den

sity

-.5 0 .5 1Effect



on 4-Year College EntryAcross High Schools

01

23

Den

sity

-.5 0 .5 1Effect



on 2-Year College EntryAcross High Schools

01

23

Den

sity

-.5 0 .5 1Effect



on Any College EntryAcross High Schools

39

Figure 4: Relationship Between School Characteristics and Estimated High School-Level Effects of Completing Algebra 1 (or Higher) by 10th Grade on Attending a 4-Year College

01

Effe

ct

0 5000Enrollment

01

Effe

ct

.05 .1Teacher/Pupil

01

Effe

ct

30008000Expend./Pupil

01

Effe

ct

0 100Adv. Degrees

01

Effe

ct

0 1Magnet School

01

Effe

ct

-1 18th Math Score

01

Effe

ct

0 1Pct. FRPL

Relationship Between High School Characteristicsand Effects of Algebra 1 (or Higher) by 10th Grade

on 4-Year College Entry

40

Appendix Figure 1a: Distribution of total credits taken in math by 10th Grade:

Appendix Figure 1b: Distribution of total credits taken in English by 10th Grade:

0.2

.4.6

Den

sity

0 2 4 6 8 10(sum) emat_tot

Kernel density estimateNormal density


Kernel density estimate0

.2.4

.6D

ensi

ty

0 2 4 6 8(sum) eeng_tot



Kernel density estimate

Appendix Figure 1c: Distribution of total credits taken in science by 10th Grade:

Appendix Figure 1d: Distribution of total credits taken in social studies by 10th Grade:

Appendix Figure 1e: Distribution of total credits taken in foreign language by 10th Grade

0.2

.4.6

.8D

ensi

ty

0 2 4 6 8(sum) esci_tot



Kernel density estimate0

.2.4

.6D

ensit

y

0 2 4 6 8(sum) esoc_tot




0.2

.4.6

.8D

ensit

y

0 1 2 3 4(sum) efor_tot




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