Dlauen.web.unc.edu
Exposure to Classroom Poverty and Test Score Achievement:Contextual Effects or Selection?Douglas Lee LauenAssistant ProfessorDepartment of Public PolicyUniversity of North Carolina at Chapel HillS. Michael GaddisDepartment of SociologyUniversity of North Carolina at Chapel HillKeywords: poverty, contextual effects, academic achievement, growth model, fixed effects, marginal structural modelCorresponding Author:Douglas Lee LauenDepartment of Public PolicyUniversity of North Carolina at Chapel HillAbernethy Hall, CB #3435Chapel Hill, NC 27599-3435919-843-5010dlauen@unc.eduAcknowledgements: The authors gratefully acknowledge the support of the Spencer Foundation and the North Carolina Education Research Data Center for providing the data. We thank Kyle Crowder, Patrick Curran, Mike Foster, Eric Grodsky, Ashu Handa, Roz Mickelson, Mike Shanahan, Chris Wiesen, and especially Stephen R. Cole for their assistance and many useful comments. AbstractSocial scientists and policymakers generally share the widely held belief that impoverished contexts have harmful effects on children. Disentangling the influence of the effects of individual and family background from the effects of context, however, is conceptually and methodologically complex, making causal claims about contextual effects suspect. This study examines the effect of exposure to classroom poverty on student math and reading test achievement using data on a complete cohort of North Carolina children who entered third grade in 2001 and were followed up through grade eight. Using cross-sectional methods, we observe a substantial negative association between exposure to high poverty classrooms and math test scores that grows with grade level and becomes especially large for middle school students. Evidence from growth models, however, produces much smaller effects of classroom poverty exposure on math and reading test score achievement. Even smaller effects emerge from student fixed effects models, which control for time-invariant unobservables, and marginal structural models, which properly adjust for observable time-dependent confounding. These findings suggest that causal claims about the effects of classroom poverty exposure on cognitive achievement may be unwarranted. Scholars have spent decades researching and debating the influence of school and neighborhood context on academic achievement, aspirations and attitudes PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5GZWxtbGVlPC9BdXRob3I+PFllYXI+MTk4MzwvWWVhcj48
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ADDIN EN.CITE.DATA (Crane 1991; Harding 2003; South, Baumer and Lutz 2003). For example, Coleman and colleagues, in their seminal Equality of Educational Opportunity report, argued that peer effects were strong predictors of academic achievement: “the social composition of the student body is more highly related to achievement, independent of the student’s own social background, than is any other school factor” ADDIN EN.CITE <EndNote><Cite><Author>Coleman</Author><Year>1966</Year><RecNum>12</RecNum><Suffix>: 325</Suffix><DisplayText>(Coleman et al. 1966: 325)</DisplayText><record><rec-number>12</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">12</key></foreign-keys><ref-type name="Report">27</ref-type><contributors><authors><author>Coleman, James S.</author><author>Campbell, Ernest Q.</author><author>Hobson, Carol J.</author><author>McPartland, James</author><author>Mood, Alexander J.</author><author>Weinfeld, Frederic D.</author><author>York, Robert L.</author></authors></contributors><titles><title>Equality of Educational Opportunity</title></titles><dates><year>1966</year></dates><pub-location>Washington</pub-location><publisher>USGPO</publisher><urls></urls></record></Cite></EndNote>(Coleman et al. 1966: 325). Social science evidence on contextual effects has informed social science theory and educational policy in the United States, which for the past four decades has sought to mix students by racial background and, more recently, by poverty status PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5CYXplbG9uPC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE.DATA (Bazelon 2008; Grant 2009; Kahlenberg 2001). The relevance of contextual effects research is demonstrated by the prominent role such research played in the recent social science statement submitted as an amicus curiae brief in a 2007 school assignment Supreme Court case.The scholarly consensus on contextual effects, however, rests largely upon cross-sectional studies, which do not provide a strong basis for causal inference. Selection bias, perhaps the most important threat to the validity of point-in-time studies, can give rise to what Hauser ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Hauser</Author><Year>1970</Year><RecNum>16</RecNum><DisplayText>(1970)</DisplayText><record><rec-number>16</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">16</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hauser, Robert M.</author></authors></contributors><titles><title>Context and Consex - Cautionary Tale</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>645-&</pages><volume>75</volume><number>4</number><dates><year>1970</year></dates><isbn>0002-9602</isbn><accession-num>ISI:A1970G165400004</accession-num><reviewed-item>Keep</reviewed-item><urls><related-urls><url><Go to ISI>://A1970G165400004</url></related-urls></urls><research-notes>Times Cited: 158</research-notes></record></Cite></EndNote>(1970) termed the “contextual fallacy”: “…the contextual method rests on the arbitrary identification of residual group differences in the dependent variable with correlated aspects of group composition on an independent variable…The only way to eliminate such correlations is to assign individuals randomly to groups, and this is impossible with observational data” (p. 660). Recent work in sociology PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Dcm9zbm9lPC9BdXRob3I+PFllYXI+MjAwOTwvWWVhcj48
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ADDIN EN.CITE.DATA (Kling, Liebman and Katz 2007; Orr et al. 2003; Sanbonmatsu et al. 2006). Some of this recent work raises important questions about whether causal inferences about contextual effects are warranted ADDIN EN.CITE <EndNote><Cite><Author>Mouw</Author><Year>2006</Year><RecNum>23</RecNum><DisplayText>(Mouw 2006)</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">23</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Mouw, Ted</author></authors></contributors><titles><title>Estimating the causal effect of social capital: A review of recent research</title><secondary-title>Annual Review of Sociology</secondary-title></titles><periodical><full-title>Annual Review of Sociology</full-title></periodical><pages>79-102</pages><volume>32</volume><dates><year>2006</year></dates><isbn>0360-0572</isbn><accession-num>ISI:000240319100004</accession-num><urls><related-urls><url><Go to ISI>://000240319100004</url></related-urls></urls><electronic-resource-num>10.1146/annurev.soc.32.061604.123150</electronic-resource-num></record></Cite></EndNote>(Mouw 2006). Finally, very few longitudinal contextual effects studies account for time-dependent confounding. Time-dependent confounders, which predict both future treatment and future outcome, conditional on past treatment, present a challenge to estimating unbiased treatment effects. For example, in estimating the effect of poverty context on child outcomes, one may wish to control for intermediate outcomes such as educational experiences while in school (such as assignment to gifted and remedial programs or being retained in grade). If these intermediate outcomes then predict both future treatment and future outcome, standard methods – controlling for these factors, omitting them, or controlling for baseline values – can produce biased estimates ADDIN EN.CITE <EndNote><Cite><Author>Robins</Author><Year>2000</Year><RecNum>24</RecNum><DisplayText>(Hong and Raudenbush 2008; Robins, Hernan and Brumback 2000)</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robins, James M.