The impact of charter school attendance

potentially misleading estimates of the impact of charter attendance on student achievement. Students who

Journal of Public Economics 91 (2007) 849876www.elsevier.com/locate/econbase

We thank Lori Taylor, Tim Sass, two anonymous referees, and seminar participants at Texas A&M University andnterprise ResearchUniversity of Tennessee Knoxville for comments. We acknowledge financial support from the Private E

Center at Texas A&M University.remain in charters largely recover from the initial disruption within approximately 3 years, and there isweak evidence that there may be overall gains from charter attendance within this period. Furthermore,students who return to traditional public schools after just 1 or 2 years in a charter do not appear to suffer alasting negative impact despite their poor average performance in their first year of charter attendance. 2006 Elsevier B.V. All rights reserved.

JEL classification: I2Keywords: Charter schools; School choice; Student mobilityon student performance

Kevin Booker a, Scott M. Gilpatric b,,Timothy Gronberg a, Dennis Jansen a

a Texas A&M University, United Statesb 505A Stokely Management Center, University of Tennessee Knoxville, Knoxville, TN 37996, United States

Received 25 August 2004; received in revised form 25 July 2006; accepted 1 September 2006Available online 30 November 2006

Abstract

We employ a panel of individual student data on math and reading test performance for five cohorts ofstudents in Texas to study the impact of charter school attendance. We control for school mobility effectsand distinguish movement to a charter school from movement within and between traditional public schooldistricts. We find students experience poor test score growth in their initial year in a charter school, but thatthis is followed by recovery in the subsequent years. Failure to account for this pattern may lead to Corresponding author. Tel.: +1 865 974 1696.E-mail address: sgilpatr@utk.edu (S.M. Gilpatric).

0047-2727/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.jpubeco.2006.09.011

850 K. Booker et al. / Journal of Public Economics 91 (2007) 8498761. Introduction

During their short history charter schools have stirred debate over their academic effectivenessand success as an institution for creating public school choice. Studies such as the 2003 NationalAssessment of Education Progress (NAEP) have received widespread publicity and have beenbroadly interpreted as evidence that charter schools are performing poorly. The NAEP results,based on a national sample of fourth graders, indicate that fewer students in charter schools testedat or above grade level compared with students in traditional public schools, and this remained truefor almost every racial, geographic, and income category. Based on this, The New York Timesopined (August 18, 2004) that long-awaited federal data showed that children in charter schoolswere performingworse onmath and reading tests than their counterparts in regular public schools.

Simple cross-sectional analyses of level scores, such as the NAEP results, do not provideparticularly useful evaluations of charter sector performance. The comparison of sectoral averagesfails to separate the impact of differences in the student populations between sectors from theimpact of differences in the quality of schools between sectors. It is the latter impact which shouldbe of primary policy interest. Identification of that impact requires controls for the relevant non-school (student, family, peer) inputs and for the nonrandom sorting of students into charterschools. Recent papers by Bifulco and Ladd (2005), Sass (2005), and Hanushek, Kain, Rivkin,and Branch (2005) provide more careful evaluations of charter schools in North Carolina, Florida,and Texas, respectively. These papers use panel data on student test scores to estimate modelswhich measure output as score growth (valued added) and employ student fixed effects to controlfor non-school inputs and for selection bias.

In addition to the student population control concerns above, there are two other importantissues to be addressed when assessing the evidence of success or failure of the charter schoolinstitutional experiment. The charter school sector is still in its infancy and many of theobservations of charter school performance come from new operators. It is likely that startup costsfor charters could be significant and first-year charter supplier quality could differ markedly frommature charter quality. The vintage effect on quality across charter schools is likely to be greaterthan across traditional public schools to the extent that choice and competition are successful inweeding out lower-quality suppliers. The longer-run features of the charter school program can bebetter evaluated by separating student performance in more mature charters from studentperformance in newer entrants. The three studies alluded to above all consider and all findevidence of charter school vintage effects. A second feature of charter schools during theirdevelopmental phase is the preponderance of students who are in their first year in attendance at acharter school. As identified in a recent study by Hanushek, Kain, and Rivkin (2004), studentswho switch among public schools can exhibit significant performance effects in the year of themove.1 A priori, a move from a traditional public school setting to a charter school setting couldinvolve a much more significant change in environment than a within-traditional public sectormove and the attendant mover effects could be more pronounced than those found in Hanushek,et al. Although the mover year experience is an important part of the charter school story,conclusions drawn from estimates which are largely driven by mover year observations providean incomplete and potentially misleading evaluation of charter impacts on student performance.Our objective in this paper is to provide a more complete assessment of the impact of charterschool attendance by focusing upon the performance path of students both as they enter chartersand as they either stay in charters or return to traditional public schools.1 Hanushek, et al. find negative disruption effects most strongly associated with intradistrict moves.

In this study we look at student performance in charter schools using a panel of data fromTexas. For Texas data, it may be particularly important to adopt a value-added approach, becausemany charter schools in Texas were explicitly chartered to serve at-risk students, typicallydefined as those students failing to achieve the passing standard on the statewide TAAS math andreading exams. The use of panel data allows us to address the selection issue. We track individuals

851K. Booker et al. / Journal of Public Economics 91 (2007) 849876over time and schools, including transitions from traditional public schools to charter schools.Individual student data and student-specific fixed effects allow us to estimate an individualstudent's performance in charters controlling for that same student's performance in thealternative traditional public school.

We find evidence that students who move to a charter school follow a distinct pattern of testscore decline (relative to expected performance in a traditional public school) in the firsttransitional year of charter attendance. Students experience a recovery from the initialdisruption over the next several years in a charter, so that within 2 or 3 years of moving to a charterstudents are achieving roughly the same test scores as their expected performance in a traditionalpublic school. Furthermore, students who return to traditional public schools after just 1 or 2 yearsin a charter do not appear to suffer a lasting negative impact despite their poor performance intheir first year of charter attendance.

2. The Texas charter school industry

Since the passage of the original charter school legislation in 1995, the number of charterschool districts, charter school campuses, and students in charter schools in Texas has beenexpanding rapidly. The expansion is at least partly attributable to the supportive charter lawenvironment. The charter law structure in Texas was ranked as the seventh most charter-friendlyin the United States by the Center for Education Reform (1997). An idiosyncrasy of the Texascharter legislation is that, beginning with the 199899 school year, some charters were grantedon the condition that they serve primarily (at least 75%) academically at-risk students.2 Thenumber of charters issued to this type of school was not capped as it was for open enrollmentcharters. This charter law incentive structure had an effect, as well over half of the new charterschools which opened in academic years 199899 and 199900 were of the at-risk type. Thisdistinction between charter types and chartering rules was eliminated prior to the 200001academic year.3

Much of the growth in students enrolled in charters is driven by the entrance of new charterschools, as opposed to the expansion of existing charter schools. As shown in Table 1a, therewere 16 charter schools in academic year 199697, the first year of charter operation. This grewto 61 charters in 199899, 142 in 199900, and 179 in 200102. Enrollment in charters alsogrew rapidly, from 2412 in 199697 to 12,226 in 199899, 25,687 in 199900, and 46,939 in200102. To put this in perspective, by academic year 200102 charter schools were enrollingover 1% of the total public school student body in Texas. Table 1b illustrates that throughout thetime series the number of students attending charter schools continued to grow rapidly, with a

2 Under Section 29.081 of the Texas Education Code a student may be classified as at risk for a variety of reasonsincluding failure to advance from one grade level to the next, failure of two or more classes, and failure of a section of theTAAS exam, as well as reasons having to do with personal circumstances such as becoming pregnant.3 Open enrollment charters were initially capped at 60 for academic year 199899, then 120 for 199900. In 2001 thelegislature eliminated the at-risk exemption and capped the number of charters at 215, while also allowing for unlimitedcharters sponsored by colleges or universities.

Table 1aNumber and enrollment of charter schools in Texas

Academic year Charter schools Percent of total public school enrollment

Number in operation Enrollment

20012002 179 46,939 1.1320002001 158 37,956 0.93

852 K. Booker et al. / Journal of Public Economics 91 (2007) 849876substantial share of this growth arising from new entrants in the industry even in the later yearsof the series.

Charter schools in Texas are spatially concentrated. Although there are charter schoolsoperating in 41 of the State's 254 counties, over 60% are located in counties within the five largestmetropolitan areas: Houston, Dallas-Fort Worth, San Antonio, Austin, and El Paso (see Table 2).These six counties (Bexar, Dallas, El Paso, Harris, Tarrant, and Travis) contain almost 48% of thepopulation of Texas. There are 35 additional counties in Texas containing 65 charters, and thesecounties account for 24% of the population of Texas. Finally, there are 213 counties in Texaswithout a single charter school.

