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Readers are free to copy display, and distribute this article, as long as the work is attributed to the author(s) and Education Policy Analysis Archives, it is distributed for noncommercial purposes only, and no alte ration or transformation is made in the work. More details of this Creative Commons license are available at http:/ /creativecommons.org/licen ses/by-nc-nd/2.5/. All other uses must be approved by the author(s) or EPAA EPAA is published jointly by the Colleges of Education at Arizona State University and the Universi ty of South Florida. Articles are indexed by H.W. Wilson & Co. Accepted under the editorship of Sherman Dorn. Send commentary to Casey Cobb (casey.cobb@uconn.edu) and errata notes to Sh erman Dorn (epaa-editor@shermandorn.com). EDUCATION POLICY ANALYSIS ARCHIVES A peer-reviewed scholarly journal Editor: Sherman Dorn College of Education University of South Florida Volume 13 Number 51 Decemb er 23, 2005 ISSN 1068–2341 State-Level High School Completion Rates: Concepts, Measures, and Trends1 John Robert Warren University of Minnesota Citation: Warren, J. R. (2005). State-level high school completi on rates: Concepts, measures, and trends. Education Policy Analysis Archives, 13 (51). Retrieved [date] from http://epaa.asu.ed u/epaa/v13n51/. Abstract Since the mid 1970s the national rate at which incoming 9th graders have completed high school has fallen slowly but st eadily; this is also tr ue in 41 states. In 2002, about three in every four students who might have comp leted high school actually did so; in some states this figure is substantially lower. In this paper I review state-level measures of high sc hool completion rates and describe and validate a new measure that reports these rates for 1975 through 2002. Existing measures based on the Current Population Survey are conceptu ally imperfect and statistically unreliable. Measures based on Common Core Data (CCD) dropout information are unavailable for many st ates and have different conceptual weaknesses. Existing measures based on CCD enrollment and completion data are systematically biased by migration, chan ges in cohort size, and/or grade retention. The new CCD-based measure described here is considerably less biased, performs 1 This research was made possible by the Spen cer Foundation’s Major Grant program and has benefited enormously from suggestions and feedba ck from Robert M. Hauser, Evan Schofer, Duncan Chaplin, and Eric Grodsky and from pa rticipants in research workshops at the University of Minnesota, the University of Wisconsin-Madison, and Duke University However, opinions, errors, and omissions are solely the responsibility of the author.

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Education Policy Analysis Archives Vol. 13 No. 51 2 differently in empirical an alyses, and gives a differen t picture of the dropout situation across states and over time. Keywords: High school dropout; Me asurement; Common Core of Data. Each fall, and in every state, a new cohort of students enters high school for the first time. A few years later a portion of each cohort receives a hi gh school diploma and the rest does not. At first glance, the task of quantifying the proportion of entering students in each state who go on to complete high school seems straightforward. Ye ars of effort by academic and government researchers has proven otherwise. There are at least three compelling reasons to develop, analyze, and disseminate state-level high school completion rates. The first is that hi gh school completion is extremely important both socially and economically for students and for the states in which they reside. Consequently, it is inherently worth asking how successful students are in each state at reaching this critical educational milestone. Second, as part of the provisions of the 2002 No Child Left Behind legislation states must meet annual yearly progress (AYP) goals. For secondary education, states’ definitions of AYP are mandated to include “graduation rates for pub lic secondary school students (defined as the percentage of students who graduate from secondary school with a regular diploma in the standard number of years)” [Sec 1111(b)(2)(D)(i)].2 Third, researchers who are interested in the impact of state education policy initiatives—such as the impl ementation of mandatory state high school exit examinations or changes in course requirements for high school graduation—need reliable and valid state-level high school completion rates in or der to come to sound empirical conclusions. In this paper I review and critique existing measures of state-level high school completion rates and describe a new measure that reports state-level high school completion rates for the graduating classes of 1975 through 2002. This n ew measure is more conceptually sound and less biased than existing measures, performs different ly in empirical analyses, and yields a different picture of variability across states and over time in state-level high school completion rates. I conclude by using this new measure to demonstr ate that high school completion rates have fallen modestly but steadily nationwide—and in 41 states—since the mid 1970s. Conceptual and Technical Goals My goal is to develop a state-level me asure of the rate at which incoming 9th grade students complete public high school by obtaining a state-certified diploma; I do not count holders of General Educational Development (GED) certi ficates as high school completers. This conceptualization ignores high school dropout/completi on that occurs before or long after the high school years and it also ignores private high school completers.3 The state-level high school completion measure that I create is thus not a measure of the rate at which people earn any 2 Unfortunately I am not able to compute the high school completion rate developed in this paper at the school or school district level. 3 Below I discuss the implications of ig noring private high school completers.

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State-Level High School Completion Rates 3 secondary education credential; it is a measure of the rate at which people succeed in obtaining a public high school diploma.4 Following Hauser (1997), there are several desirable technical properties of any good measure of the rate of high school completion. Th ree are particularly relevant here. First, such measures should have face validity. For example, if every student in a particular incoming cohort in a particular state goes on to obtain a high school diploma then the high school completion rate for that cohort in that state should equal 100%. As I will demonstrate, widely-used and much-publicized measures of state-level high school completion ra tes fail to meet this basic standard. Second, such measures should “be consistent with a reasonable understanding of the process or processes that it purports to measure” and “should pertain to a well-defined population and set of events.” For present purposes, a good measure of state-level high school completion rates should pertain to specific cohorts of incoming students (e.g., students who first entered the 9th grade in 1988) and should adequately account for such issues as migrati on, changes over time in the size of incoming cohorts, mortality, and grade retention. Finally, such measures should be statistically robust: Good measures of state-level public high school compl etion rates should be based on enough observations to allow statistically sound comparisons across states and across cohorts of the rate at which incoming students complete public high school. Current Measures Existing measures of annual state-level high school completion and dropout rates come from one of only two sources of data: the Cu rrent Population Survey (CPS) and the Common Core of Data (CCD).5 The CPS is a monthly survey of more than 50,000 households, and is conducted by the Bureau of the Census for the Bureau of Labor Statistics. Households are selected in such a way that it is possible to make generalizations abou t the nation as a whole, and in recent years about individual states and other specific geographi c areas. Individuals in the CPS are broadly representative of the civilian, non-institutionalized population of the United States. In addition to the basic demographic and labor force questions th at are included in each monthly CPS survey, questions on selected topics are included in most months. Since 1968 the October CPS has obtained basic monthly data as well as information about school enrollment—including current enrollment status, public versus private school enrollment, gr ade attending if enrolled, most recent year of enrollment, enrollment status in the preceding October, grade of enrollment in the preceding October, and high school completion status. In recent years the October CPS has also ascertained whether high school completers earned diplomas or GED certificates. The Common Core of Data, compiled by the National Center for Education Statistics (NCES), is the federal government’s primary database on public elementary and secondary education. Each year the CCD survey collects in formation about all public elementary and secondary schools from local and state education agencies. One component of the CCD—the State Nonfiscal Survey—provides basic, annual inform ation on public elementary and secondary school 4 The measure that I create is not a four-year high sc hool completion rate measure. It is a measure of the rate at which incoming 9th grade public-school students complete pub lic high school. This means that my measure does not squarely meet the AYP definition described ab ove, which requires a measure of four year completion rates. 5 State-level high school completion and dropout r ates can also be computed from decennial census data—but only for every tenth year—and recently from th e American Community Survey. I am referring to data that allow annual state-level estimates for several high school graduating classes.

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Education Policy Analysis Archives Vol. 13 No. 51 4 students and staff for each state and the District of Columbia. CCD data from the State Nonfiscal Survey includes counts of the number of students enrolled in each grade in the fall of each academic year and the number of students who earned regu lar diplomas, who earned other diplomas, and who completed high school in some other manner in the spring of each academic year. Although the State Nonfiscal Survey has collected counts of public school dropouts since the 1991–1992 academic year, as described below many states have not provided this information or have provided it in a manner inconsistent with the standard CCD definition of dropout (U.S. Department of Education, 2000). Measures Based On CPS Data Estimates of high school completion and dropout have historically been based on CPS data. CPS-derived event dropout rates report the percentage of students in a given age range who leave school each year without first obtaini ng a diploma or GED. For example, 4.8% of 15 to 24 year olds who were enrolled in high school in October 1999 left school by October of 2000 without obtaining a diploma or GED. CPS-derived status dropout rates report the percentage of people within an age range—typically ages 16 to 24—who are not enrolled in school and who have not obtained a diploma or GED. In October 2000, about 10.9% of 16 to 24 year olds were not enrolled in school and did not have a diploma or GED (U.S. Depa rtment of Education, 2001a). Conversely, CPSbased high school completion rates reflect the percentage of 18th rough 24-year-olds who have left high school and earned a high school diploma or the equivalent, including a GED (e.g., Federal Interagency Forum on Child and Family Statistics, 20 05; U.S. Department of Education, 2001a). For example, as of October 2002 87% of 18to 24year-olds who had left school reported that they had earned a high school diploma or a GED. For present purposes there are a number of conceptual and technical problems with CPSderived measures of high school dropout and compl etion, particularly when computed at the state level. First and foremost, the sample sizes for some states are not large enough to produce reliable estimates of rates of high school completion or dropout (Kaufman, 2001; U.S. Department of Education, 2000). Even when data are aggregated across years—for example, in the Annie E. Casey Foundation’s Kids Count (2004) measure—the standard errors of estimates for some states are frequently so large that it is difficult to make meaningful comparisons across states or over time. What is more, by aggregating across years the resulting measure no longer pertains to specific cohorts of incoming students; this is a serious pr oblem for researchers interested in the effects of state education policy reforms that typically ta ke effect for specific cohorts of students. Second, until 1987 it was not possible to di stinguish high school completers from GED recipients in the CPS; since 1988 October CPS respondents who recently completed high school have been asked whether they obtained a diploma or GED, but there are serious concerns about the quality of the resulting data (Chaplin, 2002; Kauf man, 2001). Third, as noted by Greene (2002), “[status] dropout statistics derived from the Cu rrent Population Survey are based on young people who live in an area but who may not have gone to hi gh school in that area” (p. 7). To the extent that young people move from state to state after ag e 18, CPS-based state-level high school dropout rates—particularly status dropout rates based on 16 to 24 year olds—may be of questionable validity (see also U.S. Department of Education, 1992).6 Fourth, some observers have expressed concern about coverage bias in the CPS, particularly for race/ethnic minorities. The CPS is representative of 6 In computing its CPS-ba sed status dropout measure, the Annie E. Casey foundation limits the CPS sample to 16 to 19 year olds, part ially alleviating this problem.