</author><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author></authors></contributors><titles><title>Marginal Structural Models and Causal Inference in Epidemiology</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>550-560</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite><Cite><Author>Hong</Author><Year>2008</Year><RecNum>25</RecNum><record><rec-number>25</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">25</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hong, Guanglei</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Causal Inference for Time-Varying Instructional Treatments</title><secondary-title>Journal of Educational and Behavioral Statistics</secondary-title></titles><periodical><full-title>Journal of Educational and Behavioral Statistics</full-title></periodical><pages>333-362</pages><volume>33</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(Hong and Raudenbush 2008; Robins, Hernan and Brumback 2000). Methods for addressing treatment effect bias from time-dependent confounding have been developed in epidemiology by Robins and colleagues PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Sb2JpbnM8L0F1dGhvcj48WWVhcj4yMDAwPC9ZZWFyPjxS
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ADDIN EN.CITE.DATA (Cole and Hernán 2008; Hernan, Brumback and Robins 2000; Robins 1999; Robins, Hernan and Brumback 2000). Recent work using these methods has demonstrated negative effects of exposure to neighborhood concentrated disadvantage on verbal ability ADDIN EN.CITE <EndNote><Cite><Author>Sampson</Author><Year>2008</Year><RecNum>29</RecNum><DisplayText>(Sampson, Sharkey and Raudenbush 2008)</DisplayText><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sampson, Robert J.</author><author>Sharkey, Patrick</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Durable Effects of Concentrated Disadvantage on Verbal Ability among African-American Children</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title></periodical><pages>845-852</pages><volume>105</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(Sampson, Sharkey and Raudenbush 2008). This study uses longitudinal data to estimate the effect of exposure to a high poverty classroom on elementary and middle school students’ test scores. These data include interval metric and vertically equated mathematics and reading test scores and variation across time in classroom-level poverty from a complete cohort of public school children in grades three through eight in the state of North Carolina from 2001 to 2006 (N of more than 500,000 student-year observations). The study contributes to contextual effects research by carefully specifying and accounting for bias from omitted and mismeasured time-invariant student and family background characteristics. We report effects of classroom poverty based on three measures: attending a high poverty classroom (i.e., one in the top quartile of the classroom poverty distribution), cumulative exposure to a high poverty classroom, and continuous classroom poverty. We first present cross-sectional multilevel estimates of the association between classroom poverty and math test score. These estimates reproduce the negative effects reported in previous research with cross-sectional designs. The strength of the cross-sectional association increases with grade level. By eighth grade, these estimates are particularly large, which suggests that the cognitive disadvantage of classroom poverty exposure appears to accumulate over time. Growth models produce very small negative effects on two of the three measures (high poverty classroom and continuous classroom poverty) and larger negative effects on the other (cumulative exposure to a high poverty classroom). To address endogenous self-selection based on fixed unobservables, we present student fixed effects estimates, which remove between-student confounding ADDIN EN.CITE <EndNote><Cite><Author>Allison</Author><Year>2009</Year><RecNum>30</RecNum><DisplayText>(Allison 2009)</DisplayText><record><rec-number>30</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">30</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Allison, Paul D.</author></authors></contributors><titles><title>Fixed Effects Regression Models</title><secondary-title>Quantitative Applications in the Social Sciences</secondary-title></titles><dates><year>2009</year></dates><pub-location>Thousand Oaks, CA</pub-location><publisher>Sage</publisher><urls></urls></record></Cite></EndNote>(Allison 2009). This approach controls for time-invariant unmeasured and mismeasured aspects of student and family background that may predict both family choice of neighborhood and school and test score achievement. These models produce estimates distinguishable from zero, but of negligible size. We also estimate marginal structural models with inverse probability of treatment weighting to address time-dependent confounding ADDIN EN.CITE <EndNote><Cite><Author>Hong</Author><Year>2008</Year><RecNum>25</RecNum><DisplayText>(Hong and Raudenbush 2008; Robins, Hernan and Brumback 2000)</DisplayText><record><rec-number>25</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">25</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hong, Guanglei</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Causal Inference for Time-Varying Instructional Treatments</title><secondary-title>Journal of Educational and Behavioral Statistics</secondary-title></titles><periodical><full-title>Journal of Educational and Behavioral Statistics</full-title></periodical><pages>333-362</pages><volume>33</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite><Cite><Author>Robins</Author><Year>2000</Year><RecNum>24</RecNum><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robins, James M.</author><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author></authors></contributors><titles><title>Marginal Structural Models and Causal Inference in Epidemiology</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>550-560</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>(Hong and Raudenbush 2008; Robins, Hernan and Brumback 2000). 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ADDIN EN.CITE.DATA (Harris 2010; Jencks and Mayer 1990; Willms 2010). First, classroom poverty may have a negative effect on student achievement growth due to institutional mechanisms: low parental involvement in schooling, lower quality teachers, lower expectations and slower pacing, and less rigorous curriculum PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5CYXJyPC9BdXRob3I+PFllYXI+MTk4MzwvWWVhcj48UmVj