The State Board of Education is the principal chartering agency in Texas. This grantingstructure facilitates greater competition between charters and traditional local public schoolsthan in many other states in which the local public school district is also the charter-grantingagent.4 For charter schools in operation prior to the 200102 school year, the Texas schoolfinancing rules transfer 100% of the maintenance and operation formula support, conditionedupon the enrollee's personal characteristics, from the child's home district to the charter school.5

The local district revenue implications of losing a student to a charter are thus larger in Texas thanin eitherMichigan or Arizona, two states which have been the focus of much of the charter schoolresearch to date. In both of those states, only the state portion of the pupil funding follows thestudent to the charter school.

Any discussion of student performance in charter schools must quickly turn to thecharacteristics of the students who attend them. Because many charter schools are geared toward

19992000 142 25,687 0.6419981999 61 12,226 0.3119971998 19 3856 0.1019961997 16 2412 0.0619951996 0 0 at-risk students, and because charter schools are predominantly located in major urban areas, it isnot at all surprising that the demographic profile of charter schools differs in several ways fromthat of traditional public schools. Table 3 indicates that charter schools serve a substantially largershare of AfricanAmerican students, and a smaller share of Anglo students, than traditionalpublic schools. Charters have a larger percentage of economically disadvantaged students(defined as those eligible for a free or reduced-price school lunch) than traditional public schools.6

4 We study exclusively charter schools chartered by the state, so called open enrollment charter schools.5 Charters in Texas do not receive capital funds, nor do they receive the small school adjustments from the state funding

formula.6 When generating this table we treat as missing data the 31 charter schools that are reported to have zero disadvantaged

students. We believe these are most likely schools that have chosen not to participate in the federal school lunch program.This does not affect our statistical analysis since we do not include disadvantaged status as a regressor because effects ofa student's economic status should be captured by the student fixed effect.

Table 1bBreakdown of new charter students in each year

Academic year Increase in number of charterstudents from previous year

Number of students innew charter schools

Percent of growth in charterpopulation due to new schools

20012002 9983 2926 29

853K. Booker et al. / Journal of Public Economics 91 (2007) 849876Charter schools on average have a somewhat lower percentage of their students in specialeducation.

3. Modeling the effect of charter schools on student achievement

Advocates of charter schools and school choice programs in general argue that there areseveral reasons why charter schools may improve students' academic performance. Becausecharter schools must compete for students they must convince students and parents that theyprovide an environment that is superior to the traditional public school alternative. If academicachievement is a principal criterion by which families evaluate schools, then this competitiveeffect should drive charter schools to improve the academic performance of their students.7

Charter schools may improve student performance by structuring their programs to better suitparticular groups of students, whether they be poorly performing at-risk students, gifted students,or students who are in some other way better served by a non-standard program. To the extent thatstudents are heterogeneous in their education needs, the availability of charter schools maybenefit students by simply allowing a degree of sorting into schools better suited to individualneeds. Furthermore, charter schools may indirectly benefit students through peer effects onlearning (Eberts and Hollenbeck, 2002). Peer effects may be more positive when a student entersa charter if students in the charter are more motivated or have greater parental involvement due toself selection, or if students benefit from the sorting generated by a charter which puts them ingreater contact with classmates with similar educational needs. (Of course it is also possible that

20002001 12,269 2662 2219992000 13,461 11,770 8719981999 8370 6427 7719971998 1444 364 2519961997 2412 2412 10019951996 0 0 0peer effects are negative.) Our analysis attempts to measure the overall impact of charter schoolattendance on student performance.

In evaluating the performance of charter schools it is important to look beyond simpledifferences in average TAAS score levels or passing rates between charters and traditional publicschools.8 Given that many charter schools were established to draw primarily students who are at-risk, a classification that is most often applied to students who fail one or more sections of theTAAS test, any suggestion that the average level of performance of students in charters compared

7 Competition from charter schools, either realized or potential could also spur academic improvements in traditionalpublic schools (a subject we address in a separate paper, Booker et al., 2004, and which is also addressed in Sass, 2005,and Bifulco and Ladd, 2005). To the extent that this occurs, the estimated direct effects of charter attendance, the focus ofour current analysis, will be downward biased.8 These are the primary techniques employed by the evaluation of charter schools prepared for the TEA. See TCER

(2002). For a previous critique of this approach, see Gronberg and Jansen (2001).

Table 2Charter schools by county and county population, 20012002

County or set of counties Number ofcharter schools

Population in county(or counties)*

Percent ofTexas population

Charters in major metropolitan counties:Bexar (San Antonio) 21 1,392,931 6.68Dallas (Dallas) 28 2,218,899 10.64El Paso (El Paso) 4 679,622 3.26Harris (Houston) 43 3,400,578 16.31Tarrant (Ft. Worth) 8 1,446,219 6.94Travis (Austin) 10 812,280 3.90

Charters in other counties:Hidalgo 7 569,463 2.7Jefferson, Nueces 5 each 565,696 2.7Lubbock 4 242,628 1.16

854 K. Booker et al. / Journal of Public Economics 91 (2007) 849876Bell, McLennan, Midland, Smith 3 each 742,206 3.6Brazos, Cameron, Galveston, Hays, Webb 2 each 1,028,506 4.9Angelina, Bee, Bowie, Brooks, Comal, Denton, Ellis, Erath,Gregg, Hunt, Lampasas, Montgomery, Panola, Potter, Real,Somervell, Taylor, Uvalde, Val Verde, Van Zandt, Walker,Wichita

1 each 1,949,691 9.4to traditional public schools is an indicator of the quality of education provided by charters ismisleading. Even if average scores in charters are compared to those for similarly composedgroups in traditional public schools with regard to observable characteristics such as race, limitedEnglish proficiency and economically disadvantaged status, these comparisons are still likely tobe biased because such labels almost certainly do not fully account for differences in the

Total Population of Texas 20,851,820 100TX Counties with Charters-41 counties 179 charters 14,965,719 72.8TX Counties without Charters-213 counties 0 charters 5,886,101 28.2

*Source: Bureau of the Census, GCT-PH1: Population, Housing Units, Area, and Density: 2000 Data Set: Census 2000Summary File 1 (SF 1) 100-Percent Data, Geographic Area: Texas.

Table 3Student demographics: charters vs. traditional public schools, 20012002

Student group Charter schools (179) Traditional public school districts (1041)

(%) (%)Anglo 20.4 41.1African-American 39.7 14.1Hispanic 38.3 41.7Asian 1.3 2.8Native American 0.2 0.3Economically disadvantaged 57.6 50.4Limited English proficiency 6.7 14.6Special education 9.0 11.7Career & technology 11.7 19.4Gifted & talented 1.7 8.3At-risk 47.3* 32.0*

* At-risk percentages taken from campus level TAAS data, and reflect % at-risk in grades 38 and 10.

composition of the students who attend charter schools. Charter students are unlikely to be arandom selection or representative of any classification of students because the very act ofchoosing to attend a charter distinguishes these students.9

Examination of differences between charters and traditional public schools in terms of averagechanges or growth in TAAS test scores is more appropriate since this method controls for the levelof performance of students prior to entering a charter school. Nevertheless, analysis of TAASscore growth still suffers in two important respects. First, charter students may systematicallydiffer from students in traditional public schools not just in their level of performance but in theirgrowth trend or ability to improve. That is, they may be more or less likely to show improvement

855K. Booker et al. / Journal of Public Economics 91 (2007) 849876in scores from year to year than the noncharter population. If so, the selection problem would notbe resolved by the use of score growth rather than levels. Those students who choose to attendcharters may well be different from other students in their performance growth trends as well astheir levels of performance. Second, because the charter sector has experienced substantial growthin each year since charters began operating, any average of students' score changes may beheavily influenced by the effects of changing schools since a very large share of the observationswill be students in their first year in the charter.