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State-Level High School Completion Rates 5 the civilian, non-institutionalized population of the United States, and so young people who are incarcerated or in the military are not represented To the extent that these populations differ from the rest of the population with respect to frequency and method of high school completion, there is the potential for bias in estimates. Finally, subst antial changes over time in CPS questionnaire design, administration, and survey items have ma de year-to-year comparisons difficult (Hauser, 1997; Kaufman, 2001). For these reasons, the state-level high school completion rate measure that I construct is based primarily on CCD data, not on CPS data. In the sections that follow I describe existing techniques for estimating state-level high school completion rates using CCD data. Each technique has serious conceptual shortcomings and is subject to random data errors, and below I demonstrate that each technique also yields systematically biased estimates. The CCD-based measure that I subsequently develop is still subject to random data errors, but overcomes major conceptual shortcomings and is thus much less systematically biased. Measures Based on Common Core Data I: The NCES Completion Rate (NCES) Since the early 1990s NCES has asked state ed ucation agencies to report the number of students who drop out in each year; state-level dr opout rates have been part of the CCD beginning with the 1992–1993 data collection (U.S. Departme nt of Education, 2002b) which asked about the 1991–1992 academic year. On October 1 of each yea r the NCES asks states to define as a dropout any student who (1) was enrolled at any point du ring the previous academic year, (2) was not enrolled at the beginning of the current academic year, and (3) has not graduated or completed an approved education program (e.g., obtained a GED). Students are not counted as dropouts if they died, if they are absent from school for reasons of health or temporary suspension, or if they transfer to another jurisdiction. NCES then comp utes annual event dropout rates by dividing the number of 9th through 12th grade dropouts by the total 9th through 12th grade enrollment as of October 1. Using these dropout data, NCES also reports a 4-year high school completion rate as: Year X Academic 1 Year X Academic 2 Year X Academic 3 Year X Academic Year X Academic of Spring Year X Academic of Spring 12 Gr from Dropouts 11 Gr from Dropouts 10 Gr from Dropouts 9 Gr from Dropouts Completers H.S. Completers H.S. NCES. (1) Under this formulation, high school completers include students who receive regular diplomas, students who receive alternative (nonstandard) diplomas, and students who complete high school in some other manner. However, regular diploma recipients comprise almost 99% of all high school completers (U.S. Department of Education, 2002a). A conceptual problem with this measure stems from the fact that many students dr op out of school in one academic year, only to reenroll in subsequent years. It is possible, then, fo r some students to be counted as dropouts more than once in the denominator of Equation 1; it is also possible for students who are counted as dropouts in the denominator to also be counted as high school completers in the numerator. Beyond these conceptual problems, NCES dropout and high school completion measures have serious practical limitations. First, event dropout rates are available beginning only with academic year 1991–1992 (U.S. De partment of Education, 2002a), and so completion rates are available beginning only in 1995–199 6, making analyses of historical trends difficult. Second, many

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Education Policy Analysis Archives Vol. 13 No. 51 6 states do not report these dropout rates, and ot hers report them in a manner that does not correspond with the NCES dropout definition (U.S. De partment of Education, 2002a). As a result, for academic year 1999–2000 dropout rates are avai lable for only 36 states and the D.C. and high school completion rates are available for only 32 states (U.S. Department of Education, 2002b).7 Measures Based on Common Core Data II: Basic Completion Rates (BCR–9 and BCR–8) As described above, CCD data include (1) counts of the number of public school students who are enrolled in each grade at the beginning of each academic year and (2) counts of the number of public school students who complete high school each spring. Using these two sets of figures, it is intuitively appealing to compute a Basic Completion Rate (BCR–9) by simply comparing the number of enrolled public school 9th graders in the fall of one academic year to the number of high school completers three academic years later, when that cohort of 9th graders should have obtained diplomas. If we do so, the Basic Completion Rate is: 3 Year X Academic of Fall th Year X Academic of Spring Enrollment Grade 9 Completers School High BCR (2) Indeed Haney (2000; 2001) has used exactly such a measure in highly publicized and muchcited work on the impact of state high school exit examinations on rates of high school completion. The BCR is purportedly a measure of the overall high school completion rate, not a measure of the four-year high school completion rate. However, the BCR has at least four problems, each of which induces systematic bias in the measure. The first problem with the BCR has to do wi th migration. Students who appear as 9th graders in a state in the fall of academic year X may move to another state before the spring of academic year X+3; they may be replaced by (a smaller or larger number of) students who are counted among the number of high school complete rs in the spring of academic year X+3 but who lived in another state in the fall of academic year X. A second problem with the BCR has to do with grade retention. If we are interest ed in the number of incoming 9th graders who go on to complete high school, then measures like the BCR are problemat ic to the extent that the denominator includes 9th graders who are enrolled in the 9th grade in more than one acad emic year; essentially, such measures count retained 9th graders in the denominator for more than one year but in the numerator a maximum of one time. As I demonstrate below in a series of simulations, each of these first two issues call into question the validity of the BCR as a measure of state high school completion rates. In recent work, Haney and colleagues (2004) have tr ied to overcome the grade retention problem by using the number of 8th graders enrolled in academic year X-4 as the denominator (which I will refer to as BCR–8). Since many fewer students are made to repeat 8th grade than are made to repeat 9th grade, this partially alleviates the grade retenti on bias; however, the longer time horizon exacerbates the migration bias. A third problem with the BCR has to do with mortality: Students who die before they complete high school are counted as dropouts. A fourth problem has to do with students who 7 These data problems are related to states’ own widely disparate efforts to measure rates of high school completion and dropout. As noted recently by the National Governors Association in its Compact on State High School Graduation Data “the quality of state high school graduation and dropout data is such that most states cannot fully account for their students as they progress through high school. Until recently, many states had not collected both graduation and dropout data, and those th at have collected these data have not generally obtained accurate information (National Governors Association 2005a).”

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State-Level High School Completion Rates 7 are in un-graded (frequently special education) pr ograms and who might be counted as high school completers in the numerator but not as 9th grader s in the denominator. Because less than 0.2% of young people die during the modal ages of high school enrollment (Arias, 2002) and because the percentage of students in un-graded programs in any given state is also us ually very low—typically about 2% in 1986–1987 and about 1% in 1999–2000—I do not dwell on these issues in this paper.8 Measures Based on Common Core Data III: Av eraged Freshman Graduation Rate (AFGR) I am not the first to recognize the potential consequences of migration and grade retention for CCD-based state-level high school completi on rates like the BCR. The National Center for Education Statistics recently endorsed the Aver aged Freshman Graduation Rate (AFGR) “based on a technical review and analysis of a set of altern ative estimates” (U.S. Department of Education, 2006, p. 1). The AFGR can be computed as 3 Year X Academic of Fall th Year X Academic of Spring Enrollment Grade 9 Smoothed" Recipients Diploma School gh Regular Hi AFGR (3) where 3 Enrollment Grade 10 Enrollment Grade 9 Enrollment Grade 8 Enrollment Grade 9 Smoothed" "2 Year X Acad. of Fall th 3 Year X Acad. of Fall th 4 Year X Acad. of Fall th 3 Year X Acad. of Fall th (4) Note that the AFGR differs from the BCR measures by limiting the numerator to regular high school diplomas; other types of high sc hool diplomas or completions are ignored. The averaging in the denominator is “intended to accoun t for higher grade retentions in the ninth grade” (U.S. Department of Education, 2006, p. 1). As dem onstrated in a series of simulations below, the AFGR does not, in fact, accomplish that goal. What is more, the AFGR does nothing to account for migration or other systematic bias es that are common to CCD-based measures of states’ high school completion rates. Measures Based on Common Core Data IV: Ad justed Completion Rate (ACR I and ACR II) Greene and Winters (2002; 2005) have constructe d two distinct sets of state-level high school completion rates by dividing the number of regular diplomas—again, not the total number of diplomas—issued by public schools in each state by an estimate of the number students at risk of receiving those diplomas. Greene and Winters (2002) Adjusted Completion Rate (ACR I) is computed as t Adjustmen Migration Enrollment Grade 9 Smoothed" Recipients Diploma School gh Regular Hi ACR3 Year X Academic of Fall th Year X Academic of Spring (5) 8 It is worth noting, however, that the measure I develop does account for student mortality.

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Education Policy Analysis Archives Vol. 13 No. 51 8 where 3 Enrollment Grade 10 Enrollment Grade 9 Enrollment Grade 8 Enrollment Grade 9 Smoothed" "2 Year X Acad. of Fall th 3 Year X Acad. of Fall th 4 Year X Acad. of Fall th 3 Year X Acad. of Fall th (6) and 3 Year X Academic of Fall th th 3 Year X Academic of Fall th th Year X Academic of Fall th thEnrollment Grade 12 9 Total Enrollment Grade 12 9 Total Enrollment Grade 12 9 Total 1 t Adjustmen Migration. (7) As with the AFGR, “smoothing” the 9th grade enrollments is designed to minimize the bias introduced by grade retention. The migration adju stment in the 2002 estimate s (which I will refer to as ACR I) is designed to account for bias introd uced by net migration between academic years X-3 and X. The authors revised their migration adjustment for the 2005 estimates (ACR II) such that 4 Year X Academic of Summer 4 Year X Academic of Summer 1 Year X Academic of Summer Olds Year 14 of Number Olds Year 14 of Number Olds Year 17 of Number 1 t Adjustmen Migration. (8) As I will show below in a series of simulations, these adjustments produce valid state-level completion rates only under very specific (and relatively unlikely) demographic circumstances. Although ACR I and ACR II are intended to adjust for the two major problems in completion rates like the BCR, as I show below the details of the ACR I actually produce less valid results than the BCR under most circumstances and the ACR II suffers from the same 9th-grade-retention-induced biases as the BCR and the ACR I. What is more, because states differ among them selves and over time with respect to whether and how they differentiate between “regular diplom as,” “other diplomas,” and “other high school completers,” the AFGR and ACR measures include a new form of potential bias by restricting the numerator to “regular diplomas.” For ex ample, in the CCD data the number of regular diplomas issued in New York fell by 7% from 165,379 in 1988 to 154,580 in 1989—apparently reflecting a dramatic one year change in the number of high school completers. However, the total number of high school completers in New York fell by only about 4% from 165,379 in 1988 to 157,678 in 1989—reflecting much less change. This is because the CCD data report that 3,098 “other diplomas” were issued in New York in 1989, while none were issued in 1988. It is clear that this is a change in classification, not a change in reality. In producing our own state-level completion rates

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State-Level High School Completion Rates 9 we follow NCES and other researchers by combining these types of diplomas (and by continuing to exclude GED recipients from the cate gory of high school completers). Measures Based on Common Core Data V: Cumulative Promotion Index (CPI) Swanson (2003) recently proposed an innovative method for calculating a state-level fouryear high school completion rate which “approximates the probability that a student entering the 9th grade will complete high school on time with a regula r diploma. It does this by representing high school graduation rate [sic] as a stepwise process composed of three grade-to-grade promotion transitions (9 to 10, 10 to 11, and 11to 12) in a ddition to the ultimate high school graduation event (grade 12 to diploma)” (p. 14). Specifica lly, the Cumulative Promotion Index is: 19 Grade Year X Acad. 10 Grade 1 Year X Acad. 10 Grade Year X Acad. 11 Grade 1 Year X Acad. 11 Grade Year X Acad. 12 Grade 1 Year X Acad. 12 Grade Year X Acad. Year X Acad.E E E E E E E Diplomas CPI (9) where Grade12 Year X Acad.E equals the number of 12th graders enrolled in the fall of academic year X. The author notes that this approach “estimates the likelihood of a 9th grader from a particular district completing high school with a regular diploma in four years given the conditions in that district during the [given] school year” (p. 15; emphasis in original). Swanson (2003) argues that this measure has the virtues of being timely and reflective of current education system performance because it requires data from only two academic years. As I w ill demonstrate below, the CPI is systematically biased except when there is no net student migrat ion between geographic units. What is more, the CPI shares with the AFGR and the ACR measures the technical weakness of including only regular diploma recipients in the numerator; in his defe nse, Swanson’s (2003) includes only regular diploma recipients in his four-year high school completion rate because this is what is required under the AYP provisions of No Child Left Behind. As described in more detail below, the measure that I introduce—the Estimated Completion Rate (ECR)—begins with the BCR and then introduces adjustments to the denominator to account for grade retention and migration. The ECR concep tually represents the ratio of the number of diplomas that are issued in a state in a particular ye ar to the number of students at risk of obtaining those diplomas. As discussed below, the ECR is not completely unbiased, but the magnitude of the bias in the ECR is considerably smaller than th e biases in the measures reviewed above. All CCDbased measures are subject to a certain amount of random error (resulting from reporting errors, for example), and all are subject to a common set of sy stematic error (as descri bed below). However, the ECR overcomes the two most serious forms of systematic error in CCD-based measures by accounting for 9th grade retention and state-to-state migr ation in an empirically sound manner. Evaluating Measures Base d on Common Core Data Table 1 presents a series of simulations of enrollment counts, high school completer counts, and high school completion rates in one geog raphic area over ten academic years. For demonstration purposes, the first three simulations stipulate that every single student obtains a high school diploma. By design, then, valid measures of overall high school completion rates should report a 100% completion rate for every academic year in these simulations; four-year completion rates (the CPI) may be less than 100% in the presence of grade retention (which would delay students’