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ADDIN EN.CITE.DATA (Attewell 2001; Crosnoe 2009; Davis 1966). Fourth, classroom poverty may have no effect on student achievement growth once student background is properly controlled, which could point to a selection mechanism, i.e., that the apparent effect of context is due to the selection of families into schools and classrooms based on factors that are also correlated with test score growth and classroom poverty level ADDIN EN.CITE <EndNote><Cite><Author>Hauser</Author><Year>1970</Year><RecNum>16</RecNum><DisplayText>(Hauser 1970; Mouw 2006)</DisplayText><record><rec-number>16</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">16</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hauser, Robert M.</author></authors></contributors><titles><title>Context and Consex - Cautionary Tale</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>645-&</pages><volume>75</volume><number>4</number><dates><year>1970</year></dates><isbn>0002-9602</isbn><accession-num>ISI:A1970G165400004</accession-num><reviewed-item>Keep</reviewed-item><urls><related-urls><url><Go to ISI>://A1970G165400004</url></related-urls></urls><research-notes>Times Cited: 158</research-notes></record></Cite><Cite><Author>Mouw</Author><Year>2006</Year><RecNum>23</RecNum><record><rec-number>23</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">23</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Mouw, Ted</author></authors></contributors><titles><title>Estimating the causal effect of social capital: A review of recent research</title><secondary-title>Annual Review of Sociology</secondary-title></titles><periodical><full-title>Annual Review of Sociology</full-title></periodical><pages>79-102</pages><volume>32</volume><dates><year>2006</year></dates><isbn>0360-0572</isbn><accession-num>ISI:000240319100004</accession-num><urls><related-urls><url><Go to ISI>://000240319100004</url></related-urls></urls><electronic-resource-num>10.1146/annurev.soc.32.061604.123150</electronic-resource-num></record></Cite></EndNote>(Hauser 1970; Mouw 2006). In the next section, we summarize the cross-sectional contextual effects literature, organizing studies by the type of effects reported (i.e., positive effect of affluent context, negative effect of affluent context, no significant effect). We then discuss findings from alternative designs (longitudinal and experimental). To conclude our review we critique existing literature and outline the contributions of our study. Cross-Sectional EvidenceCross-sectional contextual effects research generally finds a positive association between socially desirable youth outcomes and average school and neighborhood socioeconomic status (SES). For example, studies find positive effects of school mean parental education on standardized test scores ADDIN EN.CITE <EndNote><Cite><Author>Entwisle</Author><Year>1994</Year><RecNum>7</RecNum><DisplayText>(Entwisle, Alexander and Olson 1994)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">7</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Entwisle, Doris R.</author><author>Alexander, Karl L.</author><author>Olson, Linda S.</author></authors></contributors><titles><title>The Gender Gap in Math: Its Possible Origins in Neighborhood Effects</title><secondary-title>American Sociological Review</secondary-title></titles><periodical><full-title>American Sociological Review</full-title></periodical><pages>822-838</pages><volume>59</volume><number>6</number><dates><year>1994</year></dates><publisher>American Sociological Association</publisher><isbn>00031224</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Entwisle, Alexander and Olson 1994) and 4-year college enrollment ADDIN EN.CITE <EndNote><Cite><Author>Choi</Author><Year>2008</Year><RecNum>39</RecNum><DisplayText>(Choi et al. 2008)</DisplayText><record><rec-number>39</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">39</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Choi, Kate H.</author><author>Raley, R. Kelly</author><author>Muller, Chandra</author><author>Riegle-Crumb, Catherine</author></authors></contributors><auth-address>[Choi, Kate H.] Univ Calif Los Angeles, Los Angeles, CA 90095 USA. [Raley, R. Kelly; Muller, Chandra; Riegle-Crumb, Catherine] Univ Texas Austin, Austin, TX 78712 USA.
Choi, KH, Univ Calif Los Angeles, 264 Haines Hall,375 Portola Plaza, Los Angeles, CA 90095 USA.
katechoi@ucla.edu</auth-address><titles><title>Class Composition: Socioeconomic Characteristics of Coursemates and College Enrollment</title><secondary-title>Social Science Quarterly</secondary-title><alt-title>Soc. Sci. Q.</alt-title></titles><periodical><full-title>Social Science Quarterly</full-title><abbr-1>Soc. Sci. Q.</abbr-1></periodical><alt-periodical><full-title>Social Science Quarterly</full-title><abbr-1>Soc. Sci. Q.</abbr-1></alt-periodical><pages>846-866</pages><volume>89</volume><number>4</number><keywords><keyword>HIGH-SCHOOL</keyword><keyword>ACADEMIC-ACHIEVEMENT</keyword><keyword>FAMILY-STRUCTURE</keyword><keyword>RACE</keyword><keyword>INEQUALITIES</keyword><keyword>SEGREGATION</keyword><keyword>STUDENTS</keyword></keywords><dates><year>2008</year><pub-dates><date>Dec</date></pub-dates></dates><isbn>0038-4941</isbn><accession-num>ISI:000260099000002</accession-num><urls><related-urls><url><Go to ISI>://000260099000002 </url></related-urls></urls><research-notes>Times Cited: 0</research-notes><language>English</language></record></Cite></EndNote>(Choi et al. 2008), positive effects of school mean SES on grades and attainment ADDIN EN.CITE <EndNote><Cite><Author>Willms</Author><Year>1986</Year><RecNum>8</RecNum><DisplayText>(Willms 1986)</DisplayText><record><rec-number>8</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">8</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Willms, J. Douglas</author></authors></contributors><titles><title>Social Class Segregation and Its Relationship to Pupils' Examination Results in Scotland</title><secondary-title>American Sociological Review</secondary-title></titles><periodical><full-title>American Sociological Review</full-title></periodical><pages>224-241</pages><volume>51</volume><number>2</number><dates><year>1986</year></dates><publisher>American Sociological Association</publisher><isbn>00031224</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Willms 1986), and negative effects of the school mean poverty rate on academic self-esteem, educational aspirations and expectations, and standardized test scores ADDIN EN.CITE <EndNote><Cite><Author>Battistich</Author><Year>1995</Year><RecNum>40</RecNum><DisplayText>(Battistich et al. 1995)</DisplayText><record><rec-number>40</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">40</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Battistich, Victor</author><author>Solomon, Daniel</author><author>Kim, Dong-il</author><author>Watson, Marilyn</author><author>Schaps, Eric</author></authors></contributors><titles><title>Schools as Communities, Poverty Levels of Student Populations, and Students Attitudes, Motives, and Performance - a Multilevel Analysis</title><secondary-title>American Educational Research Journal</secondary-title></titles><periodical><full-title>American Educational Research Journal</full-title></periodical><pages>627-658</pages><volume>32</volume><number>3</number><keywords><keyword>ACHIEVEMENT</keyword><keyword>CHILDREN</keyword><keyword>SENSE</keyword><keyword>SCALE</keyword></keywords><dates><year>1995</year><pub-dates><date>Fal</date></pub-dates></dates><isbn>0002-8312</isbn><accession-num>ISI:A1995RU48800008</accession-num><urls><related-urls><url><Go to ISI>://A1995RU48800008 </url></related-urls></urls></record></Cite></EndNote>(Battistich et al. 1995). Neighborhood effects research finds positive effects of high poverty neighborhoods on teenage pregnancy and high school drop-out rates PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IYXJkaW5nPC9BdXRob3I+PFllYXI+MjAwMzwvWWVhcj48