We use yearly test score data from the Texas Assessment of Academic Skills (TAAS) forstudents in grades three through eight in reading and math to track individual students over timeas some students move from traditional public schools into charters.10 The availability of paneldata enables us to deal much more effectively with the problem of selection bias than whenstudying aggregate data. By including student fixed-effects in our empirical model we cangenerate estimates of the mean effect of charter attendance on test scores by comparing the growthtrend of particular students while they attend a charter with their trend while attending traditionalpublic schools.11 This method obviates the need to model the process by which students areselected into charter schools (such as the techniques pioneered by Heckman, 1979) or to establishan appropriate comparison set of traditional public school students based on limited observablecharacteristics or random selection (e.g. Peterson and Howell, 2003). As Hanushek, Kain, Rivkin,and Branch (2005) note, while the student fixed-effect method effectively controls for time-invariant student, family and peer effects, there remains some concern that students mayexperience a change in one of these factors contemporaneous with the move to a charter school.For example, the family's decision that the student attend a charter may be stimulated by adisciplinary problem or, more positively, by the emergence of a previously lacking parentalawareness or concern for a student's academic progress. Such changes in students' externalcircumstances represent one source of potential bias to our estimates, but only if there is asystematic pattern of such occurrences contemporaneously with the movement of students tocharter schools.12

11 Note that because our data series begins prior to the establishment of charter schools in Texas, and because manystudents first enter a charter after fourth grade (the first point at which we observe their test score growth), we observemost charter students in a traditional public school prior to entering the charter.12 Hanushek, Kain, Rivkin, and Branch (2005) find little evidence that students who move to a charter school experience

9 We use student fixed-effects in our microdata panel to address this issue. Some studies have data available to addressthis selection issue in school choice settings by constructing control groups, such as students who sought to attend achoice school but, due to oversubscription, were unable to do so due to random selection (e.g. Hoxby, 2003, Rouse,1998).10 Unfortunately the fact that high school students are tested only once (in tenth grade) prevents us from applying thetype of analysis employed herein to the performance of charter high schools.a temporary negative shock that precipitates the move. Interestingly, Hanushek, Kain, and Rivkin (2002) also did not findevidence of a temporary dip or improvement prior to student entry into special education programs.

In order to establish the effect of charter attendance on student achievement, we seek to isolateshort-term student mobility effects and new school start-up effects from the longer-term impact ofattending a school structured as a charter. These two similar but distinct factors may affect student

856 K. Booker et al. / Journal of Public Economics 91 (2007) 849876test scores when they enter charter schools and confound estimates of the underlying contributionof charters to student achievement. Consider first the potential for disruption of student'sacademic progress due to switching schools. Hanushek, Kain, and Rivkin (2004) have shown,using Texas data similar to ours, that mobility can be significantly detrimental. They distinguishbetween interdistrict moves (which are further subdivided between moves within a region of thestate and across regions) and intradistrict moves. Their study finds that the disruptive effect ofmoving is greatest for moves within a district, which the authors argue are likely to be moves ofnecessity rather than choice. Bifulco and Ladd (2005) and Sass (2005) also find a disruptive effectof moving (in North Carolina and Florida respectively). They distinguish between structural andnon-structural moves, and both find a larger disruption effect from structural moves than fromnon-structural moves.

We employ this distinction between structural, interdistrict, and intradistrict moves, but wealso believe it is important to distinguish the effect of movement to a charter school from otherinterdistrict moves which take place within the traditional public school system. If mobility isdisruptive to academic progress because of difficulty in transitioning to a new environment, theeffect may be quite different when switching to a charter school because of potentially largerdifferences in instructional style, curriculum, peer groups, and other factors which distinguishcharter schools. At the same time, a move to a charter indicates a family choice to move in favor ofa superior school, as judged by family preferences.

To isolate the mobility effects on student achievement, we include indicators for students whohave switched campuses or districts within the public school system, and separate indicators for amove from a traditional public school to a charter, a move from one charter to another, and for amove from a charter to a traditional public school. Like Sass (2005) and Bifulco and Ladd (2005),we explicitly control for structural moves. We follow Hanushek, Kain, and Rivkin (2004),classifying a move as structural if the move is made by 30% or more of a student's cohort. We findthat structural moves have a greater disruptive impact than either interdistrict or non-structuralintradistrict moves, and this matches what Sass (2005) and Bifulco and Ladd (2005) found inother states.13

A second confounding factor that we wish to isolate in our analysis is start-up difficulties thatcharter schools may experience in their initial years of operation. For this reason we disaggregateour estimates of charter school effects by the number of years a school has been in operation.These two factors that may impact student performancethe student's transition to a new schooland the school itself being neware inherently intertwined. For example, almost all students at anew charter school are also students who have just transitioned from a traditional public school toa charter. In order to better understand these influences on student performance we also estimate amatrix of effects based on the number of years a charter school has operated and the number ofyears a student has been attending the charter.

In keeping with the value-added framework for measuring student achievement discussedabove, the dependent variable in our analysis is individual student Texas Learning Index14 (TLI)

13 We thank an anonymous referee for suggesting that structural moves may have a significant impact and should be

included.14 The Texas Learning Index is a scaled test score, described in more detail in Section 4.

score gains in either reading or math.15 We model test score gains for student (i ) in grade (g) attime (t ) as a function of vectors of time-varying school-programmatic characteristics (X ), schooldemographic characteristics (SD), school movement indicators (M ), indicators for attendance of acharter school by the number of years the charter has been operating (C ), year-by-grade fixed-effects (), student fixed-effects (), and a random error (). This gives us the followingestimation equation:

DTLIigt Xigtb SDit/Migt/ Citg ggt li eigt 1

The school-programmatic characteristic we include is enrollment in special education.16 Year

857K. Booker et al. / Journal of Public Economics 91 (2007) 849876by grade fixed-effects are included because, despite the intention that TLI scores be comparableacross grades and years, we find that average score growth differs across grades and years and thatthese fixed-effects are significant throughout our estimation.17 Due to computational limitations,in some of our specifications we randomly sample 50% of the students who never attend a charterschool (all students who are ever observed in a charter are retained). The regressions are weightedto account for sampling probabilities.

We do not include any measures of inputs, such as expenditures per pupil or student teacherratios. The charter effect therefore captures all systematic differences between charters andtraditional public schools, which may entail different quantities of inputs and choices of how toallocate inputs, as well as institutional differences between charters and traditional public schools.

In the student fixed-effect methodology the estimated effect of attending a charter school isdetermined by the change in achievement gains for students who are observed in both traditionalpublic school and charter school environments. One disadvantage of this method is that a studentwho is in a charter school throughout the period will have the impact of attending a chartercaptured by the individual fixed-effect and will not provide information on the impact of charterschools. However, this problem is fairly minor in our sample since we observe most charterstudents in a traditional public school prior to entering a charter.18

4. The data

All of the data for this project were obtained from the Texas Education Agency and consist ofobservations at the district, campus, and student levels. The student-level data consists ofobservations on all students in grades 38 and 10 (the grades in which the TAAS test isadministered) from 1995 through 2002. Our data set ends with 2002 because Texas adopted a newannual test, the TAKS test, in 2003. This new test instrument and testing environment issubstantially different from the TAAS environment.

15 See Hanushek and Taylor (1990) for a discussion of the benefits of value-added methodology.16 Note that all time-invariant student characteristics such as gender and ethnicity are replaced by the individual studentfixed-effect. Enrollment in special education changes over time and therefore is included. Hanushek, Kain, and Rivkin(2002) use methodology similar to ours to find a positive effect of enrollment in special education on studentperformance. Our results confirm their finding.17 We report HuberWhite corrected standard errors. We also conducted the analysis using the robust cluster estimatorwhich relaxes the independence assumption by requiring only the observations be independent across clusters (in thiscase students). We found little difference in the estimates.18 Approximately 63% of the students we observe in a charter are first observed in a traditional public school. Of theremainder only about 11% are observed in a charter in grade 4, while about 26% are not observed in the sample at all

prior to being observed in a charter school in grade 5 or higher. This latter group presumably consists of students whotransfer to a charter from a private school or from out of the state.

We track five cohorts of students from fourth grade (the first point at which we are able toobserve score growth) through the point at which they are no longer observed in our dataset. Thismeans that we follow a student who does not exit the Texas public school system from fourththrough eighth grade for students that were in fourth grade between 1996 and 1998. Students infourth grade in 1999 are last observed in seventh grade in 2002; those in fourth grade in 2000 are

858 K. Booker et al. / Journal of Public Economics 91 (2007) 849876last observed in sixth grade in 2002. Each student has a unique identification number in the data,which allows us to follow students as they switch schools. The data contain student, family, andprogram characteristics including gender, ethnicity, eligibility for a free or reduced-price lunch(which is used an indicator of economically disadvantaged status), limited English proficiency,and participation in special education.19 As discussed earlier, the student fixed-effectmethodology we employ eliminates the need for time-invariant student characteristics, such asgender and ethnicity, but this data is used to examine how charter schools differentially impactstudents of different ethnicities.