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Education Policy Analysis Archives Vol. 13 No. 51 10 graduation). The first three simulations differ only with respect to assumptions about changes over time in the numbers of incoming 8th graders, net migration rates, and grade retention rates. Each of these three simulations begin with 1,000 students entering the 8th grade for the first time in the fall of the 1994–1995 academic year and follows that and subsequent cohorts of students over ten academic years under a variety of assumptions about cohort sizes, net migration, and grade retention. Panel A of Table 1 simulates a situation in which the size of the incoming 8th grade cohort increases by 3% annually, from 1,000 in 1994–1995 to 1,030 in 1995– 1996 and so forth; there is no net migration, no students are ever retained in gr ade, and all students obtain a high diploma. Given these parameters, all of the 1,000 students who enter 8th grade in the fall of 1994 progress to the 9th grade in the fall of 1995, to the 10th grade in the fall of 1996, to the 11th grade in the fall of 1997, and to the 12th grade in the fall of 1998, and all 1,000 r eceive diplomas in the spring of 1999. The incoming cohort of 8th graders in fall 1995 enjoys similar succe ss, such that all 1,020 obtain regular diplomas in spring 2000. As repor ted at the bottom of the panel, each of the CCD-based completion rates correctly reports a 100% high school comple tion rate—except the ACR I. The ACR I equals 109% under these conditions. In general, if the annual change in the size of 8th grade cohorts equals X (e.g., 0.03 in Panel A), then the ACR I equals the true rate times (1+X)3. Panel B of Table 1 simulates a situation in which the net migration rate equals +2% at each grade level, such that the number of students in ea ch grade and in each year grows by 2% during the course of the academic year because more studen ts move into the geographic than leave it. Here there is no annual change in the size of incoming cohorts of 8th graders, no students are ever retained in grade, and no student drops out. Under this scenario, most of the CCD-based high school completion rates are biased. The BCR–8 yi elds a 110% completion rate, while the other measures each yield a 108% completion rate. In genera l, if the annual net migration rate is expressed as proportion Y, then the BCR–9, the AFGR, the ACR I, and the CPI yield completion rates that equal the true rate times (1+Y)4. Note that if the net migration rate is negative then each of these measures will be downwardly biased. In the end on ly the ACR II and the ECR are not biased by net migration. Panel C of Table 1 presents a simulation in which the percentage of 9th graders made to repeat the 9th grade begins at 5% in 1994–1995 and then rises by 3% each subsequent year. Here there is no annual change in the size of incoming cohorts of 8th graders, there is no net migration, and every student obtains a high school dipl oma. Although 1,000 students enter the 9th grade for the first time in each academic year, not all of them move on to the 10th grade in the succeeding academic year. Consequently, the observed number of 9th graders in each year is higher than the number of new, incoming 9th graders in that year. Except for th e BCR–8 and the ECR, each of the CCD-based measures of overall high school completion rates described above is downwardly biased when any 9th graders are retained—even though all incoming 9th graders end up completing high school.9 This is because the biased measures count retained students in their denominators twice (once in the year in which they first entered the 9th grade and once in the following year) but in their numerators only once. The fact that more students repeat 9th grade than any other high school grade—combined with recent claims that rates of 9th grade retention are increasing (Haney et al., 2004)—is troubling, since retention in the 9th grade has such deleterious consequences for the validity of all of these measures with the exception of the BCR–8 and the ECR. 9 The CPI—again, a four-year measure of completion rates—is not biased in this way.

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State-Level High School Completion Rates 11 A. Cohort Sizes Increase by 3% Annually 1994-'95'95-'96'96-'97'97-'98'98-'99' 99-'00 '00-'01 '01-'02'02-'03'03-'04 No. of New 8th Graders1,000 1,020 1,040 1,061 1,082 1,104 1,126 1,149 1,172 1,195 Fall Enrollment, Grade 81,000 1,030 1,061 1,093 1,126 1,159 1,194 1,230 1,267 1,305 Fall Enrollment, Grade 91,000 1,030 1,061 1,093 1,126 1,159 1,194 1,230 1,267 Fall Enrollment, Grade 101,000 1,030 1,061 1,093 1,126 1,159 1,194 1,230 Fall Enrollment, Grade 111,000 1,030 1,061 1,093 1,126 1,159 1,194 Fall Enrollment, Grade 121,000 1,030 1,061 1,093 1,126 1,159 Number of High School Completers in Spring1,000 1,030 1,061 1,093 1,126 1,159 BCR-9 (e.g., Haney 2000) a100%100%100%100%100% BCR-8 (e.g., Haney et al. 2004) a100%100%100%100%100% AFGR (National Center for Ed ucation Statistics 2005) a100%100%100%100%100% ACR I (e.g., Greene and Winters 2002) aaaa109%109% ACR II (e.g., Greene and Winters 2005) 100%100%100%100%100% CPI (e.g., Swanson 2003) a100%100%100%100%a ECR (Current Paper) a100%100%100%100%100% B. Net Migration Rate of +2% at Each Grade Level 1994-'95'95-'96'96-'97'97-'98'98-'99' 99-'00 '00-'01 '01-'02'02-'03'03-'04 No. of New 8th Graders1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 81,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 91,020 1,020 1,020 1,020 1,020 1,020 1,020 1,020 1,020 Fall Enrollment, Grade 101,040 1,040 1,040 1,040 1,040 1,040 1,040 1,040 Fall Enrollment, Grade 111,061 1,061 1,061 1,061 1,061 1,061 1,061 Fall Enrollment, Grade 121,082 1,082 1,082 1,082 1,082 1,082 Number of High School Completers in Spring1,104 1,104 1,104 1,104 1,104 1,104 BCR-9 (e.g., Haney 2000) a108%108%108%108%108% BCR-8 (e.g., Haney et al. 2004) a110%110%110%110%110% AFGR (National Center for Ed ucation Statistics 2005) a108%108%108%108%108% ACR I (e.g., Greene and Winters 2002) aaaa108%108% ACR II (e.g., Greene and Winters 2005) a100%100%100%100%100% CPI (e.g., Swanson 2003) a108%108%108%108%a ECR (Current Paper) a100%100%100%100%100% a Completion rate cannot be computed for this academic year given the data in this table.Table 1 High School Completion Rates Under Different Assumptions: A Simulation

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Education Policy Analysis Archives Vol. 13 No. 51 12 C. 9th Grade Retention Begins at 5%, Rises 3% Annually 1994-'95'95-'96'96-'97'97-'98'98-'99'99-'00 '00-'01 '01-'02'02-'03'03-'04 No. of New 8th Graders1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 81,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 91,000 1,052 1,056 1,058 1,060 1,061 1,063 1,065 1,067 Fall Enrollment, Grade 10949 996 998 998 998 998 998 998 Fall Enrollment, Grade 11949 996 998 998 998 998 998 Fall Enrollment, Grade 12949 996 998 998 998 998 Number of High School Completers in Spring949 996 998 998 998 998 BCR-9 (e.g., Haney 2000) a95%95%94%94%94% BCR-8 (e.g., Haney et al. 2004) a100%100%100%100%100% AFGR (National Center for Education Statistics 2005) a98%98%98%98%98% ACR I (e.g., Greene and Winters 2002) aaaa98%98% ACR II (e.g., Greene and Winters 2005) a98%98%98%98%98% CPI (e.g., Swanson 2003) a94%94%94%94%a ECR (Current Paper) a100%100%100%100%100% D. 5% of 9th Graders Drop Out 1994-'95'95-'96'96-'97'97-'98'98-'99'99-'00 '00-'01 '01-'02'02-'03'03-'04 No. of New 8th Graders1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 81,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 91,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 Fall Enrollment, Grade 10950 950 950 950 950 950 950 950 Fall Enrollment, Grade 11950 950 950 950 950 950 950 Fall Enrollment, Grade 12950 950 950 950 950 950 Number of High School Completers in Spring950 950 950 950 950 950 BCR-9 (e.g., Haney 2000) a95%95%95%95%95% BCR-8 (e.g., Haney et al. 2004) a95%95%95%95%95% AFGR (National Center for Education Statistics 2005) a97%97%97%97%97% ACR I (e.g., Greene and Winters 2002) aaaa97%97% ACR II (e.g., Greene and Winters 2005) a97%97%97%97%97% CPI (e.g., Swanson 2003) a95%95%95%95%95% ECR (Current Paper) a95%95%95%95%95% a Completion rate cannot be computed for this academic year given the data in this table.Table 1 (Continued) High School Completion Rates Under Different Assumptions: A Simulation

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State-Level High School Completion Rates 13 Finally, Panel D of Table 1 simulates a situation in which 5% of 9th graders drop out of school during the academic year. Under this scenario, I have specified no change in the size of 8th grade cohorts, no net migration, and no grade rete ntion. Thus, unbiased measure of high school completion rates should equal 95%. As shown in Table 1, all measures except the AFGR and the ACR II do equal 95%. The AFGR and the ACR II each equal 97% under these conditions. The simulations in Table 1 make the point that CCD-based high school completion rates like those reviewed above—including newer and “improved” measures introduced by Greene and Winters (2005) and the U.S. Department of Educat ion (2006)—are systematically biased. The ACR I is uniquely biased by changes in the size of incoming cohorts of 8th graders; the BCR–8, the BCR–9, the AFGR, the ACR I, and the CPI are systematica lly biased by migration; the BRC–9, the AFGR, the ACR I, the ACR II, and the CPI are systematically biased by 9th grade retention; and the AFGR, the ACR I, and the ACR II are systematically biased by 9th grade high school dropout. The direction and magnitude of these biases depend on the c onfiguration of demographic and grade retention patterns in particular states in partic ular years. Beyond misrepresenting the absolute rates of states’ high school completion, this means that these measures also misrepresent differences across states and trends over time in high school completion rates—unless net migration, the size of incoming cohorts of 8th graders, and rates of 9th grade retention remain stable over time and across states. What is more, as I will show below these alternat e measures produce substantively different results in empirical analyses. A New Method for Measur ing States’ High School Completion Rates In this section I describe a new CCD-based measure of state-level high school completion rates—labeled the Estimated Completion Rates (ECR )—that I have computed for the graduating classes of 1975 through 2002. As shown in Table 1, this new measure produces estimates of the rate of public high school diploma acquisition that are not systematically biased by migration, grade retention, or changes over time in incoming cohort sizes. After describing the construction of this new measure I employ it for the purposes of co mparing high school completion rates across states and over time. The ECR conceptually represents the proportion of incoming public school 9th graders in a particular state and in a particular year who go on to obtain a high school diploma (and so it is an overall completion rate, not a four-year completion rate). The ECR is computed as t Adjustmen Migration Graders 9 First Time of # Estimated Completers School High ECR3 Year X Acad. of Fall th Year X Academic of Spring (10) For reasons described above, the numerator in Equation 10 is the total number of public high school completers (excluding GED recipients), regardless of whether co mpleters earned regular diplomas, earned “other diplomas,” or completed hi gh school in some other way. Historically about 99% of completers have earned regular diplomas. The denominator begins with an estimate of the number of first-time 9th graders in each state and in each academic year and then adjusts those estimates to account for net migrat ion (and, incidentally, mortality).

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Education Policy Analysis Archives Vol. 13 No. 51 14 Estimating the Number of First-Time 9th Graders Like Haney and colleagues (2004) I use the number of public school 8th graders in a state in the fall of one year as an estimate of th e number of first-time public school 9th graders in that state in the fall of the following year. This estimation tec hnique is fundamentally justified by the fact that 8th grade retention rates are generally extremely low— usually less than 2 or 3%—even in states with high retention rates in other grades. For example, for the 1998–1999 academic year the 8th grade retention rate in North Carolina was reported to be 2.4% while the 9th grade retention rate was reported to be 16.6% (North Carolina State Board of Education, 2004). How accurate is this technique for estimating the number of first-time 9th graders? Table 2 makes use of published administrative data from Massachusetts, Texas, and North Carolina (Massachusetts Department of Education, 2005; North Carolina State Board of Education, 2004; Texas Education Agency, 2000). For various academic years each state has reported the statewide percentage of public-school 9th graders who were required to repeat the 9th grade; these figures appear in Column 3 of Table 2. This table has tw o purposes: First, to validate states’ reported 9th grade retention rates and second, to validate the use of the number of 8th graders in one academic year as an estimate of the number of first-time 9th graders the following academic year. Column 4 in Table 2 reports the total number of 9th graders in academic year X+1 that we might expect on the basis of the total numbers of 8th and 9th graders in academic year X and the percentage of 9th graders retained after academic year X. So, for example, in the fall of 1994 in Massachusetts there were 64,097 8th graders and 66,707 9th graders; 6.3% of those 9th graders were retained. We would expect, then, that the total number of 9th graders in the fall of 1995 in that state would equal the number of 8th graders in the fall of 1994 plus 6.3% of the number of 9th graders in the fall of 1994: So, 64,097 + (0.063)(66,707) = 68,300. It is then possible to compare that estimate to the observed total number of 9th graders in academic year X+1 (shown in column 5). Column 6 reports that the expected total number of 9th graders in academic year X+ 1 falls within 2 percentage points of the observed number in all three states an d in each academic year for which requisite data are available—even before accounting for migration or mortality. This suggests that for these states in these years, the reported 9th grade retention rates are quite plausible. Column 7 reports the estimated number of first-time 9th graders for these states in these selected years. These estimates are based on the number of 9th graders in the previous year, the number of 9th graders in the current year, and the 9th grade retention rate the previous year. So, for example, the estimated number of first-time 9th graders in Massachusetts in the fall of 1995 equals the total number of 9th graders in that state in that year (68,623) minus the product of the total number of 9th graders the previous academic year (66,707) times the percentage of 9th graders retained the previous year (6.3%): 68,623-(66,707 x 0. 063) = 64,420. That is, using plausible data on the 9th grade retention rate in Massachusetts after th e 1994–1995 academic year I estimate that there were 64,420 first-time 9th graders in Massachusetts in the fall of 1995. The ECR uses the number of 8th graders in academic year X as an es timate of the number of first-time 9th graders in academic year X+1. How good is this estimate? Column 8 in Table 2 demonstrates that the number of 8th graders in academic year X falls within 2.2 percentage points of the estimated number of first time 9th graders in each state and academic year considered.