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ADDIN EN.CITE.DATA (Crane 1991; Harding 2003), negative effects of early childhood neighborhood poverty on educational attainment measured in adulthood ADDIN EN.CITE <EndNote><Cite><Author>Entwisle</Author><Year>2005</Year><RecNum>41</RecNum><DisplayText>(Entwisle, Alexander and Olson 2005)</DisplayText><record><rec-number>41</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">41</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Doris R. Entwisle</author><author>Karl L. Alexander</author><author>Linda S. Olson</author></authors></contributors><titles><title>First Grade and Educational Attainment by Age 22: A New Story</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>1458-1502</pages><volume>110</volume><number>5</number><dates><year>2005</year></dates><urls><related-urls><url> </url></related-urls></urls><electronic-resource-num>doi:10.1086/428444</electronic-resource-num></record></Cite></EndNote>(Entwisle, Alexander and Olson 2005), and negative effects of neighborhood deprivation on educational attainment in Scotland ADDIN EN.CITE <EndNote><Cite><Author>Garner</Author><Year>1991</Year><RecNum>42</RecNum><DisplayText>(Garner and Raudenbush 1991)</DisplayText><record><rec-number>42</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">42</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Garner, Catherine L.</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Neighborhood Effects on Educational Attainment: A Multilevel Analysis</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>251-262</pages><volume>64</volume><number>4</number><dates><year>1991</year></dates><publisher>American Sociological Association</publisher><isbn>00380407</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Garner and Raudenbush 1991). Similarly, low levels of neighborhood poverty have been associated with positive effects on educational attainment ADDIN EN.CITE <EndNote><Cite><Author>Duncan</Author><Year>1994</Year><RecNum>43</RecNum><DisplayText>(Duncan 1994)</DisplayText><record><rec-number>43</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">43</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Duncan, Greg J.</author></authors></contributors><titles><title>Families and Neighbors as Sources of Disadvantage in the Schooling Decisions of White and Black Adolescents</title><secondary-title>American Journal of Education</secondary-title></titles><periodical><full-title>American Journal of Education</full-title></periodical><pages>20-53</pages><volume>103</volume><number>1</number><dates><year>1994</year></dates><publisher>The University of Chicago Press</publisher><isbn>01956744</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Duncan 1994), positive effects on standardized test scores ADDIN EN.CITE <EndNote><Cite><Author>Entwisle</Author><Year>1994</Year><RecNum>7</RecNum><DisplayText>(Entwisle, Alexander and Olson 1994)</DisplayText><record><rec-number>7</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">7</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Entwisle, Doris R.</author><author>Alexander, Karl L.</author><author>Olson, Linda S.</author></authors></contributors><titles><title>The Gender Gap in Math: Its Possible Origins in Neighborhood Effects</title><secondary-title>American Sociological Review</secondary-title></titles><periodical><full-title>American Sociological Review</full-title></periodical><pages>822-838</pages><volume>59</volume><number>6</number><dates><year>1994</year></dates><publisher>American Sociological Association</publisher><isbn>00031224</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Entwisle, Alexander and Olson 1994), positive effects on IQ, and negative effects on high school dropout rates ADDIN EN.CITE <EndNote><Cite><Author>Brooks-Gunn</Author><Year>1993</Year><RecNum>6</RecNum><DisplayText>(Brooks-Gunn et al. 1993)</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">6</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brooks-Gunn, Jeanne</author><author>Duncan, Greg J.</author><author>Klebanov, Pamela Kato</author><author>Sealand, Naomi</author></authors></contributors><titles><title>Do Neighborhoods Influence Child and Adolescent Development?</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>353-395</pages><volume>99</volume><number>2</number><dates><year>1993</year></dates><publisher>The University of Chicago Press</publisher><isbn>00029602</isbn><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(Brooks-Gunn et al. 1993). Finally, there is some evidence of positive additive effects of both high SES neighborhoods and high SES schools on earning a bachelor's degree ADDIN EN.CITE <EndNote><Cite><Author>Owens</Author><Year>2010</Year><RecNum>44</RecNum><DisplayText>(Owens 2010)</DisplayText><record><rec-number>44</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">44</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Owens, Ann</author></authors></contributors><titles><title>Neighborhoods and Schools as Competing and Reinforcing Contexts for Educational Attainment</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>287-311</pages><volume>83</volume><number>4</number><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>(Owens 2010).There is also evidence to support the hypothesis that affluent peers and neighbors can have negative effects on youth outcomes. 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ADDIN EN.CITE.DATA (Attewell 2001; Bachman and O'Malley 1986; Crosnoe 2009; Davis 1966; Jencks and Mayer 1990; Marsh 1987; Marsh and Parker 1984). Though it may be advantageous to associate with affluent neighbors and peers, high achieving peers may harm aspirations, grades, curricular placement, and other academic outcomes, especially when students must compete for scarce resources. For example, Davis ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Davis</Author><Year>1966</Year><RecNum>37</RecNum><DisplayText>(1966)</DisplayText><record><rec-number>37</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">37</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Davis, James A.</author></authors></contributors><titles><title>Campus as a Frog Pond - Application of Theory of Relative Deprivation to Career Decisions of College Men</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>17-31</pages><volume>72</volume><number>1</number><dates><year>1966</year></dates><isbn>0002-9602</isbn><accession-num>ISI:A1966ZA47800002</accession-num><reviewed-item>Yes</reviewed-item><urls><related-urls><url><Go to ISI>://A1966ZA47800002</url></related-urls></urls><research-notes>Times Cited: 168</research-notes></record></Cite></EndNote>(1966) investigated whether the theory of relative deprivation explained college student career and graduate school application decisions. His results indicate that school mean achievement may have a negative effect on career aspirations, suggesting that students in more competitive environments may remove themselves from contention for high status careers and graduate schools. Another study finds that students in elite public high schools suffer a competitive disadvantage in entering elite colleges due to the importance of class rank in the college admissions process ADDIN EN.CITE <EndNote><Cite><Author>Attewell</Author><Year>2001</Year><RecNum>38</RecNum><DisplayText>(Attewell 2001)</DisplayText><record><rec-number>38</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">38</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Attewell, Paul</author></authors></contributors><titles><title>The