The TAAS test in math and in reading is administered in the spring to all students in grades 3through 8 and 10, although some special education students and limited English proficiencystudents are exempt if a school committee determines that the TAAS test is not educationallyappropriate for the student. Approximately 15% of students in the relevant grades do not take thetest either because they are exempt or they are absent on testing days. The average percentagecorrect differs across grades and years, as does the number correct required to be consideredpassing on this criterion referenced test. In order to make comparisons across years and gradesand evaluate students' progress, the TEA transforms the raw scores into the Texas Learning Index(TLI) scaled score which we use in our analysis. TLI scores range roughly from 0 to 100 with thepassing standard fixed at 70. A raw score is converted to a TLI by determining where the scorewould place the student in the reference year (1994) distribution in which the passing standardwas established. Thus if the passing standard was set at the 40th percentile of the 1994 distributionthen a student taking the test in later years whose raw score would place him exactly at the 40thpercentile of the reference distribution would receive a TLI score of 70. If a student's score placedhim one standard deviation above the passing level in the reference distribution then his TLI scorewould be 85 because the TLI is constructed such that one standard deviation in the referencepopulation corresponds to 15 TLI points.20

In addition to student-level data we utilize data on the composition of the student body at eachcampus. We include in our model the percentage of students by ethnicity, limited Englishproficiency, disadvantaged status, and enrollment in special education. Note that this campus-level data is based on the entire student body rather than only those grades in which the TAAS isadministered.

Careful treatment of school mobility is important when studying the effect of charter schoolson student performance. As discussed earlier, we follow Hanushek, Kain, and Rivkin (2004) indistinguishing between interdistrict moves and intradistrict moves, as well as between structuraland non-structural moves. A student is labeled as having made an interdistrict move if she tookthe TAAS test in a different district in year t1 than year t. She is labeled as having made an

19 Due to confidentiality concerns at TEA, the data on student characteristics such as ethnicity are masked if there arefewer than five students in a cell in a single grade at a campus. Thus if there is only one Hispanic student in fifth grade ata school in particular year, that student's ethnicity is listed as missing. Additionally, though we have an indicator forwhether a student participates in special education, we do not have information on what type of instruction the studentreceives or the student's specific disability. Thus the special education indicator encompasses a very wide range of

students from those with speech difficulties or learning disabilities to the deaf or blind.20 See the TEA Technical Digest for a complete description of the method of computing the TLI.

Table 4Distribution of charter schools by years of operation in each year

Years in operation 1997 1998 1999 2000 2001 2002

New 16 3 42 82 20 232nd year 16 3 40 80 18

859K. Booker et al. / Journal of Public Economics 91 (2007) 849876intradistrict move is she is observed in different campuses from 1 year to the next, but remains inthe same district and the move is not considered structural. A move is considered structural if thestudent remains with 30% or more of her previous classmates. Structural moves are common inour dataset as students progress from elementary to middle school. Unlike previous studies, wegenerally treat movement to and from charter schools as distinct from movement betweentraditional public schools. We include indicators for movement from a traditional public school toa charter, from a charter to a traditional public school, and from one charter to another. Forcomparison we include results from some specifications in which movement to or from a charteris grouped with other interdistrict moves.21 We are interested in examining how transitions to acharter school might or might not differ from the other transitions.

In addition to the mobility effect we are also concerned with differentiating the performance ofcharter schools in their initial year of operation from those that have been operating for some time.Table 4 shows the distribution of charter schools by number of years in operation for each of theyears of our sample and Table 5 indicates the number of individual student-year observations oursample contains corresponding to each category of charter schools by years of operation. Beforeturning to the econometric results it is informative to observe some simple statistics regardingstudent test score growth. Tables 6a and b show average score growth for all students in ourdataset and various subsets. Notice that charter students as a group perform notably less well thanthe population average, but within this group we see that students in their first year in a charterperform much more poorly than students continuing in a charter school. Conversely, this mobilityeffect is not as evident among students in traditional public schools who change schools eitherwithin or between districts.

5. The effect of charter schools on student performance gains

22

3rd year 16 3 40 804th year 16 3 405th year 15 36th year 15Table 7 presents our baseline results for math and reading. The columns titled CommonMobility Effects report estimates of a specification that essentially replicates the methodology ofearlier studies in which movement to, from, and between charters are classified as equivalent to aninterdistrict move and therefore rolled into the District Mover indicator. The columns titledDisaggregated Charter Mobility Effects report estimates of a specification that includes an

21 Because our study is focused on open-enrollment charter schools (i.e. those chartered by the State Board ofEducation) and does not consider district-chartered schools, all moves to and from a charter school are interdistrictmoves.22 We also conducted our baseline analysis using z-scores, which represent a student's performance as the number ofstandard deviations above or below the test mean, rather than TLI scores. The results are essentially identical other thanthe obvious effect of scaling on the coefficients on TLI gains.

Table 5Number of individual student-year observations for charters by years of operation

Years in operation Number of observations

New 20132nd year 28863rd year 26744th year 17425th year 5876th year 256

860 K. Booker et al. / Journal of Public Economics 91 (2007) 849876indicator for movement to a charter school (or the first year of charter attendance), and movementfrom a charter school to a traditional public school (or the first year back in the traditional publicschool sector after a spell in a charter). Systematic effects of the first year of charter attendance,including potential differences in the transitional impact of a move to a charter compared to othermoves, will be captured by the indicator for movement to a charter. In specifications discussedbelow we seek to better separate transition costs of movement from start-up effects at charterschools or poor first-charter-year performance resulting from students being a bad fit with thecharter. Both sets of regressions include separate indicators for charter school attendance based onthe number of years the school has been operating. These specifications also include year-by-grade fixed-effects which are not shown but are generally very significant. The campuspopulation percentages, included to control for peer effects, are also generally significant. Thecoefficients on the campus percentage African-American, Hispanic, and Special Education arenegative throughout, and the coefficients on percent Limited English Proficiency and percentEconomically Disadvantaged are consistently positive.

We find that the indicators for movement from a traditional public school to a charter schooland for movement from a charter school to a traditional public school included in the secondspecification are highly significant. The estimated coefficient on the indicator for movement to acharter school is 2.68 points for math score growth and 2.88 points for reading score growth.The estimated coefficient for the indicator on movement from a charter school to a public schoolis 3.08 points for math score growth and 2.62 points for reading score growth.

In comparison, our estimates of the effect of movement between traditional public schools arefairly consistent with Hanushek, Kain, and Rivkin (2004). In that paper the authors used mathscores from three cohorts of students in Texas (they utilize earlier cohorts that are not part of ourdataset) to study mobility effects. They sought to distinguish disruption effects of mobility fromschool quality (or Tiebout) effects, and found evidence of school quality gains from interdistrictTable 6aAverage TLI math growth

Mean growth

All students 1.36All charter students 0.50Students in 1st year at charter 1.12Students in later years at charter 2.04Continuing students in traditional public 1.35Students who changed traditional public district 1.41Students who changed traditional public campus 1.10

moves within the same region of the state and negative disruption effects associated particularlystrongly with intradistrict moves. We find that intradistrict movement is associated with a .650effect on math, .737 on reading. The estimated effect of interdistrict movement is of lowermagnitude, .328 for math and .423 for reading, in line with the Hanushek, Kain and Rivkinsuggestion that these moves reflect Tiebout improvement offsetting negative disruption effects.We find that structural moves have an estimated effect of 1.21 in math and 1.32 in reading,nearly twice as detrimental as other intradistrict moves, which is consistent with the results foundby Bifulco and Ladd (2005) in North Carolina and Sass (2005) in Florida. It is not clear whystructural moves would be particularly disruptive, and we note that year-by-grade fixed effectscontrol for potential differences in test difficulty (thus the effect cannot be explained by, say, moststructural moves occurring in seventh grade together with lower average performance on thegrade 7 exam). This result does give some context to the effect of movement to a charter, which isroughly double the magnitude of a structural move. Like structural moves, movement to a chartertypically does not entail a change in residence.

A substantial portion of all observations of students in charter schools represents students inthe first year of charter attendance. In our dataset we have 4842 (math) observations of students intheir first year in a charter, 3501 in their second year, 1467 in their third year, and 341 in theirfourth year, so first year observations account for 48% of the total observations of students incharter schools. Given the estimated mobility effects above, it is not at all surprising that theestimated impact of charter attendance is much lower when movement to a charter is confoundedwith other interdistrict moves, as it is in Hanushek, Kain, Rivkin, and Branch (2005) and Sass

Table 6bAverage TLI reading growth

Mean growth

All students 1.66All charter students 0.94Students in 1st year at charter 0.77Students in later years at charter 2.57Continuing students in traditional public 1.67Students who changed traditional public district 1.48Students who changed traditional public campus 1.15

861K. Booker et al. / Journal of Public Economics 91 (2007) 849876(2005). In the absence of specific indicators for movement to and from a charter, the estimatedeffect of charter attendance is negative for nearly all ages of charter schools in both math andreading. The oldest vintage charters (6th year) are the lone exception. We see the largest negativecoefficient on charters in their first year of operation, which of course almost exclusively containsstudents in their first year of charter attendance. Conversely, when we include indicators formovement to and from a charter school we find significantly positive estimates on the indicatorsfor attendance of all vintages of charter schools in both math and reading with the exception of 5thyear charters and, in math, first year charters. However, one must keep in mind that the total effectof charter attendance combines movement effects (which are strongly negative for moves tocharter schools) with the effect of charter attendance. In an appendix to the paper available on thejournal's website we provide results with 2nd though 6th year charter schools effects aggregatedas a pooled continuing charter school effect. We also report results disaggregated by studentperformance quartile (students are classified according to their third grade test scores) and byethnicity.