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State-Level High School Completion Rates 15 (1)(2)(3)(4)(5)(6)(7)(8) Massachusetts 1994-1995 64,09766,707 6.3%68,30068,6230.5%64,420-0.5% 1995-1996 65,72468,623 6.3%70,047 70,811 1.1%66,488-1.1% 1997-1998 69,38872,256 6.8%74,30174,6680.5%69,755-0.5% 1998-1999 72,10174,668 7.1%77,40277,7330.4%72,432-0.5% 1999-2000 72,54577,733 8.1%78,84178,201-0.8%71,9050.9% 2000-2001 74,52778,201 8.4%81,096 80,394 -0.9%73,8251.0% Texas 1994-1995 281,109323,162 16.8%335,400335,8190.1%281,528-0.1% 1995-1996 284,875335,819 17.8%344,651343,867-0.2%284,0910.3% 1996-1997 290,666343,867 17.8%351,874347,951-1.1%286,7431.4% 1997-1998 292,648347,951 17.6%353,887 350,743 -0.9%289,5041.1% North Carolina 1998-1999 95,522108,749 16.6%113,574111,493-1.8%93,4412.2% 1999-2000 96,542111,493 16.1%114,492112,416-1.8%94,4662.2% 2000-2001 99,295112,416 14.6%115,708114,236-1.3%97,8231.5% 2001-2002 102,126114,236 14.7%118,919117,724-1.0%100,9311.2%Table 28th Graders Observed in Acad. Year X 9th Graders Observed in Acad. Year X 9th Graders Retained after Acad. Year X EXPECTED Number of 9th Graders in Acad. Year X+1 OBSERVED Number of 9th Graders in Acad. Year X+1 % Difference between Column 5 and Column 4 ESTIMATED Number of 1st Time 9th Graders in Acad. Year X+1 % Difference between Column 1 and Column 7 State and Academic YearUsing the Number of 8th Graders in Academic Year X as a Proxy for the Number of New 9th Graders in Academic Year X+1Note : Data for columns 1, 2, and 5 were derived from CC D data. Data for column 3 were derived from the Texas Education Agency (2000), the Massachusetts Depa rtment of Education (2005), and the North Carolina State Board of Education (2005). Although the number of 8th graders in one academic year appears to be a pretty good estimate of the number of new 9th graders the following academic year, there are four potential sources of error inherent in this estimation procedure. The first is random error: random data collection/recording errors are inherent in larg e administrative data sets, and the CCD is no exception. The second source of error is more system atic and has to do with migration: The number

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Education Policy Analysis Archives Vol. 13 No. 51 16 of 8th graders in a state in academic year X is only equal to the number of first-time 9th graders in academic year X+1 if no 8th graders die and if net migration of 8th graders equals zero. As described below, however, the migration adjustment in th e ECR accounts for inter-state migration (and mortality) between grades 8 and 9. The third potential source of error introduced by this technique for estimating the number of first-time 9th graders has to do with 8th grade retention. Although 8th grade retention rates are low it is nonetheless true that 8th grade retention downwardly biases the ECR; this is also true of the BCR–8. However, unlike the other measures reviewed above the ECR is not biased by 9th grade retention. Given that rates of retention are much higher after the 9th grade than after the 8th grade, the extent of downward bias in the ECR introduced by 8th grade retention is vastly smaller in magnitude than the extent of bias in other measures introduced by 9th grade retention. A fourth and final potential source of erro r in this procedure for estimating the number of first-time 9th graders has to do with students transitioni ng from private school to public school (or vise versa) between grades 8 and 9. This bias will only be large, however, when there are high rates of net migration between public and private schools between grades 8 and 9. Separate analyses of 2000 U.S. Census data (the results of which are not shown) indicate that in only 9 states did the percentage of 5th–8th graders attending private schools differ from the percentage of 9th–12th graders attending private school by as much as 2 percentage points. In the end this technique for estimating the number of first-time 9th graders is slightly downwardly biased by 8th grade retention and slightly biased (upwardly or downwardly) by net migrations of 8th graders into or out of private schools. Adjusting for Migration Similar to the ACR II, the adjustment for migration in the denominator of the ECR is based on a comparison of the total population of 17 year olds—the modal age of fall 12th graders—in a state on July 1 of one year to the total popula tion of 13 year olds—the modal age of fall 8th graders—in that state on July 1 four years earlie r. These estimates are derived from published, annual state-by-age population estimates produced by the Population Division of the U.S. Bureau of the Census (U.S. Bureau of the Census, 2001a, 20 01b, 2002) which are readily available for all years between 1970 and 2003. For example, there we re 402,721 people age 13 in California on July 1 of 1970. In that state in 1974 there were 407,812 people age 17—a +1.3% net increase. To improve the reliability of these estimates, I ha ve computed three year moving averages.10 The net migration estimate for California for the graduating class of 1980 thus represents the point estimates for the classes of 1979 through 1981.11 Again, these migration estimate s are subject to random error; however, their degree of systematic bias is small. In any case, these estimates are preferable to either ignoring migration or to using systematic ally biased estimates of migration. There are three potential problems with this t echnique for estimating migration rates. The first issue is that these migration estimates pert ain to the net change in the population size of all 13 year olds over the ensuing four years—not to net change in the population size of all 13 year old students. However, more than 98% of 13 year olds are enrolled in school; consequently, the empirical biases resulting from this conceptual issu e are likely trivial. The second issue is that these estimates cover only four years of migration betw een ages 13 and 17 (and implicitly between the 10 This is a tradeoff between statistical reliability and a lack of sensitivity of the ECR to short-term changes in migration patterns 11 Although I refer to these as estimates of net migrati on, these figures actually represent the influence of both net migration and mortality; indeed only migration and mortality can lead to differences between the numbers of 13 year olds in a state in one year and the number s of 17 year olds in that state four years later.

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State-Level High School Completion Rates 17 beginning of grades 8 and 12). Surely there is so me migration among high school students between ages 17 and 18 (implicitly during the senior year of high school), and this migration is missed in my estimates. Although it is possible to use the Census Bureau’s population figures to estimate migration between ages 17 and 18, these estimates wo uld capture a great deal of inter-state migration among 18 year olds who are moving for the purpose of attending college or taking jobs out of state. Consequently, my estimated migration rates are likely a bit conservative (although the direction of bias depends on whether net migration is positive or negative within states). The third issue is that this technique counts international in-migrants who come to the U.S. between ages 13 and 17—but never enroll in high school—as non-completers. As I show below, this exerts modest downward bias on the ECR, particularly in states with high levels of international in-migration. Above and beyond the technical issues involved in estimating the number of first-time 9th graders and adjusting for migration, a potential technical weakness of the ECR more generally concerns its treatment of students who are made to repeat any high school grade other than grade 9. Students enrolled in the 9th grade in academic year X-3 who ar e made to repeat one grade during high school are not at risk of completing high school in the spring of academic year X—but they may still complete high school in academic year X+1. Consequently, the ECR may seem like a downwardly biased estimator of high school comp letion rates. However, consider the fact that students enrolled in the 9th grade in academic year X-3 who ar e made to repeat one grade during high school are at risk of completing high school in the spring of academic year X+1. What this means is that as long as grade retention rate s do not change dramatically from year to year— regardless of their absolute levels—the ECR su ffers from only a very small degree of bias.12 What is more, the ECR is not biased by changes in 9th grade retention rates (as shown in Table 1)—only by changes in retention rates in grades 10 through 12. In short, extreme annual changes in grade retention rates in grades 10 through 12—but not the grade retention rates themselves—produce very small biases in the ECR (but very large biases in the other CCD-based measures reviewed above). The ECR: An Example To illustrate the computation of the ECR in practice, consider that there were 65,724 students in 8th grade in Massachusetts in the fall of 1995—and thus I presume that there were 65,724 first-time 9th graders in Massachusetts in the fall of 1996—and that there were 52,950 high school completers in that state in 2000 (all according to CCD data). However, the population of 17 year olds in Massachusetts on July 1 of 1999 was 3.18% larger than the population of 13 year olds in that state in 1995. Consequently, I estimate that 65,724 x 1.0318 = 67,814 individuals were actually at risk of completing high school in Massachusetts in the spring of 2000. The ECR thus equals %. 1 78 814 67 52,950 ECR 12 For example, imagine that the 9th grade retention rate is 5% in one year and then goes up by 10% annually … from 5.00% to 5.50% to 6.05% to 6.66% to 7.32% and so on. Under this dramatic scenario (as can be shown in simulations like those in Table 1) the ECR is downwardly biased by just 1% after several years. In contrast, the CCD-based measures reviewed above are typically biased by an additional 1% each academic year

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Education Policy Analysis Archives Vol. 13 No. 51 18 Validating the ECR Although the ECR is designed to produce valid estimates of state-level public high school completion rates, it is worth asking how national estimates derived from the ECR compare to high school completion rates derived from longitudinal su rveys of students—surveys in which we actually observe the percentage of students who obtain a hi gh school diploma among those at risk of doing so. For example, the National Educational Longitud inal Study of 1988 (NELS–88) is a longitudinal study of more than 25,000 students who were 8th graders in the spring of 1988 (U.S. Department of Education, 2002c). If I restrict the NELS–88 sample to public school students who were included in the 1994 follow-up survey, I find that 79.6% of respondents completed high school (except via GED certification) by 1992 (which is to say, within four academic years). For the graduating class of 1992 the ECR equals 74.4%. However, because the migration component of the ECR—which equals +5.35% in 1992—reflects patterns of international migration that are not captured in NELS– 88,13 a more reasonable comparison would be to the ECR without including the migration adjustment. For 1992, the ECR without including the migration adjustment equals 78.4%. That is, if we compare conceptually similar rates we observe that the NELS–88 figure and the modified ECR differ by about one percentage point; none of th e other measures described above as closely approximate the experience of th e NELS–88 cohort; the CPI, for instance, equals 71.2% in 1992. State-Level High School Co mpletion Rates, 1975–2002 Table 3 reports the ECR by state and year of high school completion. Figure 1 depicts national high school completion rates as reflected by the BCR–9 and by the ECR for the graduating classes of 1975 through 2002. Both estimators show that the high school completion rate in the United States has generally declined over this pe riod. The ECR is 3.8 percentage points higher than the BCR–9 in 1975 and 4.2 percentage points lowe r by 2000. While one or two percentage points may seem substantively trivial, one should keep in mind that more than three and half million students are in the denominator nationwide each year. One percentage point in these rates is a difference of about 35,000 young people nationwide. This means that in 2002 the BCR–9 and ECR estimates of the number of non-completers di ffered by about 140,000 students nationwide. For any particular state in any particular year, whether the ECR yields substantially higher or lower estimates than the BCR–9 or other meas ures is a largely a function of how much 9th grade retention and net migration those states experience. For states with low 9th grade retention rates and low net migration the ECR is virtually equivalent to the BCR–9 and to other measures. However, in states with high rates of 9th grade retention and/or high levels of net migration the ECR can produce very different estimates. For example, Figure 2 plots the BCR–9 and the ECR for Nevada for the graduating classes of 1975 through 2002. Because Ne vada has experienced very high rates of net inmigration annually—the population of 17 year olds is often more than 15% larger than the population of 13 year olds four years earlier—the ECR is as much as five to ten percentage points lower than the BCR–9 in many years. In contrast, New York experienced moderate net outmigration until the mid–1980s and has experienced mo derate net in-migration ever since then. The consequence, as shown in Figure 3, is a grad ual narrowing of the gap between the ECR and the BCR–9 over time. 13 In-migrants who came to the U.S. after 1988 were not eligible to be counted among NELS–88 high school completers