Winner-Take-All High School: Organizational Adaptations to Educational Stratification</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>267-295</pages><volume>74</volume><number>4</number><dates><year>2001</year><pub-dates><date>Oct</date></pub-dates></dates><isbn>0038-0407</isbn><accession-num>ISI:000172008200001</accession-num><urls><related-urls><url><Go to ISI>://000172008200001</url></related-urls></urls></record></Cite></EndNote>(Attewell 2001). This disadvantage may produce an organizational adaptation to triage resources in favor of the top students. Therefore, students in high, but not the highest quantiles of class rank, may receive worse grades and take less advanced courses than they would if they had attended a less elite public high school (ibid).On the other hand, peers may have little or no influence on individual outcomes. Contextual effects of classroom poverty and affluence may simply reflect self-selection PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5RdWlnbGV5PC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE.DATA (Evans, Oates and Schwab 1992; Hauser 1970; Leventhal and Brooks-Gunn 2000; Quigley and Raphael 2008). Important omitted and mismeasured family and student background characteristics may be causal determinants of both test score achievement and how individuals sort into neighborhoods and schools. Controlling for these factors may greatly reduce the unadjusted difference in outcomes between students from high and low poverty contexts. For instance, Alexander and colleagues investigate the nature of school effects and find that controlling for individual SES reduces the effect of school mean SES on college plans to near zero ADDIN EN.CITE <EndNote><Cite><Author>Alexander</Author><Year>1979</Year><RecNum>51</RecNum><DisplayText>(Alexander et al. 1979)</DisplayText><record><rec-number>51</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">51</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Alexander, Karl L.</author><author>Fennessey, James</author><author>McDill, Edward L.</author><author>D'Amico, Ronald J.</author></authors></contributors><titles><title>School SES Influences - Composition or Context</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>222-237</pages><volume>52</volume><number>4</number><dates><year>1979</year></dates><isbn>0038-0407</isbn><accession-num>ISI:A1979HU85600003</accession-num><reviewed-item>Yes - Junk</reviewed-item><urls><related-urls><url><Go to ISI>://A1979HU85600003</url></related-urls></urls><research-notes>Times Cited: 16</research-notes></record></Cite></EndNote>(Alexander et al. 1979). Their conclusion is that “the school SES influences are shown to result to a considerable degree simply from SES differences in the kinds of students attending various schools” (235). Cross-sectional research that controls for prior test scores or grades has reported relatively small and statistically insignificant contextual effects. In a study of high school students, ADDIN EN.CITE <EndNote><Cite AuthorYear="1"><Author>Gamoran</Author><Year>1987</Year><RecNum>52</RecNum><DisplayText>Gamoran (1987)</DisplayText><record><rec-number>52</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">52</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Gamoran, Adam</author></authors></contributors><titles><title>The Stratification of High-School Learning Opportunities</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>135-155</pages><volume>60</volume><number>3</number><dates><year>1987</year><pub-dates><date>Jul</date></pub-dates></dates><isbn>0038-0407</isbn><accession-num>ISI:A1987J582200001</accession-num><reviewed-item>Keep</reviewed-item><urls><related-urls><url><Go to ISI>://A1987J582200001 </url></related-urls></urls><research-notes>Times Cited: 119</research-notes></record></Cite></EndNote>Gamoran (1987) finds very minimal and mostly non-significant effects of school mean SES on test score outcomes in six subjects while controlling for prior achievement. The author incorporates mediators of the contextual effect, such as types of coursework and tracking variables, and concludes that within-school differences in opportunity to learn are more important than, and perhaps explanations for, contextual effects.Alternative Designs of Contextual EffectsMuch of the research discussed thus far employs cross-sectional designs, which ignore the cumulative nature of students’ educational development and do not adequately control for self-selection bias. This section summarizes research from two strands of literature: studies with longitudinal designs and neighborhood relocation experiments. A point-in-time study captures the effect of schooling in a focal year as well as the effects of prior educational experiences and student and family background. Reviews of the literature note the importance of controlling for exogenous factors (i.e., those that do not depend on type of neighborhood/school) and call for more longitudinal designs PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5KZW5ja3M8L0F1dGhvcj48WWVhcj4xOTkwPC9ZZWFyPjxS
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ADDIN EN.CITE.DATA (Duncan and Raudenbush 1999; Galster et al. 2007; Harris 2010; Jencks and Mayer 1990; Saporito and Sohoni 2007). Rumberger and Palardy ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Rumberger</Author><Year>2005</Year><RecNum>56</RecNum><DisplayText>(2005)</DisplayText><record><rec-number>56</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">56</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Rumberger, Russell W.</author><author>Palardy, Gregory J.</author></authors></contributors><titles><title>Does Segregation Still Matter? The Impact of Student Composition on Academic Achievement in High School</title><secondary-title>The Teachers College Record</secondary-title></titles><periodical><full-title>The Teachers College Record</full-title></periodical><pages>1999-2045</pages><volume>107</volume><number>9</number><dates><year>2005</year></dates><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>(2005) examine the effect of school SES composition on test score growth in high school with NELS, a nationally representative database. They use a three-level growth model (time within student within school), finding that the predictive power of school SES on composite test score growth is as strong as family SES (.12σ effect size for individual SES and a .11σ effect size for school SES). As the authors note, these effects on a standardized composite test score mask important differences across different subjects. Effects of school SES on test score growth in math and reading are relatively small (.05σ and .06σ, respectively), while effects in science and history, perhaps because of differential opportunity to learn these subjects in low SES high schools, are larger (.21σ and .14σ, respectively). Another contribution of this study is showing that the effect of school SES is explained by teacher expectations, the amount of homework students do, course taking, and student perceptions of school safety. Although this study uses an impressive array of control variables to adjust for observable differences in student populations that could confound the school SES effect, its design does not permit ruling out bias from the sorting of students into schools based on unobservables. It also does not account for the problem of time-dependent confounding, which could arise if a student’s school SES is a function of lagged values of school SES and lagged values of the outcome. The gold-standard for addressing unobservables in contextual effects research is an experimental design ADDIN EN.CITE <EndNote><Cite><Author>Kling</Author><Year>2007</Year><RecNum>20</RecNum><DisplayText>(Kling, Liebman and Katz 2007; Sampson 2008)</DisplayText><record><rec-number>20</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">20</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Kling, Jeffrey R.