Table 7Baseline estimates of the effect of charter attendance on TLI math and reading score growth

862 K. Booker et al. / Journal of Public Economics 91 (2007) 849876Table 8 presents results from a specification which differs from the baseline by includingseparate public-to-charter and charter-to-public mover indicators for students who attend a charterfor one, two, and three or more years. These indicators are on only in the year the student moves.

Math Reading

Commonmobility effects

Disaggregated chartermobility effects

Commonmobility effects

Disaggregated chartermobility effects

New charter 3.27 .097 2.12 1.11(11.59) (0.25) (6.85) (2.48)

2nd year charter 1.05 1.11 1.71 .450(4.61) (3.87) (6.49) (1.37)

3rd year charter .759 1.05 .0011 1.82(3.28) (3.80) (0.00) (5.77)

4th year charter .553 .993 .327 1.22(2.09) (3.45) (1.05) (3.60)

5th year charter 1.43 .295 1.68 .570(3.22) (0.65) (3.16) (1.07)

6th year charter 1.52 2.39 1.85 2.73(1.91) (2.97) (1.95) (2.89)

District mover .317 .328 .415 .423(15.70) (16.17) (16.90) (17.10)

Campus mover .652 .650 .739 .737(32.42) (32.32) (29.95) (29.88)

Structural mover 1.21 1.21 1.32 1.32(118.42) (118.38) (99.88) (99.85)

Moved to charter fromtrad. public

2.68 2.88(10.59) (9.77)

Moved to trad. public from charter 3.08 2.62(12.69) (9.55)

Moved from one charter to another .196 .506(0.20) (0.50)

Student is in specialeducation

.365 .364 .301 .300(8.21) (8.18) (5.62) (5.60)

Campus % African-American

.00939 .009 .0053 .005(10.33) (10.18) (4.91) (4.78)

Campus % Hispanic .0229 .023 .0091 .009(23.98) (23.95) (7.88) (7.84)

Campus % Asian .015 .016 .0229 .023(6.41) (6.52) (7.78) (7.88)

Campus % NativeAmerican

.0178 .018 .0265 .026(1.21) (1.21) (1.44) (1.43)

Campus %Disadvantaged

.0277 .028 .0158 .016(36.95) (36.85) (17.44) (17.37)

Campus % Specialeducation

.0421 .042 .0091 .009(24.88) (24.99) (4.39) (4.48)

Campus % Lmtd. Eng.Prof.

.0276 .028 .0130 .013(35.79) (35.85) (13.52) (13.56)

Number of obs. 4,687,981 4,687,981 4,614,464 4,614,464Number of students 1,411,711 1,411,711 1,395,361 1,395,361F-statistic 4282.63 3977.80 4048.59 3756.99

Absolute value of HuberWhite adjusted t-statistics in parentheses.

Table 8Effect of movement to a charter and from a charter disaggregated by years the student spends in the charter school

Math Reading

New charter .518 1.32(1.31) (2.89)

2nd through 6th year charters .848 1.07(3.67) (4.01)

District mover .323 .423(16.19) (17.09)

Campus mover .650 .736(32.33) (29.86)

Structural mover 1.21 1.32(118.43) (99.82)

Moved to charter (& remained 1 year) 3.31 3.87

863K. Booker et al. / Journal of Public Economics 91 (2007) 849876By disaggregating the mover indicators by years of charter attendance we can examine whetherstudents who exit after spending 1 year in a charter school display especially poor performance inthat year and whether it is these students who account for the large observed mover effects forcharter entry and exit. We find limited evidence that the effect of movement to a charter is lessnegative for students who remain in the charter for 2 years and for three or more years ascompared with students who spend only 1 year in a charter. The difference in the estimated effectsis small and not statistically significant in math, but larger and statistically significant in reading.We interpret this pattern of coefficient estimates as indicating that students who experiencerelatively poor performance in their first charter year are somewhat less likely to continue in thecharter. In the baseline specification (Table 7) the coefficient estimate on the movement indicatoris thus driven in part by those students who immediately return to a traditional public school.However, the transition effect of movement to a charter remains very significantly negative for allgroups of students, including those who will remain in the charter at least 3 years. A greaterdifference is observed in the effect of movement from a charter to a traditional public schoolthe

(7.92) (8.07)Moved to charter (& remained 2 years) 2.05 2.36

(5.53) (5.55)Moved to charter (& remained at least 3 years) 2.84 2.84

(8.83) (7.50)Moved from charter after 1 year 2.94 2.81

(9.94) (8.35)Moved from charter after 2 years 3.56 2.30

(7.46) (4.26)Moved from charter after at least 3 years .563 .886

(0.62) (.91)Number of obs. 4,687,072 4,613,588Number of students 1,411,584 1,395,231F-statistic 3977.83 3755.84

Absolute value of HuberWhite adjusted t-statistics in parentheses.This table reports results from regressions very close to the specifications in Table 7, except that the indicators formovement to a charter from a traditional public school and movement to a traditional public school from a charter aredisaggregated into three separate indicators based on the number of years the student appears in a charter school in the data.We drop observations of students who move to a charter and are observed there for 1 or 2 years but then are no longerobserved in the data. We are unable to determine whether these students in fact remained in a charter for additional years orreturned to a traditional public school. Control variables for campus demographics and mobility within the traditionalpublic school sector are included just as in the baseline model, but are not reported.

exit year effect. In both reading and math the estimated effect declines markedly from 2.94 inmath and 2.81 in reading (both significantly positive) for students who exit after just 1 year in acharter to .563 in math and .886 in reading (neither significant) for students who exit after three ormore years in a charter. We've seen that students who remain in a charter for multiple yearsrecover from a poor first year in subsequent years. The results here indicate that if this recovery

864 K. Booker et al. / Journal of Public Economics 91 (2007) 849876has occurred in a charter then the positive charter exit phenomenon largely disappears.23

To gain a fuller understanding of the roles played by student tenure in a charter and the length oftime of charter school operation we utilize a specification that includes a set of indicatorsrepresenting possible combinations of student and school tenure. We employ a four-by-four matrix:student's tenure and school tenure are classified as 1 year, 2 years, 3 years, or at least 4 years.24

The results in Table 9 yield some important insights. First, they strengthen the conclusion thatthe student's first year or transition to a charter differs greatly from subsequent years, regardless ofthe vintage of the charter school. For schools of all ages, first year students see a significantnegative impact on test performance in math and reading.

Second, there is evidence from the math results in particular that first year students in newschools fare particularly poorly (the coefficient on this cell is significantly lower than for first yearstudents in schools of older vintage). This evidence is consistent with an improvement in thequality of charter schools as they mature. It suggests that the estimated improvement in averagevalue-added for older vintage charters reported in Table 7 is not completely driven by the studentvintage (in a charter) differences between new and older charters.

Third, these results allow us to learn more about the impact of continued charter attendance. Bydisaggregating students further by years of tenure we are better able to understand the post-firstyear recovery period. We find that the there is a generally positive effect of charter attendance inthe third year which is not markedly different than that for students in their second year. In otherwords, the positive effect of charter attendance after the transition year does not appear to bedriven solely by a second year rebound, it persists into the third year. Both math and reading showa negative but insignificant effect of the fourth year of charter attendance. What remains is toevaluate the effect of a charter attendance spell over several years to determine whether therecovery in later years offsets the initial decline. We address this in the following section.

6. Evaluation of charter attendance spells

A fundamental problem in attempting to estimate a single average effect of charter attendanceon student performance is that different approaches imply different relative weights on thetransition year and subsequent years. This is compounded by the transition path identified above:a strong negative effect of attending a charter in the first year and a recovery in the second andthird year of charter attendance. If one simply uses a panel of data such as ours to estimate a singlecharter school effect, without separate controls for the first year or mobility effect, then theestimated charter effect will be heavily weighted toward the impact of the first year transitionsimply because there are relatively more observations in this category in the data. (As noted

23 Another simple approach to determining to what degree our baseline estimates of charter attendance and mobilityeffects are impacted by students who spend only a year or two in the charter sector is to simply drop these students fromthe dataset. We report results using this approach in Table 5 of the Appendix available the journal's website. We find thatthe estimated effects of charter attendance do not differ substantially from the baseline treatment.24 We drop the small number of students who move from one charter to another charter, thus we have six empty cells inthe matrix (those representing student tenure in a charter greater than the tenure of the charter school they attend).