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State-Level High School Completion Rates 19 1975197619771978197919801981198219831984 US 78.4%78.0%77.5%76.7%75.4%74.5%75.1%75.5%76.9%77.7% A L65.5%67.5%67.7%68.9%69.5%67.4%68.7%70.2%70.5%69.5% A K65.7%59.2%62.1%69.2%76.2%77.7%78.0%74.5%73.8%72.9% A Z69.7%68.4%74.0%78.1%72.9%66.1%64.5%66.7%66.1%70.6% AR 65.9%66.9%66.9%72.1%72.4%73.6%73.3%74.4%76.2%76.1% CA76.7%77.0%74.2%71.6%67.6%67.5%67.0%67.7%71.1%72.9% CO81.7%80.2%80.2%79.6%78.5%78.6%82.5%77.5%79.3%79.4% CT87.6%81.3%78.6%76.9%74.2%75.4%75.7%75.4%76.3%76.3% DE80.7%80.3%78.4%80.0%78.4%78.2%77.6%77.7%82.2%84.9% DC47.9%48.5%50.4%48.4%49.2%45.7%48.4%52.4%54.7%50.0% FL67.6%69.8%68.8%70.6%64.1%62.8%63.0%62.5%63.9%65.9% GA62.6%64.8%65.7%64.0%64.2%62.5%64.7%65.8%64.9%67.7% HI81.1%80.7%81.7%79.6%83.5%84.4%84.7%91.4%89.0%90.7% ID79.6%73.5%79.2%77.9%79.0%77.4%78.1%79.1%79.0%78.3% IL84.4%84.6%80.0%78.4%77.1%78.0%82.2%85.5%85.1%84.7% IN78.6%82.0%79.9%77.9%78.0%77.4%79.2%81.2%84.2%84.9% IA88.1%88.5%86.1%87.0%87.5%87.5%88.4%89.7%92.8%93.7% KS79.2%79.9%81.1%80.6%82.6%81.1%81.3%82.5%84.6%86.3% K Y 67.8%67.1%65.7%65.5%65.0%67.0%68.5%70.5%72.8%75.4% LA70.0%69.3%68.6%67.4%67.6%67.1%68.6%57.6%58.5%59.7% ME77.4%77.3%75.6%75.9%74.8%74.6%75.1%73.3%75.4%76.2% MD80.8%80.5%78.1%76.4%75.4%76.4%75.1%75.7%78.4%81.5% MA87.9%87.6%80.0%82.3%80.6%76.0%77.6%78.7%80.3%77.8% MI89.1%77.7%81.6%80.0%77.8%75.8%77.7%78.8%81.4%82.8% MN94.6%93.8%92.6%90.9%88.5%87.2%89.4%91.6%94.8%95.5% MS59.3%59.6%59.3%60.4%61.3%60.2%62.3%63.4%63.8%64.4% MO78.7%79.8%79.0%77.2%76.9%77.3%77.7%79.6%81.7%82.5% MT85.0%83.9%84.6%85.1%82.4%83.4%84.1%83.8%84.9%84.2% NE88.8%90.0%89.0%89.3%87.9%86.9%85.6%86.9%89.3%88.9% N V 70.0%71.4%73.1%70.4%66.8%66.1%71.3%73.2%73.8%77.2% NH86.8%79.6%81.6%77.9%79.3%78.6%75.9%78.5%79.7%80.2% NJ91.3%89.1%87.8%88.0%85.3%83.4%81.8%83.6%84.9%85.3% NM79.4%76.3%74.9%75.3%75.2%74.9%73.4%74.4%74.1%75.9% N Y 83.6%83.6%83.2%81.8%80.6%79.5%77.5%76.9%76.9%76.7% NC68.8%69.5%69.7%69.5%69.7%68.5%68.6%70.5%72.2%73.4% ND87.2%87.6%86.2%87.2%86.8%85.0%87.2%89.0%88.7%90.8% OH85.5%84.9%84.3%83.1%83.7%81.4%84.0%83.4%86.2%88.1% OK74.7%74.0%75.6%76.6%76.3%76.0%75.8%75.4%78.0%78.5% O R 77.2%77.4%76.3%71.7%70.8%70.3%70.4%73.3%76.4%77.1% PA88.7%88.9%87.0%86.0%85.6%84.0%83.8%84.3%86.4%87.9% RI79.2%76.5%75.4%74.0%76.0%76.5%77.9%76.7%78.6%76.3% SC67.9%67.8%68.1%70.6%67.6%69.6%69.9%70.4%70.4%70.9% SD88.4%85.5%84.7%84.0%83.1%83.1%83.2%83.8%85.6%86.5% T N64.3%66.1%72.1%65.1%67.5%66.7%71.1%69.7%66.3%67.2% T X67.5%68.1%71.6%72.3%71.3%70.8%69.9%69.4%70.7%69.9% UT80.0%80.2%79.9%81.3%77.4%77.8%79.4%80.5%83.7%85.1% V T73.7%77.8%75.7%76.9%72.2%72.7%70.0%72.9%72.8%77.2% V A69.0%69.7%70.5%69.7%70.4%71.2%72.1%72.2%73.9%72.5% WA77.4%77.9%78.0%76.7%75.3%73.4%74.0%75.9%75.4%77.8% W V 71.4%72.0%71.1%70.8%71.8%73.1%74.1%74.1%78.1%78.8% WI99.6%97.3%96.3%94.4%92.6%91.2%92.3%94.2%96.7%97.6% W Y 78.0%80.6%78.5%80.3%78.0%79.1%78.3%77.7%79.8%80.8%Table 3ECR by State and Graduating Class

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Education Policy Analysis Archives Vol. 13 No. 51 20 1985198619871988198919901991199219931994 US 76.6%76.0%75.5%75.1%74.4%74.5%74.2%74.4%74.2%73.1% A L67.0%66.3%70.5%71.4%70.5%67.2%66.4%65.7%61.5%58.2% A K69.2%73.1%74.2%73.4%72.5%77.1%83.4%81.2%77.1%71.1% A Z67.7%64.9%66.4%63.7%66.3%68.0%74.5%71.0%74.2%68.1% AR 75.4%75.9%76.0%75.8%74.1%73.5%73.0%73.5%73.0%70.4% CA69.5%67.7%65.9%66.3%65.7%65.8%66.6%69.6%71.8%71.4% CO76.1%73.7%75.6%77.5%78.7%78.8%77.9%79.1%76.6%72.9% CT76.1%81.4%73.6%76.9%78.1%77.9%81.8%83.4%83.8%84.1% DE85.5%87.4%78.1%75.9%77.6%74.2%72.9%75.6%75.6%70.5% DC51.0%52.3%52.6%52.6%49.0%55.1%53.0%61.0%65.1%69.3% FL62.5%62.5%59.6%60.8%59.9%60.2%61.0%64.7%62.5%61.9% GA67.1%66.7%66.0%64.8%65.4%67.1%68.1%67.2%65.4%62.9% HI93.3%93.7%91.9%90.5%90.2%90.0%83.0%81.4%79.2%79.6% ID80.1%78.9%80.0%78.2%78.6%78.6%77.9%76.9%74.3%72.2% IL84.6%85.8%86.3%84.6%84.8%83.2%83.4%83.7%83.6%80.6% IN83.7%80.7%81.1%82.3%79.3%78.4%78.0%76.8%74.6%72.6% IA93.4%92.8%91.7%91.5%90.3%89.6%86.2%87.1%86.7%84.9% KS86.2%86.0%86.8%83.5%83.2%82.9%82.1%80.1%79.9%78.9% K Y 74.6%73.6%72.2%75.3%72.6%74.7%75.2%73.6%74.9%77.7% LA63.2%65.0%62.9%66.7%64.6%65.6%61.3%59.8%60.8%64.0% ME76.7%74.6%76.2%75.5%73.8%79.6%79.1%82.2%75.5%72.8% MD80.5%79.9%77.1%77.6%76.8%75.9%76.9%79.8%80.4%79.8% MA75.4%75.5%77.2%75.6%76.4%81.5%78.7%82.4%81.9%81.2% MI81.9%80.1%80.5%79.6%78.1%77.4%75.8%76.3%75.0%74.4% MN93.0%90.6%90.7%91.0%89.2%89.9%89.0%88.0%88.5%86.5% MS63.8%63.1%64.2%67.3%61.0%67.0%64.0%63.7%63.2%61.6% MO81.7%80.5%80.2%79.0%78.7%78.6%77.9%77.0%76.2%75.8% MT83.2%84.6%85.1%86.4%86.9%85.1%85.8%84.4%83.7%81.4% NE89.3%89.8%89.2%87.5%87.4%86.9%85.4%86.1%85.2%84.0% N V 74.7%75.4%74.6%71.4%63.8%66.4%64.7%59.1%59.6%59.4% NH79.2%75.7%74.3%75.8%72.7%73.3%75.5%78.2%80.8%80.7% NJ84.4%83.3%82.9%82.6%82.5%83.2%85.2%86.6%89.0%88.4% NM75.9%75.7%76.8%77.7%76.6%74.0%75.6%73.1%72.4%70.2% N Y 76.5%78.5%78.5%76.4%75.5%75.5%73.7%75.5%75.1%75.1% NC74.0%72.5%70.5%70.5%71.5%69.6%70.1%70.1%69.3%68.0% ND90.5%89.4%90.5%93.1%92.4%92.8%91.1%90.6%87.1%86.9% OH87.6%87.2%86.6%82.4%82.0%80.4%79.0%78.0%80.3%80.1% OK77.0%76.4%75.6%77.2%79.3%82.0%79.3%78.8%76.9%74.9% O R 76.5%74.2%73.8%73.1%71.7%71.7%69.8%69.9%68.9%66.9% PA87.6%87.1%86.7%86.0%84.4%84.0%83.6%84.6%85.0%84.0% RI74.8%75.5%74.6%71.8%72.4%71.1%74.3%79.0%79.6%77.7% SC68.1%68.7%69.9%68.1%67.3%61.3%64.2%60.8%62.2%61.7% SD87.8%83.9%84.9%85.0%84.5%83.5%83.0%83.0%85.5%86.1% T N66.8%67.0%66.9%69.3%68.8%68.5%68.7%69.8%68.7%64.3% T X68.1%66.8%67.6%67.4%68.1%69.9%71.7%66.5%64.4%63.2% UT81.9%80.5%82.0%81.3%81.8%78.0%76.3%77.4%76.0%74.4% V T77.0%76.7%76.7%75.3%74.6%81.9%72.9%73.7%78.7%75.3% V A73.7%75.1%75.9%73.3%75.1%74.7%74.9%75.2%76.2%74.6% WA78.0%76.4%79.6%78.7%75.0%75.9%71.2%73.1%72.4%74.1% W V 79.5%79.2%79.2%79.5%80.2%80.4%78.9%76.7%77.1%74.9% WI96.1%96.5%94.8%94.2%91.7%93.6%90.8%89.4%89.2%87.2% W Y 82.0%80.4%82.5%86.8%85.8%85.0%85.6%87.0%82.6%81.9%Table 3 (Continued)ECR by State and Graduating Class