</author><author>Liebman, Jeffrey B.</author><author>Katz, Lawrence F.</author></authors></contributors><titles><title>Experimental Analysis of Neighborhood Effects</title><secondary-title>Econometrica</secondary-title></titles><periodical><full-title>Econometrica</full-title></periodical><pages>83-119</pages><volume>75</volume><number>1</number><dates><year>2007</year></dates><urls></urls></record></Cite><Cite><Author>Sampson</Author><Year>2008</Year><RecNum>57</RecNum><record><rec-number>57</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">57</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sampson, Robert J.</author></authors></contributors><titles><title>Moving to Inequality: Neighborhood Effects and Experiments Meet Social Structure</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>189-231</pages><volume>118</volume><number>1</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(Kling, Liebman and Katz 2007; Sampson 2008). Although no experiment conducted to date allows for direct examination of school contextual effects, evaluations of a housing relocation program, Moving to Opportunity (MTO), provide suggestive evidence about the impact of changes in both neighborhood and school context ADDIN EN.CITE <EndNote><Cite><Author>DeLuca</Author><Year>2009</Year><RecNum>58</RecNum><Prefix>see </Prefix><Suffix> for a review of this research</Suffix><DisplayText>(see DeLuca and Dayton 2009 for a review of this research)</DisplayText><record><rec-number>58</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">58</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>DeLuca, Stefanie</author><author>Dayton, Elizabeth</author></authors></contributors><titles><title>Switching Social Contexts: The Effects of Housing Mobility and School Choice Programs on Youth Outcomes</title><secondary-title>Annual Review of Sociology</secondary-title></titles><periodical><full-title>Annual Review of Sociology</full-title></periodical><pages>457-91</pages><volume>35</volume><dates><year>2009</year></dates><urls></urls></record></Cite></EndNote>(see DeLuca and Dayton 2009 for a review of this research). 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ADDIN EN.CITE.DATA (Kling, Liebman and Katz 2007; Orr et al. 2003; Sanbonmatsu et al. 2006). To our knowledge only two studies of poverty context account for time-dependent confounding in modeling effects on children’s cognitive outcomes. In the first, Sampson, Sharkey, and Raudenbush ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Sampson</Author><Year>2008</Year><RecNum>29</RecNum><DisplayText>(2008)</DisplayText><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sampson, Robert J.</author><author>Sharkey, Patrick</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Durable Effects of Concentrated Disadvantage on Verbal Ability among African-American Children</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title></periodical><pages>845-852</pages><volume>105</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(2008) examine the effect of changes in neighborhood concentrated disadvantage on children’s verbal ability across three waves of African American families in the Project on Human Development in Chicago Neighborhoods study. To address the problem of time-varying confounding, this authors estimate a marginal structural model (MSM) with inverse probability of treatment weighting (IPTW) and report that the effect of neighborhood concentrated disadvantage on children’s verbal ability is large and negative, equivalent to missing a year of school (ibid). In the second, ADDIN EN.CITE <EndNote><Cite AuthorYear="1"><Author>Sharkey</Author><Year>2011</Year><RecNum>59</RecNum><DisplayText>Sharkey and Elwert (2011)</DisplayText><record><rec-number>59</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">59</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sharkey, Patrick</author><author>Elwert, Felix</author></authors></contributors><titles><title>The Legacy of Disadvantage: Multigenerational Neighborhood Effects on Cognitive Ability</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>1934-1981</pages><volume>116</volume><number>6</number><dates><year>2011</year></dates><urls></urls></record></Cite></EndNote>Sharkey and Elwert (2011) also estimate a MSM with IPTW and find that multigenerational neighborhood poverty has a negative effect on children's cognitive ability.In summary, existing research on school contextual effects rests primarily on a base of cross-sectional designs of correlational evidence. One study of school contextual effects employs a longitudinal design, but ignores the problem of unobserved heterogeneity and time-dependent confounding. Housing relocation studies provide evidence about changes in neighborhood, which also involve changes in school context, but suffer from limitations of generalizability to non-poor and non-minority populations and leave unexamined the effects of increases in classroom poverty. Two studies from the neighborhood effects literature use appropriate techniques to address time-dependent confounding and report negative effects of neighborhood poverty on children’s cognitive ability. The present study makes a contribution to existing research on school contextual effects by employing a rigorous longitudinal research design. First, we estimate a quadratic growth curve models over six years (grades three through eight) that relate the effect of changes in classroom poverty to changes in students’ test score achievement. Second, we address selection bias by including student fixed effects into our growth model. A large literature in economics and a growing literature in sociology PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Lb2NhazwvQXV0aG9yPjxZZWFyPjIwMDg8L1llYXI+PFJl
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ADDIN EN.CITE.DATA (e.g. England, Allison and Wu 2007; Jacobs and Carmichael 2001; Jacobs and Tope 2007; Kocak and Carroll 2008; Mouw 2003; Schneiberg, King and Smith 2008) uses fixed effects methods to control for time-invariant unobserved heterogeneity. These models, which require treatment variation within units over time, remove confounding bias that can emerge from omitted observable, mismeasured, or unobservable time-invariant student or group characteristics PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5BbGxpc29uPC9BdXRob3I+PFllYXI+MjAwOTwvWWVhcj48