Table 9

865K. Booker et al. / Journal of Public Economics 91 (2007) 849876Matrix of effects of charter attendance by years of student tenure in charter and years of charter operation

Charter in1st year ofoperation

Charter in2nd year ofoperation

Charter in3rd year ofoperation

Charter in 4th orhigher year ofoperation

Math Student in 1st yearat charter

3.54 1.81 2.82 1.07(11.42) (5.41) (8.43) (2.67)

2,354,921 obs.709,817 students

Student in 2nd yearat charter

.349 1.22 .680(1.01) (2.78) (1.79)

F=1910.60 Student in 3rd yearat charter

.855 .693(1.83) (1.55)

Student in 4th or higheryear at charter

.108(.20)

Reading Student in 1st yearat charter

2.37 2.51 1.90 1.61(6.93) (6.48) (4.68) (3.45)

2,317,659 obs.701,505 studentsF=1786.05

Student in 2nd yearat charter

.270 1.66 .564(.68) (3.39) (1.22)

Student in 3rd yearat charter

1.70 .886(3.24) (1.66)earlier, first year observations account for 48% observations of students in charter schools in ourdataset, and these observations are given commensurate weight in estimating the effect of charterattendance.) This approach corresponds to the first and third columns of results in Table 7. On theother hand, if one includes an indicator to capture the first-year transition effect, as we do in thesecond and fourth columns of Table 7, then second-year observations similarly dominate theestimate of the effect of charter attendance on students beyond the first year, accounting for 67%of observations of students beyond the first year of charter attendance in our sample.

In order to lookmore carefully at the overall effect of enrolling in a charter, we identify the set ofpossible enrollment paths followed by students in our dataset who attend charters. Because we areattempting to better understand the overall impact of charter attendance including the transitioneffect of moving to a charter school, we restrict our sample to students that we first observe in apublic school. Thus any student who is enrolled in a charter school when they first appear in ourdata set is not included in our sample. After this first year in a public school, we have at most foursubsequent observations on a student. Thus a student who appears in our sample might appear in apublic school for 1, 2, 3, or 4 years and then move to a charter school for the last year of oursample.25 We call the indicator for this path Students who attend charter only last year in sample.

Student in 4th or higheryear at charter

.395(.63)

Absolute value of HuberWhite adjusted t-statistics in parentheses.This table indicates regression results from a specification which differs from the baseline insofar as indicators for charterattendance and movement to a charter have been replaced by indicators for charter attendance corresponding to each cell ofthe matrix based on a student's tenure in the charter he attends and the age of the charter school. We do not include studentswho move from one charter to another (a very small number) and this gives rise to the empty cells in the matrix. Controlvariables for campus demographics and mobility within the traditional public school sector are included just as in thebaseline model, but are not reported. Due to computational limitations we randomly sample 50% of the students who neverattend a charter school (all students who are ever observed in a charter are retained). The regressions are weighted toaccount for sampling probabilities.

25 In this category we also included students who reached eighth grade prior to the end of our sample period, since theywould then exit our sample.

Another path is for a student in our sample to appear in a public school for 1, 2, or 3 years beforemoving to a charter for the last 2 years of our sample. We call the indicator for this path Studentswho attend charter only last 2 years in sample.We also have indicators for Students who attendcharter last 3 years in sample, and Students who attend charter last 4 years in sample.

We also look at students who begin in a public school, move to a charter, and thenmove back to apublic school before the end of our sample. We have three specific paths to consider. First, a student

866 K. Booker et al. / Journal of Public Economics 91 (2007) 849876may attend a charter school exactly 1 year and then return to a public school by the end of our sample.This student spends the first year and perhaps more in public schools at the beginning of herappearance in our sample, 1 year in a charter, and at least one but perhaps more years in a publicschool at the end of our sample.We call this indicator Students who attend a charter exactly one yearthen return to traditional public school. Second, we have students who attend a charter school fortwo consecutive years but then return to a traditional public school before the end of our sample. Wecall this indicator Students who attend charter exactly two years then return to traditional publicschool. Finally, we have students who attend a charter school for three consecutive years but thenreturn to a traditional public school before the end of our sample. We call this indicator Studentswho attend charter exactly three years then return to traditional public school.

We exclude any student for which we had a missing year of observation prior to the end of theirinclusion in our sample, because it would be unclear whether they attended a charter or traditionalpublic in that missing year. In the end our observation of students through five grades with theconstraint that at least 1 year must be spent in a traditional public school prior to charterattendance yields seven possible paths involving attendance of charter at some point: those whospend exactly 1 year, exactly 2 years, or exactly 3 years in a charter and then return to a traditionalpublic school, and those who spend the final 1, 2, 3, or 4 years in a charter.

Having identified these paths we employ them to study the effect of charter attendance in twodifferent ways. First, we generate a single indicator for each path. For the paths identifyingstudents who moved to a charter and stayed there for the remainder of the sample (whether that is1, 2, 3, or 4 years) the applicable path indicator is on in each year of charter attendance. For thepaths identifying students who moved to a charter but later returned to a traditional public school(whether after 1, 2, or 3 years of charter attendance) the applicable indicator is on in the years ofcharter attendance and in the year in which the student returns to the traditional public sector. Thecoefficients on these indicators therefore capture the effect of a charter attendance spellaveraged over all the years of charter attendance and, where applicable, the year of return to atraditional public school. Because attending a charter is characterized by an initial test scoredecline followed by subsequent movement toward recovery (either as the student continues in thecharter or returns to a traditional public school), we seek to identify the overall effect, i.e. whetherthe recovery more than offsets the initial decline.

The first group of paths, those for students who move to a charter and remain there through theend of our sample, allows us to see how the estimated average effect of charter attendance changesas the duration of charter attendance increases.26 Our previous results have strongly indicated that

26 Focusing on students who remain in a charter through the end of the sample period avoids using the year of return to atraditional public school (the exit year) as part of the control set of observations of the student in a traditional publicschool. As noted, students tend to experience above-trend score growth in the exit year, so including those years in thecontrol set renders the apparent performance of the years in a charter relatively worse. However, obviously one cannotmake such a move without attending a charter first. Because we want to estimate the entire effect of charter attendance

including the negative effect of the initial transition to a charter, it is more appropriate to use only years prior to astudent's attending a charter as the control group.

the longer a student remains in a charter the more positive the overall effect will be as the studentrecovers from the transition year, and our results reported in Table 10 generally support to thatfinding. Table 10 shows that a single year of charter attendance has a negative impact on studentperformance in both reading and math. This corresponds to the negative initial effect observed inTable 7. Two years of charter attendance has an essentially neutral impact on student mathperformance and a positive impact on student reading performance that is significant at the 90%confidence level, and a similar result is found for students who attend a charter for the final 3 yearsin the sample. Finally, students who attended a charter for the last 4 years of the sample areestimated to have experienced a negative but statistically insignificant impact on performance.(There are only 126 students who follow this path.)

Because these coefficients are on for the entire period that a student is in a charter school,they represent per-year average effects over the total span of charter attendance. Since theseestimates are based on students who remain in a charter through the end of our sample, theeffect of charter attendance is estimated using only years prior to charter attendance forcomparison. It should be noted that, while the inclusion of student fixed-effects controls forselection of students into charters by estimating the impact of charter attendance from therelative performance of students in charters versus their own performance prior to entering acharter, when estimating the impact of multiple years in a charter the sample is self-selecting.Those students who remain in a charter for two or more years are likely to be those for whom acharter school was a good fit. Put differently, the estimates provide some evidence that those

Table 10Aggregated effects of charter attendance paths

Path Number of students Math Reading

867K. Booker et al. / Journal of Public Economics 91 (2007) 849876observed in category

Students who attend charter only last year in sample 3223 .847 .686(3.04) (2.03)

Students who attend charter only last 2 years in sample 1443 .237 .701(.74) (1.87)

Students who attend charter only last 3 years in sample 703 .499 .830(1.08) (1.62)

Students who attend charter only last 4 years in sample 126 .809 1.16(0.79) (1.14)

Students who attend charter exactly 1 year then return totraditional public school

1594 .746 .569(2.23) (1.53)

Students who attend charter exactly 2 years then return totraditional public school

350 .481 .250(.82) (0.34)

Students who attend charter exactly 3 years then return totraditional public school

18 8.10 .352(3.20) (.16)

Number of observations 2,346,030 2,309,013Number of students 705,452 697,207F-statistic 2098.11 1963.56

Absolute value of HuberWhite adjusted t-statistics in parentheses.This table indicates regression results from a specification which differs from the baseline insofar as indicators for charterattendance and movement to a charter have been replaced by indicators for a student's being part of each of the identifiedpaths. These indicators are on in the years of charter attendance and, for the groups who return to a traditional publicschool, in the year of that return. Control variables for campus demographics and mobility within the traditional publicschool sector are included just as in the baseline model, but are not reported. Due to computational limitations we randomly

sample 50% of the students who never attend a charter school (all students who are ever observed in a charter are retained).The regressions are weighted to account for sampling probabilities.