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State-Level High School Completion Rates 21 19951996199719981999200020012002 US 71.6%70.6%71.3%71.0%71.3%71.9%71.1%72.2% A L58.5%56.6%56.4%58.4%56.6%58.6%59.1%57.1% A K66.4%64.0%64.2%64.8%65.6%64.3%67.2%68.0% A Z60.5%56.1%61.6%60.2%57.9%61.0%69.6%70.7% AR 66.6%67.5%65.4%69.6%70.7%71.7%70.0%70.8% CA70.2%70.8%72.2%71.5%72.5%71.9%71.0%71.9% CO69.8%67.6%67.2%66.5%66.3%68.2%68.6%72.5% CT81.3%79.5%80.6%81.3%80.8%85.0%78.3%79.4% DE67.0%69.5%69.3%72.6%70.1%65.2%67.4%64.8% DC62.2%57.2%59.7%58.0%53.4%53.2%54.2%60.5% FL61.5%61.2%63.2%62.8%62.7%61.7%61.1%63.1% GA60.0%58.3%58.3%54.9%54.7%56.9%55.3%57.8% HI78.2%78.7%72.3%69.9%68.7%73.1%70.2%71.5% ID71.7%71.7%71.8%72.3%72.5%74.1%73.7%74.4% IL78.2%77.9%78.4%79.4%80.2%80.8%74.8%76.2% IN70.9%70.3%70.3%70.0%71.0%68.7%69.6%71.6% IA83.4%83.6%84.3%84.0%83.8%84.1%83.9%86.9% KS76.8%74.9%74.6%72.4%72.9%74.8%75.4%77.5% K Y 72.3%68.8%68.6%68.0%68.9%69.6%71.2%69.7% LA64.4%62.5%60.9%63.0%61.4%63.0%63.8%65.2% ME72.9%72.7%73.3%75.0%70.8%71.7%72.3%70.8% MD79.3%79.4%78.7%78.2%78.5%78.5%79.1%79.6% MA79.2%78.6%78.5%78.6%78.1%78.1%78.1%76.5% MI73.1%71.9%74.2%75.2%76.4%79.5%77.1%78.7% MN85.6%84.3%84.5%83.9%86.0%85.3%83.5%83.8% MS58.3%56.7%56.7%57.3%56.6%57.2%57.7%58.7% MO74.6%73.7%74.0%74.5%75.9%76.6%75.6%77.2% MT79.6%76.6%76.8%76.0%76.6%77.3%76.7%77.3% NE83.2%81.5%81.7%82.0%84.5%83.9%82.7%83.4% N V 58.5%58.9%66.8%64.0%65.1%64.3%63.4%65.8% NH78.9%76.5%76.1%75.9%75.0%75.9%76.7%75.8% NJ87.2%86.9%88.1%80.8%82.6%88.9%88.6%87.6% NM67.0%66.2%66.8%62.1%64.6%66.5%67.0%67.6% N Y 72.0%72.1%74.5%72.5%71.1%69.7%67.3%64.9% NC66.8%64.4%64.2%65.0%66.4%67.6%66.3%68.3% ND84.3%84.8%83.2%83.2%83.1%84.9%83.2%83.5% OH78.4%73.3%74.5%75.2%75.3%76.2%77.6%78.5% OK74.7%72.7%72.7%73.4%75.1%74.4%74.0%74.5% O R 68.4%64.0%64.5%65.1%65.2%67.2%66.0%69.6% PA82.9%82.8%83.0%82.8%83.0%82.0%81.6%82.0% RI78.0%76.0%77.6%77.0%77.8%76.8%75.3%75.4% SC58.8%58.5%57.0%56.6%56.4%56.2%54.3%56.7% SD81.9%81.1%82.7%75.9%72.1%76.4%74.6%74.0% T N65.2%65.0%60.4%57.5%58.1%58.6%57.2%58.9% T X63.3%62.6%63.9%65.8%66.0%68.0%67.4%70.4% UT72.1%70.8%75.0%75.4%77.6%78.6%77.8%77.3% V T80.6%78.7%81.0%82.0%79.4%80.2%78.2%80.1% V A73.2%71.8%72.8%73.6%73.2%74.1%74.9%73.7% WA71.9%72.0%70.9%70.4%70.3%71.7%68.1%72.1% W V 72.1%73.7%74.3%74.6%76.0%75.5%75.4%74.0% WI85.6%85.0%85.6%84.5%84.7%86.1%86.9%89.1% W Y 74.1%72.0%73.4%72.9%73.2%75.3%71.5%72.5%ECR by State and Graduating ClassTable 3 (Continued)

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Education Policy Analysis Archives Vol. 13 No. 51 22 50% 60% 70% 80% 90% 100%1975 1980 1985 1990 1995 2000 2002 ECR BCR-9 Figure 1 High School Completion Rates in the United States, Graduating Classes of 1975–2002 50% 60% 70% 80% 90% 100%1975 1980 1985 1990 1995 2000 2002 ECR BCR-9 Figure 2 High School Completion Rates in the Nevada, Graduating Classes of 1975–2002 The BCR–9 equals the number of hi gh school completers (not includ ing GED recipients) in spring of academic year X divided by the number of 9th graders in fall of academic year X-3. The ECR adjusts the denominator to account for net migration and 9th grade retention. See text for details.

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State-Level High School Completion Rates 23 50% 60% 70% 80% 90% 100%1975 1980 1985 1990 1995 2000 2002 ECR BCR-9 Figure 3 High School Completion Rates in the New York, Graduating Classes of 1975–2002 WI NJ IA MN ND NE PA VT MD CT MI OH KS MT UT MO MA IL NH RI OK ID SD WV VA CO WY WA CA IN HI ME AR AZ TX KY OR NC AK NM LA NY DE FL DC TN MS GA AL SC NV-20 -15 -10 -5 0 5 10 15 20BCR-9 Ranking Minus ECR Ranking Figure 4 State Rankings on High School Completion Rate Measures, 2002 The BCR–9 equals the number of hi gh school completers (not includ ing GED recipients) in spring of academic year X divided by the number of 9th graders in fall of academic year X-3. The ECR adjusts the denominator to account for net migration and 9th grade retention. See text for details.

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Education Policy Analysis Archives Vol. 13 No. 51 24 The point that the ECR can sometimes portray a very different picture about individual states’ high school completion rates is made more dr amatically by comparing st ates’ relative rankings on the BCR–9 and the ECR. The X-axis of Figure 4 arrays states according to their ranking on the ECR for the graduating class of 2002, where 1 re presents the highest completion rate in 2002 (in Wisconsin) and 51 represents the lowest completion rate (in South Carolina). The states’ postal abbreviations are arrayed on the Y-axis according to the difference in relative rankings between the ECR and the BCR–9. For example, whereas Wisconsin ranked 7th on the BCR–9 in 2002, it ranked 1st on the ECR in that year—a difference of +6. If the BCR–9 and the ECR yielded the same relative rankings of states—regardle ss of differences in absolute rates14—then we would expect to see all of the postal abbreviations in a line on the Xaxis. But this is not what Figure 4 shows. How are states like Michigan, Ohio, Maine, and Arkansas doing relative to other states with respect to high school completion rates? The answer depends on one’s choice of measure. Figure 5 depicts the ECR for each state for the graduating class of 2002. South Carolina, Alabama, Georgia, Mississippi, an d Tennessee had the lowest public high school completion rates in 2002—all below 60%—while Wisconsin, New Jersey, Iowa, Minnesota, and North Dakota had the highest rates—all above 83%. Figure 1 above showed a modest but steady decline in the ECR over time in the U.S. as a whole, and this trend hol ds in most individual states as well. Figure 6 demonstrates that high school completion rates declined in 41 states between 1975 and 2002, but that the size of the decline varied tremendously across states. Most states saw a decline in high school completion rates of less than 10 percentage points, although New York and Delaware saw declines of more than 15 percentage points while Vermont and the District of Columbia saw gains of more than 5 percentage points. The ECR and Private School Enrollments and Completions The ECR represents the percentage of incoming public school 9th graders in a particular state and in a particular year who complete public high school by obtaining a diploma. The exclusion of private school students and graduates from the ECR could be problematic if there have been substantial changes over time in private high school enrollments and/or completions. This is particularly true if changes in private school enrollments and/or completions have occurred unevenly across socioeconomic and/or demogra phic groups or across geographic areas. For example, if racial inequalities in private school attendance and/or enrollment have widened over time, then the apparent decline in the ECR (and other public high school completion rates) over time may not be a reflection of real change in students’ chances of completing public school. To assess the extent to which changes in pr ivate school enrollments and completions are driving trends in the ECR, Figures 8–10 depicts trends in the percentage of 9th through 12th graders who are enrolled in private schools by race (Figur e 7), household head’s education (Figure 8), and region (Figure 9) and trends by geographic region in the percentage of high school completers who graduated from private schools (Figure 10). Data fo r Figures 7, 8, and 9 are derived from October CPS data for 1977 through 2000; estimates are based on weighted data and reflect three-year moving averages. 14 Although Figure 4 focuses on differences in rankings on the ECR and the BCR–9, the actual percentage point differences are of ten quite sizable. For example, in 2002 the ECR was as much as 5 percentage points higher than the BCR in 15 states and as much as 5 percentage points lower in three states.

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State-Level High School Completion Rates 25 0% 20% 40% 60% 80% 100%WI NJ IA MN ND NE PA VT MD CT MI OH KS MT UT MO MA IL NH RI OK ID SD WV VA CO WY US WA CA IN HI ME AR AZ TX KY OR NC AK NM NV LA NY DE FL DC TN MS GA AL SC Figure 5 High School Completion Rates (ECR), by State, 2002 -20% -15% -10% -5% 0% 5% 10% 15%DC VT AR VA TX WV AK KY AZ OK NC MS MD IA MO KS UT ND NJ RI NV FL LA CA GA ID WA TN NE WY US ME PA IN OH OR MT CT IL AL CO HI MI WI MN NH SC MA NM SD DE NY Figure 6 Changes in High School Graduation Rate s (ECR) between 1975 and 2002, by State The ECR equals the number of high school completers (not including GED re cipients) in spring of academic year X divided by an estimate of the number of new 9th graders in fall of academic year X-3, with adjustment to the denominator to account for net migration. See text for details.

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Education Policy Analysis Archives Vol. 13 No. 51 26 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%1977 1980 1983 1986 1989 1992 1995 1998 White Black Figure 7 Percentage Enrolled in Priva te Schools, by Race, 1977–2000 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%1977 1980 1983 1986 1989 1992 1995 1998 Head of Household Never Attended College Head of Household at Least Attended College Figure 8 Percentage Enrolled in Private Schools, by Parent’s Education, 1977–2000

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State-Level High School Completion Rates 27 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%1977 1980 1983 1986 1989 1992 1995 1998 New England Middle Atlantic East North Central West North Central South Atlantic East South Central West South Central Mountain Pacific Figure 9 Percentage Enrolled in Private Schools, by Region, 1977–2000 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%United States New England Mid. Atlantic E. N. Central W. N. Central South Atlantic E. S. Central W. S. Central Mountain Pacific 1980 1993 1997 1999 Figure 10 Percentage of High School Graduates from Private Schools, by Region, 1977–2000

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Education Policy Analysis Archives Vol. 13 No. 51 28 Data for Figure 10 come from CCD counts of public school completers and counts of private school completers from various years of the Private School Universe Survey which is conducted periodically by the National Center for Education Statistics (U.S. Department of Education, 2001b). About 9% of high school students are enrolle d in private schools. This figure has not changed perceptibly since at least 1977. Whites, students whose household head attended at least some college, and students in the New England and Middle Atlantic states are more likely than their peers to attend private high schools; none of thes e disparities in rates of private school attendance have changed perceptibly since at least 1977. Finall y, as depicted in Figure 10, there are notable regional differences in the rate at which high school completers graduate from private schools. However, neither the overall percentage of comple ters graduating from private schools nor regional differences in that percentage have changed since at least 1980. There are likely many factors behind changes over time and differences across states in public high school completion rates, but changes in private school enrollments and completions likely play a very small role. The ECR and International In-Migration The migration adjustment to the denominator of the ECR conceptually represents the net change in the size of a given cohort between ages 13 and 17; such changes can only be the result of migration and mortality. We begin with n 13 year olds in a particular state in a particular year. Over the next four years, some of the n die, some of the n leave the state, and individuals not counted among the original n move from outside of the state—either from other states or from abroad. A potential problem with this approach to adjust ing for migration concerns young people who move to the U.S. from abroad between the ages of 13 and 17 but who do not enroll in public school. These students inflate the denominator of the ECR but can never appear in the numerator, and so they reduce ECR rates. To the extent that young people immigrate to the United States between ages 13 and 17 but do not enroll in school the ECR may unfairly understate the public high school completion rate; this bias may be especially pronou nced in states that experience high levels of immigration. The size of this problem is an em pirical question that is addressed in Table 4. Columns 1 through 4 of Table 4 are based on da ta for 13 to 17 year olds from the 2000 U.S. Census 5% PUMS file. Column 1 reports the total nu mber of 13 to 17 year olds in each state as of the 2000 enumeration. Column 2 reports the number of 13 to 17 year olds who were born outside of the U.S.—about 8.1% of all 13 to 17 year olds nationwide—and Column 3 reports the number of 13 to 17 year olds who were born outside of the U.S. and who came to the U.S. after age 12. About 20.3% of foreign born 13 to 17 year olds came to the U.S. after age 12. However, Column 4 shows that the vast majority of these young recent immigrants—about 73.5%—were enrolled in school in 2000. Nonetheless, in 2000 there were more than 87,000 people between the ages of 13 and 17 who immigrated after age 12 and who were not enrolled in school. If we assume that none of these young immigrants were ever enrolled in U.S. public schools, and remove them from the migration adjustment to the denominator of the ECR, the ECR in 2000 changes from 71.9% nationwide (Column 5) to 73.7% nationwide (Column 6)—an increase of 1.8 percentage points. The ECR understates the public high school completion rate by less than 1 percentage point for 28 states, but by more than 2.5 percentage points in 7 states—all of which experience high levels of international immigration.