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ADDIN EN.CITE.DATA (Allison 2009; Halaby 2004; Mouw 2006; Wooldridge 2003). In the present context, this technique accounts for important student-level confounders such as low birth weight, early childhood education, and genetic factors, as well as family-level confounders such as parental IQ and class background. Third, following Sampson, Sharkey, and Raudenbush ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Sampson</Author><Year>2008</Year><RecNum>29</RecNum><DisplayText>(2008)</DisplayText><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sampson, Robert J.</author><author>Sharkey, Patrick</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Durable Effects of Concentrated Disadvantage on Verbal Ability among African-American Children</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title></periodical><pages>845-852</pages><volume>105</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(2008) and ADDIN EN.CITE <EndNote><Cite AuthorYear="1"><Author>Sharkey</Author><Year>2011</Year><RecNum>59</RecNum><DisplayText>Sharkey and Elwert (2011)</DisplayText><record><rec-number>59</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">59</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sharkey, Patrick</author><author>Elwert, Felix</author></authors></contributors><titles><title>The Legacy of Disadvantage: Multigenerational Neighborhood Effects on Cognitive Ability</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>1934-1981</pages><volume>116</volume><number>6</number><dates><year>2011</year></dates><urls></urls></record></Cite></EndNote>Sharkey and Elwert (2011), we account for time-dependent confounding by producing growth model estimates with inverse probability of treatment weighting. Unlike most prior school contextual research, we measure classroom poverty at the classroom level rather than the school level, which, due to the non-random sorting of students to classrooms and middle school tracking based on achievement level, may produce less valid estimates of classroom poverty effects. We measure classroom poverty three ways: attending a high poverty classroom (i.e., in the top quartile of the classroom poverty distribution), cumulative exposure to a high poverty classroom, which more accurately reflects the time-varying exposure to context over a youth’s life course, and continuous classroom poverty (defined as percent receiving free or reduced priced lunch). We examine the effects of both increases and decreases in classroom poverty among a diverse population of students enrolled in the North Carolina public school system (a population that includes in large numbers whites, blacks, Hispanics, non-poor and poor students in urban, suburban, and rural locales). Finally, we focus on elementary and middle school aged student test score growth for two reasons: 1) the effects of classroom poverty on younger students is relatively understudied, and 2) the effect of classroom poverty has been shown to be stronger for cognitive and achievement outcomes than for behavioral and health outcomes ADDIN EN.CITE <EndNote><Cite><Author>Duncan</Author><Year>1997</Year><RecNum>68</RecNum><DisplayText>(Duncan and Brooks-Gunn 1997)</DisplayText><record><rec-number>68</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">68</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Duncan, Greg J.</author><author>Brooks-Gunn, Jeanne</author></authors></contributors><titles><title>Consequences of Growing up Poor</title></titles><pages>xi, 660 p.</pages><keywords><keyword>Poor children United States.</keyword><keyword>Poverty United States.</keyword></keywords><dates><year>1997</year></dates><pub-location>New York</pub-location><publisher>Russell Sage Foundation</publisher><isbn>0871541432 (alk. paper)</isbn><call-num>Jefferson or Adams Bldg General or Area Studies Reading Rms HV741; .C623 1997
Jefferson or Adams Bldg General or Area Studies Reading Rms HV741; .C623 1997</call-num><urls></urls></record></Cite></EndNote>(Duncan and Brooks-Gunn 1997).DataThis project uses test score and related data for one cohort of public school students in North Carolina beginning in grade three in 2001 through grade eight in 2006. North Carolina is a particularly appropriate setting for this analysis because it is one of the few states to consistently administer comparable tests over this time period, with scores produced from a three-parameter logistic item response theory (IRT) model and scored on a developmental scale to allow computation of growth across grade levels. The sample includes more than 500,000 student-year observations, beginning with about 100,000 third graders in 2001. By 2006, we observe about 75% of the original sample as being enrolled in a public school in North Carolina. We analyze both reading and math, but to conserve space, we will present descriptive analysis of only math results. Math scores for students in grades three through eight range from 303 to 388, with an average of 350.8 and a standard deviation of 11.8 (table 1). By the end of third grade, the average student math score is 339; by the end of 8th grade it is 360, suggesting a linear growth rate of about 4.2. This average masks the relatively large increases in the elementary grades (6-7 points per grade) and relatively small increases in middle school grades (3 points per grade). To define high poverty classroom, we begin by standardizing the mean level of a student’s classroom peers’ free/reduced lunch status by grade. Consistent with prior research ADDIN EN.CITE <EndNote><Cite><Author>Sampson</Author><Year>2008</Year><RecNum>29</RecNum><DisplayText>(Sampson, Sharkey and Raudenbush 2008)</DisplayText><record><rec-number>29</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">29</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Sampson, Robert J.</author><author>Sharkey, Patrick</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Durable Effects of Concentrated Disadvantage on Verbal Ability among African-American Children</title><secondary-title>Proceedings of the National Academy of Sciences of the United States of America</secondary-title></titles><periodical><full-title>Proceedings of the National Academy of Sciences of the United States of America</full-title></periodical><pages>845-852</pages><volume>105</volume><number>3</number><dates><year>2008</year></dates><urls></urls></record></Cite></EndNote>(Sampson, Sharkey and Raudenbush 2008) we dichotomize this variable into a variable coded 1 if a student is in the top quartile of classroom poverty and 0 if a student is in the bottom three quartiles of classroom poverty. Classroom is defined as the group of students with whom the student took their math test in each year. Similar to recent research on neighborhood effects PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Xb2R0a2U8L0F1dGhvcj48WWVhcj4yMDExPC9ZZWFyPjxS
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ADDIN EN.CITE.DATA (Crowder and South 2011; Jackson and Mare 2007; Wodtke, Harding and Elwert 2011), we also derive an alternate measure of classroom poverty designed to better capture cumulative effects, which we call cumulative exposure to a high poverty classroom. This time-varying variable measures the proportion of years up to and including the current year a student has attended a high poverty classroom: t=1THPCtiT. Thus, a student can be coded only 0 or 1 during third grade but can be coded 0, 0.5, or 1 during fourth grade. An eighth grader coded as 0 was never exposed to a high poverty classroom, while one coded as 1 was always exposed to high poverty classrooms. Descriptive statistics in table 1 indicate that, on average, students in our cohort spend 24% of their third through eighth grade years in high poverty classrooms. About half of 8th graders were never exposed to a high poverty classroom; only 5% of 8th graders were always exposed. Since we would expect the effect of the contrast between never exposed and always exposed to be larger than the contrast between high and low poverty classroom at one point in time, the cumulative exposure measure provides perhaps the strongest possible test of the contextual effects hypothesis with