Table 11Disaggregated effects of charter attendance paths

Students observed incategory

Year ofsequence

Math Reading

Students who attend charter only last year in sample 3223 1 .866 .711(3.10) (2.10)

Students who attend charter only last 2 years in sample 1443 1 .611 .274(1.56) (.59)

2 .093 1.61(.26) (3.83)

Students who attend charter only last 3 years in sample 703 1 .944 .501(1.59) (.75)

2 1.15 1.53(2.09) (2.49)

3 1.11 1.30(2.16) (2.26)

Students who attend charter only last 4 years in sample 126 1 3.41 3.31(2.53) (2.33)

2 .110 1.31(.10) (.98)

3 .684 .176(.59) (.14)

4 .341 .728(.29) (.62)

Students who attend charter exactly 1 year then return totraditional public school

1594 1 1.85 2.37(4.16) (4.72)

2 2.97 3.16(7.16) (6.95)

3 1.14 1.50(2.19) (2.47)

4 .265 .714(.20) (.41)

Students who attend charter exactly 2 years then return totraditional public school

350 1 2.57 1.59(3.08) (1.57)

2 .0839 .821(.10) (.79)

3 3.06 1.39(4.25) (1.51)

4 .599 1.27(.50) (.77)

Students who attend charter exactly 3 years then return totraditional public school

18 1 9.57 2.94(2.44) (.87)

2 8.08 1.19(2.80) (.34)

3 5.65 2.17(2.00) (.63)

4 8.54 .0883(2.80) (.04)

Number of observations 2,346,030 2,309,013Number of students 705,452 697,207F-statistic 1518.69 1422.06

868 K. Booker et al. / Journal of Public Economics 91 (2007) 849876

students who choose to remain in charters for multiple years often benefit from this learningenvironment, but the results do not necessarily indicate that all students would benefit fromsuch an experience.

The remaining three paths all involve students who move to a charter and then return to atraditional public school. These yield evidence on the effect of experimenting with a charterschool for a short time. Our earlier results indicate that most students perform poorly in thefirst year of charter attendance but experience a recovery if they return to a traditional public

869K. Booker et al. / Journal of Public Economics 91 (2007) 849876school. This specification enables us to see how quickly students recover upon returning to atraditional public school. The results reported in Table 10 indicate that students are notadversely affected by experimenting with a charter school for a year, despite the typically poorperformance in the first year of charter attendance. The coefficient estimates for the pathsinvolving a 1 or 2 years experiment with a charter are positive (although only the result inmath for students returning after a one-year charter experiment is significant at standardconfidence levels), indicating that the recovery in the year of return to a traditional publicschool offsets the decline in the first year of charter attendance. (Again, these path indicatorsare on in both the years of charter attendance and the year of return to a traditional publicschool). For the very few (18) students we observe following the path of moving to a charter infifth grade, remaining there through seventh grade, then returning to a traditional public schoolin eighth grade (and thus spending 3 years in a charter before returning), we obtain a highlynegative estimate of the effect on math performance, 8.10. This appears to be driven largelyby the fact that these students on average performed extremely well in the single reference testyear in grade four (averaging a 6.56 point gain).

It is not clear what explains the phenomenon of students showing some benefit fromexperimenting with a charter school for 1 year despite performing poorly in the year of charterattendance, but we suggest two hypotheses. First, moves to a charter school are by their natureTiebout-type moves of choice rather than necessity. Although the charter school may berevealed to be a poor match, the act of experimenting with a charter may be indicative of achange in a family's attitude, emphasis, or attention to a student's learning. Therefore althoughthe charter school may not serve the student well, resulting in poor performance in the year ofcharter attendance, this may be more than offset by increased family resources dedicated to thestudent's learning which yield improvement when the student returns to a traditional publicschool. Alternatively, the apparently poor performance of students in their first year of charterattendance may be a consequence not of a poor match or difficulty transitioning to a differentlearning environment, but rather of charter schools preparing students less effectively for theTAAS tests, communicating less emphasis on these tests to students, or in some other wayaffecting student testing performance in a manner that is not indicative of underlyingachievement. In other words, it may be that attending a charter has a negative level effect ontesting performance which is consistent over time, while having a positive effect on

Notes to Table 11:Absolute value of HuberWhite adjusted t-statistics in parentheses.This table indicates regression results from a specification which differs from the baseline insofar as indicators for charterattendance and movement to a charter have been replaced by indicators for a student's being in a given year of theidentified path. Control variables for campus demographics and mobility within the traditional public school sector areincluded just as in the baseline model, but are not reported. Due to computational limitations we randomly sample 50% of

the students who never attend a charter school (all students who are ever observed in a charter are retained). Theregressions are weighted to account for sampling probabilities.

achievement growth over time. If this hypothesis were correct, the positive charter-to-publicmover effect observed in earlier specifications and the overall positive effect of a one-yearexperiment in a charter discussed here could be a result of improvements in true learningresulting from charter attendance which are only fully captured by the TAAS test after thestudent returns to a traditional public school. Further exploration of this phenomenon is beyondthe scope of this paper.

The second specification we employ utilizing the charter attendance paths we've identifiedincludes separate indicators for each year within each path, beginning with the first year of charterattendance. For students who attend a charter only the last year in the sample we thus simply haveone indicator that is on in this single year. For students who attend a charter only the last 2 years inthe sample we have two separate indicators for each of these 2 years, each of which is on only in asingle year. We similarly construct a set of three indicators for students who attend a charter onlythe last 3 years in the sample and a set of four indicators for those attending the last 4 years in thesample. For students who experiment with a charter but return to a traditional public school wehave separate groups of indicators for each of the three possible paths corresponding to the numberof years the student attends a charter. Within each of these groups we have a separate indicator foreach year within the path, beginning with the first year of charter attendance. For students whoattend a charter only 1 year the second year of the sequence is obviously the year of return to atraditional public school, and the third and fourth years of the sequence are also subsequently spentthere. For students who attend a charter 2 years the third year of the sequence is the return year, andso on. Note that many students in these paths were not observed beyond the year of return to atraditional public school, so the estimates on these later years of the sequences reflect someattrition.

Table 11 reports the estimates based on this model. Compared to Table 10 this specificationdisaggregates each possible path involving charter attendance into the component years of eachpath. Rather than estimating an overall effect of the charter attendance paths, this specificationestimates the effect of each year within each path relative to the comparison year(s) prior toattending a charter. As is quite familiar by now, year one of each sequence (the first year ofcharter attendance) is significantly negative, but the magnitude is generally greater for those whowill later return to a traditional public school than for those who remain in a charter through theend of the sample (the exception is students who attend a charter the last 4 years in the sample).For the most part students who are never observed returning to a traditional public school havepositive effects from charter attendance subsequent to the first year (although several of theestimates for those who attend a charter the last 4 years in the sample are negative but notsignificant). We see again the strong positive estimate associated with the year of return to atraditional public school in year 2 of the path of students who spend 1 year in a charter and inyear 3 of the path of students who spend 2 years in a charter. Subsequent years after the return donot exhibit a significantly positive effect except for year three of the 1 year charter experimentpath.

7. Conclusion

Broadly, we can summarize our results as follows: 1) Students perform poorly in their first yearin charter schools. This is true regardless of whether the charter school itself is new or has beenoperating for 2 years or three or more years, although the effect appears more pronounced in math

870 K. Booker et al. / Journal of Public Economics 91 (2007) 849876for new charter schools. The magnitude of this effect is much greater than that of movementbetween traditional public schools. 2) Students who remain in charter schools beyond the first

year recover with a positive effect of charter attendance on performance in subsequent years.3) The overall impact of charter attendance (including the initial drop and subsequent recovery)generally improves with the length of time students attend a charter. After 3 years of attendancestudents appear to have recovered from the initial drop. 4) Students who move back to traditionalpublic schools also appear to recover from their performance drop in the first year of charterattendance. They do not experience a lasting setback.