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State-Level High School Completion Rates 29 (1)(2)(3)(4)(5)(6)(7) US 19 978 798 1 622 278 330 741 87 777 71 9% 73 7% 1 8% AL 31 7, 545 6 ,7 65 1 353 594 58 6% 59 1% 0 5% AK 52 645 2 965 417 84 64 3% 64 9% 0 5% AZ 358 360 42 341 8 740 3 466 61 0% 64 6% 3 6% AR 194 320 5 4 7 1 1 418 4 7 0 7 1 .7 % 7 2 6% 0 9% CA 2 432 111 434 935 7 6 ,7 98 20 503 7 1 9% 7 5 5% 3 6% CO 301 799 24 919 6 658 2 444 68 2% 71 3% 3 1% CT 226 214 16 580 4 139 763 85 0% 86 8% 1 8% D E 51 830 3 110 548 193 65 2% 66 6% 1 4% DC 28 676 2 874 871 205 53 2% 55 4% 2 2% FL 1 017 665 119 889 27 115 5 585 61 7% 63 7% 2 1% GA 5 7 8 801 3 7, 10 7 10 642 4 418 56 9% 59 3% 2 4% HI 81 871 8 543 1 309 181 73 1% 74 1% 0 9% ID 107 171 5 327 885 246 74 1% 75 0% 0 8% I L 8 7 5 252 7 3 914 16 652 4 98 7 80 8% 83 9% 3 0% I N 439 851 11 383 2 683 7 26 68 .7 % 69 3% 0 6% IA 214 455 6 726 1 564 389 84 1% 84 9% 0 8% KS 205 690 9 519 2 113 710 74 8% 76 1% 1 4% KY 283 911 5 619 1 125 335 69 6% 7 0 1% 0 4% LA 356 135 6 497 1 217 131 63 0% 63 1% 0 1% ME 91 458 2 736 399 16 71 7% 71 8% 0 1% MD 3 7 2 324 2 7,7 24 6 106 905 7 8 5% 7 9 6% 1 2% MA 40 7,777 33 218 6 ,7 61 632 7 8 1% 7 8 8% 0 .7 % MI 719 235 27 413 5 779 991 79 5% 80 1% 0 6% MN 376 771 21 994 4 063 653 85 3% 86 1% 0 8% MS 219 934 2 658 559 240 5 7. 2% 5 7. 5% 0 3% MO 412 061 10 489 2 440 342 76 6% 77 0% 0 4% MT 72 404 1 658 271 51 77 3% 77 6% 0 3% N E 133 ,7 61 5 1 7 4 1 338 268 83 9% 84 8% 0 9% NV 129 894 16 449 3 11 7 1 190 64 3% 6 7. 8% 3 6% NH 88 759 2 757 726 108 75 9% 76 4% 0 5% NJ 548 659 66 370 12 597 2 553 88 9% 91 7% 2 8% NM 149 122 9 81 7 1 680 46 7 66 5% 6 7.7 % 1 2% NY 1 272 119 172 198 33 449 5 532 69 7% 71 6% 1 9% NC 524 338 27 629 7 177 3 162 67 6% 70 0% 2 4% ND 52 592 1 01 7 14 7 0 84 9% 84 9% 0 0% OH 809 875 16 890 3 147 600 76 2% 76 5% 0 3% OK 256 749 8 868 2 504 1 066 74 4% 76 0% 1 6% OR 242 31 7 1 7, 932 4 036 1 122 6 7. 2% 68 9% 1 .7 % PA 843 099 2 7, 232 4 655 54 7 82 0% 82 3% 0 3% RI 69 073 5 550 939 241 76 8% 78 5% 1 7% SC 280 888 7 697 1 724 455 56 2% 56 7% 0 5% SD 60 853 1 625 408 14 7 6 4% 7 6 5% 0 1% TN 388 873 11 912 2 613 779 58 6% 59 2% 0 7% TX 1 617 029 169 630 38 118 14 915 68 0% 71 4% 3 4% UT 202 640 10 886 2 ,7 6 7 868 7 8 6% 80 3% 1 .7 % VT 44 242 1 0 77 18 7 16 80 2% 80 4% 0 2% VA 477 320 34 702 6 833 1 430 74 1% 75 3% 1 2% WA 429 682 39 720 7 315 1 586 71 7% 73 1% 1 4% W V 120 538 1 014 154 0 7 5 5% 7 5 5% 0 0% WI 399 801 12 813 2 260 584 86 1% 86 9% 0 7% WY 40 309 690 173 0 75 3% 75 3% 0 0% ECR Adjusted Net ChangeTable 4ECR Original A ge 13 to 17 in 2000 U.S. Census Of (1), Foreign Born Of (2), Age > 12 at Arrival Of (3), Not EnrolledECR in 2000, by State, Before and After Accountin g for Immigrants Who Are Not Enrolled in School

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Education Policy Analysis Archives Vol. 13 No. 51 30 The figures in Table 4 can only be reliably computed for 2000, and should serve as a cautionary note: The ECR—as well as the ACR II (Greene & Winters, 2005), which uses a similar migration adjustment—modestly understates public high school completion rates in states with many international immigrants who come to the U.S. between ages 13 and 17 and who do not enroll in school. Does the Choice of Measure Drive Substantive Results? As demonstrated above, conclusions about stat es’ absolute and relative public high school completion rates differ depending on how states’ high school completion rates are measured. Beyond these descriptive differences, it is worth considering whether different state-level measures of public high school completion perform differentl y in the sorts of empirical analyses in which researchers may use them. To address this issue I have estimated models of the effect of states’ secondary school pupil-teacher ratios and states ’ unemployment rates on state-level high school completion rates using alternate measures of the dependent variable. Data on states’ secondary school pupil-teacher ratios are derived from CCD data, and data on states’ unemployment rates is derived from CPS data as computed by the Bureau of Labor Statistics. Briefly, we estimate a series of state and year fixed-effects models in whic h the 588 state-years between 1991 and 2002 are our units of analyses.15 Our models include state and year fixed effects plus one time-varying covariate: either state secondary school pupil-teacher ratios or states’ unemployment rates. These analyses are by no means complete substantive analyses; they are simply designed to investigate whether substantive conclusions might depend on how states’ high school completion rates are operationalized. Table 5 State and Year Fixed-Effect Models of High School Dropout/Completi on Rates, 1975-2002 CPS BCR ACR II CPI ECR b b b b b Variable (s.e.) (s.e.) (s.e.) (s.e.) (s.e.) Model A. Fixed-Effect Model wi th State Pupil-Teacher Ratios as a Time-Varying Covariage -0.06 -0.05 -0.23 -0.37 -0.29* Pupil/Teacher Ratios (0.09) (0.13) (0.13) (0.23) (0.12) Model B. Fixed-Effect Model with State Unem ployment Rates as a Time-Varying Covariate 0.03 -1.38** -0.32 -1.38** -0.23 Unemployment Rate (0.14) (0.20) (0.20) (0.35) (0.20) Because the ACR II does not include estimates for Arizona or Washington, D.C., for most years, these analyses are based on just 49 states. p < .05; ** p < .01 Table 5 reports the results of these models. The models in each column use a different measure of state-level high school completion ra tes: a CPS status dropout rate for 16-to–19 yearolds, the BCR–9, the ACR II, the CPI, and the ECR. Model A includes states’ secondary school pupil-teacher ratios as the only time-varying cova riate, and Model B includes states’ unemployment 15 The ACR II has only been comp uted for 1991 through 2002, and do es not include estimates for Arizona or the District of Columbia. Thus th e 588 state-years include 49 states over 12 years.

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State-Level High School Completion Rates 31 rates as the only time-varying covariate. The resu lts of Model A show that states’ secondary school pupil teacher ratios are related to high school dropout/completion rates only when the ECR is used to measure states’ high school completion rate s. The results of Model B show that state unemployment rates are associated with lower high school completion rates—but only when the BCR–9 or the CPI are the measure of high school comp letion rates. In general, the results in Table 5 suggest that substantive results may depend in important ways on how state-level high school completion rates are measured. This highlights the importance of utilizing a measure that is conceptually sound and as unbiased as possible. Discussion In this paper I reviewed and critiqued exis ting state-level measures of high school completion that use CPS or CCD data. Measures based on the CPS are conceptually inappropriate for present purposes and are typically statistically unreliable because of small sample sizes in many states. Measures based on Common Core Data (CCD) dropout information are unavailable for many states and have their own conceptual weakness. As shown in a series of simulations, existing measures based on CCD enrollment and completion data are systematically biased by migration, by changes in cohort size, and/or by grade retention. The BCR–8, the BCR–9, the ACR I, the ACR II, and the CPI systematically misrepresent absolute rates of high school completion, states’ relative standing with respect to high school completion rate s, and trends over time in rates of high school completion. After critiquing existing CCD-based measures I went on to describe a new measure—labeled an Estimated Completion Rate (ECR)—that uses th ese data to produce st ate-level public high school completion rates for 1975 through 2002. The ECR conceptually represents the percentage of incoming public school 9th graders in a particular state and in a particular year who obtain any public high school diploma. This measure is not influenced by changes over time in incoming cohort sizes, inter-state migration, or 9th grade retention. While the ECR conceptually overcomes the key systematic biases in other CCD-based high school completion rates that are produced by changes in cohort size, migration, and 9th grade retention, its empirical accuracy hinges on the validity of the estimates of first-time 9th graders and the migration adjustment (and, of course, on the quality of the CCD data themselves). However, as described ab ove the ECR does a good job of approximating high school completion rates observed in longitudinal studies like NELS–88. There is certainly some degree of random error in the ECR estimates. Howeve r, the systematic biases in the ECR are far less numerous and smaller in magnitude than the systemat ic biases in alternate measures; indeed all of the biases inherent in the ECR are also inherent in the BCR–8, the BCR–9, the ACR I, the ACR II, and the CPI. Because different measures paint very di fferent pictures of states’ absolute and relative high school completion rates, and because (as shown in Table 5) the choice of measure of states’ high school completion rates can affect substantive em pirical results, it is important for researchers to utilize a measure of state-level high school comple tion rates that is as conceptually sound and as unbiased as possible. I argue that the ECR is the best choice in this regard. While the ECR does a better job of accounting for sources of systematic bias that plague other measures that use the CCD, the ECR is certain ly limited in a number of respects and will not be useful for all purposes. First, because the EC R is a measure of the overall public high school completion rate (not of the four-year completion rate) and because I do not restrict the numerator to regular diploma recipients, the ECR is not in line with the guidelines for measuring AYP in No Child Left Behind. Second, I have not computed the ECR separately by race/ethnicity (or even gender) because the CCD data do not contain ra ce/ethnic-group specific completion counts for

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Education Policy Analysis Archives Vol. 13 No. 51 32 some states and because of the difficulties involve d in producing valid and reliable group-specific migration adjustments. Third, the ECR cannot readil y be computed at the school or school-district level. As a result I have not computed the ECR at geographic levels below the state, despite the need for local-level measures presented by the annual yearly progress requirements of the 2002 No Child Left Behind legislation. Fourth, as described above, the ECR modestly understates high school completion rates in the presence of 8th grade retention and in states with high levels of international in-migration. Fifth, the ECR categorically treats GED recipients as individuals who have not completed high school. For many purposes this is a virtue of the ECR, but for other purposes it may be seen as a weakness. It is conceivable that th e ECR could be amended to include GED recipients in the numerator using data from the GED Testing Service,16 although it would be difficult to know which year GED recipients should be counted in th e numerator of that revised ECR. Despite these limitations, the ECR is an improvement over other CPSor CCD-based measures. It is subject to random error, it is modestly biased by 8th grade retention and international in-migration, and it cannot be computed at the sub-stat e level. However, the other meas ures reviewed in this paper are also subject to the same random errors, are in so me cases biased by international in-migration, and are subject to larger systematic biases as a result of inter-state migration and 9th grade retention (which is much more prevalent than 8th grade retention). None of these measures is perfect, but the ECR minimizes systematic bias. The ECR—like all other CCD-based measures of high school completion—shows a disquieting trend: Since at least the mid–1970s the rate at which incoming 9th graders have gone on to obtain a diploma has declined modestly but stea dily. In the 2002, only about three of every four public school students who might have completed high school actually did so. In 10 states the public high school completion rate declined by more th an 10% between 1975 and 2002; it increased in only eight states and the District of Columbia. Any number of factors may account for this trend, including (but not limited to) changes in the demographic composition of students, increases in GED certification rates, and/or changes in a wide va riety of education policies. In any case, careful investigation of the sources and consequences of this trend requires a conceptually sound and empirically valid measure of high school completion rates. 16 CCD data on numbers of GED recipients varies in quality from state to state and over time.