Our study is related to the work of Hanushek, Kain, Rivkin, and Branch (2005) who alsoexamine the performance of charter schools in Texas. Their study does not distinguish theimpact of movement to a charter school from interdistrict moves among traditional publicschools or otherwise account for differences in student performance by the students' tenure in acharter. Rather, they focus on differences in performance among students depending on thenumber of years charter schools had been operating, and concluded that, after the initial start-upperiod, the performance of charters is not significantly different from that of traditional publicschools. We have argued that the poor performance of new charter schools in their study (andthe mediocre performance of established charters) results from the absence of controls for thecharter-specific mobility effect or student tenure in a charter. Hanushek et al. also generateseparate estimates of the effect of charter attendance based on whether the students' comparisonyears in a traditional public school occurred prior to entering a charter (charter entrants) or afterleaving (charter exits). They find that estimates based on entrants are significantly morepositive than those based on exits. They argue this fits with the notion that those who exitcharters have had a worse experience in a charter than the typical charter student. The result isalso consistent with our finding of a positive effect of movement from a charter to a traditionalpublic school.

Sass (2005) and Bifulco and Ladd (2005) study Florida and North Carolina charters,respectively, employing a value-added model and student fixed-effects to control for selection.These studies identify separate effects for charters of varying years of operation, but do notidentify separate estimates of student performance in the year of charter entry or otherwisecontrol the time-path of charter students. Both of these studies find that charter performanceimproves with age. Sass finds that new charters perform less well than traditional public schools,but charters that have operated for 4 years or more perform comparably. Bifulco and Ladd find anegative effect for charters of all ages, but the magnitude decreases with age. Our results suggestthat, if the performance pattern we find in Texas occurs in charter schools elsewhere, theseresults may be heavily influenced by a decline in performance in the year of transition to acharter school which is given great weight in the estimates simply by the composition of thedata.

Eberts and Hollenbeck (2002) find evidence that students in charter schools in Michiganperformed less well than students in traditional public schools in the same districts. However,their study suffers from data limitations. The Michigan students were tested in reading and mathin fourth grade, and writing and science in fifth grade. A true value-added methodology cannot beemployed (although the authors utilized the fourth grade scores as controls for ability level whenanalyzing fifth grade performance), and the lack of longitudinal data prevents the use of studentfixed-effects. The authors attempt to control for student ability at different schools principally bymeans of campus aggregate demographic data. These methods are unlikely to control adequatelyfor selection into charter schools.

Salmon, Paark, and Garcia (2001) study Arizona charter schools. Like our study, they

871K. Booker et al. / Journal of Public Economics 91 (2007) 849876estimate disaggregated charter effects based on the number of years the student attended a charter,rather than the number of years the charter has operated. They employed a sample of 3 years of

data from the Stanford Achievement Tests admini arly to students in Arirly short time-series. Ut ividual student fixed-effilar to what we have e , they report remarkably

rter schools were found ely affect student perform

is in data from this new and rapidly growing sector. By separately estimating the overall effect of

872 K. Booker et al. / Journal of Public Econ 2007) 849876charter attendance on students who remain in a charter for varying lengths of time we have foundevidence that those students who remain in charters for multiple years appear to largely recoverfrom the first year decline, and the estimates indicate they may experience net improvement.Furthermore, briefly experimenting with a charter school then returning to a traditional publicschool does not appear to result in a persistent negative impact. Although students perform poorlyin their first (and perhaps only) year of charter attendance, they appear to recover these losses inthe year of return to a traditional public school.

The existing literature evaluating the performance of the charter sector has in a senseemphasized charter schools as the focus of analysis rather than students in the charter sector. Thepapers cited above all address how the performance of charter schools improves as they progressfrom their inception, but don't account for patterns in student performance as students transitioninto the charter sector and proceed there or exit to return to the traditional public school sector.Similarly, Hanushek et al. (2005) evaluate the responsiveness of student decisions to exit a charterschool to school quality rather than to individual student performance (i.e. whether the studentherself is performing well in the school). There is no question that factors associated withindividual schools, including their age and potential start-up and growth problems, are important.But we should also expect that some students will find a charter a good fit for their educationalneeds, while others do not, independently of whether the charter school is a good school overall.We should also allow for the possibility that, just as charter schools may experience start-updifficulties, poor student performance the first year in a charter school may be an anomaly, whetherdue to difficulties transitioning to the new school or other factors.While disentangling these effectsis not a trivial task, failure to account for them may yield misleading conclusions regarding theoverall impact of charter school attendance on the achievement path of charter school students.

Appendix A

Table 1Baseline estimates (see Table 7 in text) of the effect of charter attendance on TLI math and reading score growth(aggregating 2nd6th year charter effects)

Math Reading

New charter .180 1.24(0.48) (2.88)

2nd through 6th year .984 1.06(4.55) (4.26)

District mover .328 .423both reading and math in the second and third consecutive years of attendance, but the effect inthe first year of charter attendance was negative for reading and not significantly different fromzero in math.

By taking care to control for the effect of a student's years of attendance of a charter we haveshown that the pattern of first year decline followed by recovery can yield misleadingly poorestimates of charter performance when great weight is placed on the transition year, as it naturallyto positiv(16.17)ance in

value-added methodology simresults in the respect that chamployed similar

ilizing ind ects andlongitudinal dataset with a fa

stered ye izona, aomics 91 ((17.09)

Number of students

sted t-statistics in parentheses

ndance on TLI math score gro ent quartile in third grade

1st Quartile 2n 3rd Quartile 4

.830 .0 .865 1(0.82) (0 (1.09) (22.44 1. 1.42 1(4.23) (3 (3.17) (4 .562 .378 (9.17) (8 (10.29) (91.06 .619 (17.76) (1 (16.69) (12.30 1.02 (63.55) (6 (55.63) (53.64 2.09 (5.36) (6 (4.01) (54.07 4. 3.05 2(6.83) (7 (6.11) (51.94 5.34 (0.89) (1 (2.67) (0Number of obs. 771,115 92

.55)

0,463 917,250 1

(continued on n.36)

Moved from one charter to another.80)2.91.86).870Moved to trad. public from charter 35 .80

.12) .88)Moved to charter from trad. public 3.81 2.25

3.91) 0.46)Structural mover 1.55 .602

9.43) 9.56)Campus mover .879 .501

.93) .38)District mover .396 .250

.68) .16)2nd through 6th year charters 94 .35

.08) .01)New charter 73 .16d Quartile th Quartilewth by stud

Table 2Estimates of the effect of charter atteAbsolute value of HuberWhite adju .F-statistic 4407.63 4162.26

1,411,711 1,395,361Number of obs. 4,687,981 4,614,464

(35.86) (13.66)Campus % Lmtd. Eng. Prof. .0276 .0130

(24.98) (4.45)Campus % Special education .0423 .00923

(36.86) (17.41)Campus % Disadvantaged .0276 .0157(23.96) (7.91)Campus % Asian .0158 .0233

(6.57) (7.92)Campus % Native American .0178 .0264

(1.22) (1.43)Campus % Hispanic

(10.18) .0229(4.80) .0092Campus % African-American .0092 .0052

(8.18) (5.60)Student is in special education .364 .300

(0.29) (0.53)Moved from one charter to another .277 .533

(12.71) (9.70)Moved to trad. public from charter 3.08 2.66

(10.67) (10.17)Moved to charter from trad. public 2.62 2.92

(118.39) (99.83)Structural mover 1.21 1.32

(32.33) (29.87)Campus mover .650 .737Math ReadingTable 1 (continued )873K. Booker et al. / Journal of Public Economics 91 (2007) 849876,197,447

ext page )

1st Quartile 2n 3rd Quartile 4

228,706 24 236,299 32352.27 14 1059.31 4

sted t-statistics in parentheses.This table reports results from a series of regressions identical to tho n Appendix Table 1 except tha

hose third grade math TLI sco year we observe them) places tber of observations differs subs ross quartiles due to greater attr

sted t- renthesThis table reports results from a series of reg ical to t n Appe xcept t

ose thi ng TLI year w ) placeber of o iffers su ross qua reater a

874 K. Booker et al. / Journal of Public Econ 2007) 849876Others in new charter

(2.62) .745

(1.33)(2.41).600Hispanic in continuing charter .766 .820Hispanic in new charter 1.24(2.65)2.69(4.80)(5.70) (5.59)the sample among students in lower quartiles. Control variables for campus demographics and mobility within thetraditional public school sector are included just as in the baseline model, but are not reported.

Table 4Effects of charter attendance on African-American and Hispanic popul