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State-Level High School Completion Rates 33 References Annie E. Casey Foundation. (2004). Kids count 2003 data book. Baltimore, MD: Annie E. Casey Foundation. Arias, E. (2002). United States life tables 2000. National Vital Statistics Reports, 51(3). Hyattsville, MD: National Cent er for Health Statistics. Chaplin, D. (2002). Ta ssels on the cheap. Education Next, 2, 24–29. Federal Interagency Forum on Chil d and Family St atistics. (2005). America’s children: Key national indicators of well-being, 2005. Federal Interagency Fo rum on Child and Family Statistics, Washington, D.C.: U.S. Government Printing Office. Greene, J. P., & Wint ers, M. A. (2002). High school graduation rates in the United States. New York: Center for Civic Innovat ion, Manhattan Institute. Greene, J. P., & Wint ers, M. A. (2005). Public high school graduation and college-readiness rates: 1991–2002. New York: Center for Civic In novation, Manhattan Institute. Haney, W. (2000). The myth of the Texas mi racle in education. Education Policy Analysis Archives, 8(11), retrieved July 14, 2002, from http://epaa.asu. edu/epaa/v18n41/. Haney, W. (2001). Revisiting the myth of the Texas miracl e in education: Lessons about dropout research and dropout prevention. Paper presented at the Harvard Graduate School of Education, January 13, 2001. Haney, W., Madaus, G., Abra ms, L., Wheelock, A., Miao J., & Gruia, I. (2004). The education pipeline in the Unit ed States, 1970–2000. Chestnut Hill, MA: National Board on Educational Testing and Pub lic Policy, Boston College. Hauser, R. M. (1997). Indicators of high school comple tion and dropout. In R. M. Hauser, B. V. Brown & W. R. Prosser (Eds.), Indicators of children's well-being (pp. 152–184). New York: Russell Sage Foundation. Kaufman, P. (2001). The national dropout data collec tion system: Assessing consistency. Paper presented at the Harvard Civil Ri ghts Project, January 13, 2001. Massachusetts Department of Education. (2005). Statewide grade retention rates. Boston: Massachusetts Department of Education. National Governors Association. (2005). Graduation counts: A report of the National Governors Association task force on stat e high school graduation data. Washington, D. C.: National Governors Association. North Carolina State Boar d of Education. (2004). North Carolina public schools: Statistical profile 2004. Raleigh, NC: North Carolina State Board of Education.

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Education Policy Analysis Archives Vol. 13 No. 51 34 Swanson, C. B. (2003). Keeping count and losing co unt: Calculating graduation rates for all students under NCLB accountability. Washington, D.C.: The Urban Institute, Education Policy Center. Texas Education Ag ency. (2000). 2000 Comprehensive biennial repo rt on Texas public schools. Austin, TX: Texas Education Agency. U.S. Bureau of the Census. (2001a). Population estimates: 1990 to 1999 a nnual time series of state population estimates by single year of age and sex. Washington, D.C.: U.S. Department of Commerce, retr ieved December 23, 2005, from http://www.census.gov/ popest/archives/1990s/. U.S. Bureau of the Census. (2001b). Population estimates: Historical annual time series of state population estimates and demographic components of change 19 80 to 1990, by single year of age and sex. Washington, D.C.: U.S. Department of Commerce, retrieved December 23, 2005, from http://www.census .gov/popest/ar chives/1980s/. U.S. Bureau of the Census. (2002). Intercensal estimates of the r esident population of states. Washington, D.C.: U.S. Department of Commerce, retrieved December 23, 2005, from http://www.census.gov/popest/ archives/pre-1980/ e7080sta.txt. U.S. Department of Education. (1992). Dropout rates in th e United States: 1991. NCES 92–129. Washington, D.C.: National Cent er for Education Statistics. U.S. Department of Education. (2000). A recommended approach to providing high school dropout and completion rates at the state level. NCES 2000–305. Washin gton, D.C.: National Center for Education Statistics. U.S. Department of Education. (2001a). Dropout rates in the United States: 2000. NCES 2002– 114. Washington, D.C.: National Ce nter for Education Statistics. U.S. Department of Education. (2001b). Private School Universe Survey, 1999–2000. NCES 2001–330. Washington, D.C.: National Center for Education Statistics. U.S. Department of Education. (2002a). Public high school dropouts and completers from the Common Core of Data: School years 1991–92 through 1997–98. NCES 2002–317. Washington, D.C.: National Cent er for Education Statistics. U.S. Department of Education. (2002b). Public high school dropouts and completers from the Common Core of Data: School years 1998–99 and 1999–2000. NCES 2002–382. Washington, D.C.: National Cent er for Education Statistics. U.S. Department of Education. (2002c). User's Manual: NELS:88 base -year to fourth follow-up: Student component data file. NCES 2002–323. Washington, D.C.: National Center for Education Statistics. U.S. Department of Education. (2006). The averaged freshman gr aduation rate for public high schools from the Common Co re of Data. NCES 2006–601. Washington, D.C.: National Center for Education Statistics.

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State-Level High School Completion Rates 35 About the Author John Robert Warren University of Minnesota E-mail: warre046@umn.edu John Robert Warren received his Ph.D. in Sociology from the University of WisconsinMadison in 1998. He is currently an Associate Professor of Soci ology and an affiliate of the Minnesota Population Center at the University of Minnesota. His recent work investigates the impact of state-mandated high school exit examinations on high school dropout rates, student academic achievement, and post-secondary la bor market outcomes. In other work he is investigating the degree to whic h associations between socioecono mic status and health can be attributed to the characteristics and condit ions of paid employment. Please direct correspondence to John Robert Warren, Department of Sociolog y, University of Minnesota, 909 Social Sciences, 267 ~ 19th Ave. South, Minneapolis, MN 55455 or email warre046@umn.edu.

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Education Policy Analysis Archives Vol. 13 No. 51 36 EDUCATION POLICY ANALYSIS ARCHIVES http://epaa.asu.edu Editor: Sherman Dorn, University of South Florida Production Assistant: Chris Murre ll, Arizona State University General questions about ap propriateness of topics or particular articles may be addressed to the Editor, Sherman Dorn, epaa-editor@shermandorn.com. Editorial Board Michael W. Apple University of Wisconsin David C. Berliner Arizona State University Greg Camilli Rutgers University Casey Cobb University of Connecticut Linda Darling-Hammond Stanford University Mark E. Fetler California Commission on Teacher Credentialing Gustavo E. Fischman Arizona State Univeristy Richard Garlikov Birmingham, Alabama Gene V Glass Arizona State University Thomas F. Green Syracuse University Aimee Howley Ohio University Craig B. Howley Appalachia Educational Laboratory William Hunter University of Ontario Institute of Technology Patricia Fey Jarvis Seattle, Washington Daniel Kalls Ume University Benjamin Levin University of Manitoba Thomas Mauhs-Pugh Green Mountain College Les McLean University of Toronto Heinrich Mintrop University of California, Berkeley Michele Moses Arizona State University Anthony G. Rud Jr. Purdue University Michael Scriven Western Michigan University Terrence G. Wiley Arizona State University John Willinsky University of British Columbia

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State-Level High School Completion Rates 37 EDUCATION POLICY ANALYSIS ARCHIVES English-language Graduate -Student Editorial Board Noga Admon New York University Jessica Allen University of Colorado Cheryl Aman University of British Columbia Anne Black University of Connecticut Marisa Cannata Michigan State University Chad d'Entremont Teachers College Columbia University Carol Da Silva Harvard University Tara Donahue Michigan State University Camille Farrington University of Illinois Chicago Chris Frey Indiana University Amy Garrett Dikkers University of Minnesota Misty Ginicola Yale University Jake Gross Indiana University Hee Kyung Hong Loyola University Chicago Jennifer Lloyd University of British Columbia Heather Lord Yale University Shereeza Mohammed Florida Atlantic University Ben Superfine University of Michigan John Weathers University of Pennsylvania Kyo Yamashiro University of California Los Angeles

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Education Policy Analysis Archives Vol. 13 No. 51 38 Archivos Analticos de Polticas Educativas Associate Editors Gustavo E. Fischman & Pablo Gentili Arizona State University & Universidade do Estado do Rio de Janeiro Founding Associate Editor for Spanish Language (1998—2003) Roberto Rodrguez Gmez Editorial Board Hugo Aboites Universidad Autnoma Metropolitana-Xochimilco Adrin Acosta Universidad de Guadalajara Mxico Claudio Almonacid Avila Universidad Metropolitana de Ciencias de la Educacin, Chile Dalila Andrade de Oliveira Universidade Federal de Minas Gerais, Belo Horizonte, Brasil Alejandra Birgin Ministerio de Educacin, Argentina Teresa Bracho Centro de Investigacin y Docencia Econmica-CIDE Alejandro Canales Universidad Nacional Autnoma de Mxico Ursula Casanova Arizona State University, Tempe, Arizona Sigfredo Chiroque Instituto de Pedagoga Popular, Per Erwin Epstein Loyola University, Chicago, Illinois Mariano Fernndez Enguita Universidad de Salamanca. Espaa Gaudncio Frigotto Universidade Estadual do Rio de Janeiro, Brasil Rollin Kent Universidad Autnoma de Puebla. Puebla, Mxico Walter Kohan Universidade Estadual do Rio de Janeiro, Brasil Roberto Leher Universidade Estadual do Rio de Janeiro, Brasil Daniel C. Levy University at Albany, SUNY, Albany, New York Nilma Limo Gomes Universidade Federal de Minas Gerais, Belo Horizonte Pia Lindquist Wong California State University, Sacramento, California Mara Loreto Egaa Programa Interdisciplinario de Investigacin en Educacin Mariano Narodowski Universidad To rcuato Di Tella, Argentina Iolanda de Oliveira Universidade Federal Fluminense, Brasil Grover Pango Foro Latinoamericano de Polticas Educativas, Per Vanilda Paiva Universidade Estadual Do Rio De Janeiro, Brasil Miguel Pereira Catedratico Un iversidad de Granada, Espaa Angel Ignacio Prez Gmez Universidad de Mlaga Mnica Pini Universidad Nacional de San Martin, Argentina Romualdo Portella do Oliveira Universidade de So Paulo Diana Rhoten Social Science Research Council, New York, New York Jos Gimeno Sacristn Universidad de Valencia, Espaa Daniel Schugurensky Ontario Institute for Studies in Education, Canada Susan Street Centro de Investigaciones y Estudios Superiores en Antropologia Social Occidente, Guadalajara, Mxico Nelly P. Stromquist University of Southern California, Los Angeles, California Daniel Suarez Laboratorio de Politicas Publicas-Universidad de Buenos Aires, Argentina Antonio Teodoro Universidade Lusfona Lisboa, Carlos A. Torres UCLA Jurjo Torres Santom Universidad de la Corua, Espaa


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