longitudinal data. To be consistent with research using a continuous measure, we also report results from classroom percent free or reduced price lunch eligible. For ease of exposition, below we will refer generically to the construct of classroom poverty to encompass all three measures, distinguishing among them when needed. Classroom poverty is time-varying rather than fixed because 1) students can be assigned to classrooms with varying poverty composition over time, 2) students change schools due to residential changes and school choice, and 3) students make structural school enrollment changes (i.e., those arising from policy-induced school mobility due to how grade configurations are structured, chiefly changing from an elementary to a middle school, rather than family choices). Measuring classroom poverty at the classroom level rather than the school level permits within-school variation in classroom poverty to contribute to estimates. There is considerable variation in classroom poverty both within and between schools. School average classroom poverty rates range from 0% to 100%, with an average of 50% and a standard deviation of 24%. About 75% of total variation in classroom poverty rates lies between elementary schools, while 25% of variation is between classrooms within schools. Perhaps due to early tracking, the portion of variation that lies between classrooms in middle schools is larger, at 40%, leaving 60% between schools. Control variables available for this study are race/ethnicity, gender, family poverty status, and parental education; educational designations as gifted, special education, or limited English proficient; whether the student was ever retained in grade; and structural and non-structural school transitions. Family poverty (free/reduced lunch eligibility) is a time-varying covariate because student free and reduced lunch eligibility changes from year to year due to changes in family income. For the population used in this study, the family poverty level of the student changes at least once for about 15% of the students. School mobility is separated into structural and non-structural measures based on whether a school switch was mandated by school district policy (a structural move like moving from elementary to middle school) or was a result of family choice or residential mobility (a non-structural move). We impute missing values for covariates at time t by assigning the subject-specific panel average. For example, if a student has a missing value in their panel of the family poverty indicator, we impute the average of that student’s family poverty indicators across their other panels. For the dependent variable, math test score, we drop subjects whose panels contain less than half non-missing scores and then impute with the grade level average of students who were ever missing, since students who were ever missing had lower test scores than kids who were never missing. A table of means before and after imputation for analysis variables is shown in appendix table A1.MethodsCross-Sectional Model To reproduce cross-sectional estimates commonly reported in previous research, we begin by presenting point-in-time estimates of the association of classroom poverty on student achievement from a multilevel model (students nested within classrooms). We model math achievement, A, for student i in classroom j as a function of classroom poverty, Z, and X, a vector of student covariates which includes student’s own family poverty status:Aij=β0+β1Zi+γXij+u0j+εij (1)In (1), we include a random intercept for each classroom, u0j, and estimate (1) by grade level to examine whether the effect of classroom poverty varies by grade. The classroom poverty estimate from (1) could be considered causal if X contains all confounders of the effect of Z on A, if these confounders are measured without error, and if the random effects are uncorrelated with each other and the covariates in the model. These conditions would apply if E(uoi|Zi)=0 and EεijZ,Xij,uoi=0. For example, many contextual effects studies, including the present one, have no or poorly measured information about the quality of students' early childhood education. If students with high quality early childhood education experiences are less likely to enroll in high poverty classrooms, we would expect β1 to be downwardly biased; that is, if we controlled for the quality of early childhood education, the hypothesized negative effect of attending a high poverty classroom would be closer to zero than the unadjusted estimate. Growth Model Using test score data that are interval scaled and vertically equated to allow for growth modeling, we estimate a quadratic growth model with random intercept and slopes. Researchers in sociology, psychology, education, and criminology often use multilevel methods to account for within-subject inter-correlation, a wide range of covariance structures, and empirical Bayes estimation, which weights estimates by their reliability (the ratio of the true score variance to the observed score variance) ADDIN EN.CITE <EndNote><Cite><Author>Bryk</Author><Year>1987</Year><RecNum>72</RecNum><DisplayText>(Bryk and Raudenbush 1987; Singer and Willett 2003)</DisplayText><record><rec-number>72</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">72</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Bryk, Anthony S.</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Application of Hierarchical Linear-Models to Assessing Change</title><secondary-title>Psychological Bulletin</secondary-title></titles><periodical><full-title>Psychological Bulletin</full-title></periodical><pages>147-158</pages><volume>101</volume><number>1</number><dates><year>1987</year><pub-dates><date>Jan</date></pub-dates></dates><isbn>0033-2909</isbn><accession-num>ISI:A1987F724700010</accession-num><urls><related-urls><url><Go to ISI>://A1987F724700010 </url></related-urls></urls><research-notes>Times Cited: 596</research-notes></record></Cite><Cite><Author>Singer</Author><Year>2003</Year><RecNum>73</RecNum><record><rec-number>73</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">73</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Singer, Judith D.</author><author>Willett, John B.</author></authors></contributors><titles><title>Applied Longitudinal Data Analysis</title></titles><dates><year>2003</year></dates><pub-location>New York, NY</pub-location><publisher>Oxford University Press</publisher><urls></urls></record></Cite></EndNote>(Bryk and Raudenbush 1987; Singer and Willett 2003). We formulate our quadratic growth model as:Ati=β0+β1Gradeti+β2Gradeti2+β3Zti+θXTti+ γXi+u0i+u1jGradeti+u2jGradeti2+u3iZti+εti (2)This model regresses a math achievement test score, A, at time t for student i on grade level, grade squared, a classroom poverty indicator, a vector of time-varying covariates, XT, and a vector of time-invariant covariates, X, with all covariates grand mean centered. Due to the problem of time-varying confounding, we omit from XT variables that could be affected by prior treatment status such as school mobility, and assignment to gifted, special education status, limited English proficiency, and grade retention. The model allows the intercept and slopes of Grade, Grade2, and Z to randomly vary and the variance-covariance matrix, Σ, imposes no restrictions on the covariation of these random effects (i.e., the matrix is specified as unstructured). We also estimate a model that interacts variables in X and XT with Grade and Grade2 to ensure our estimates are not biased by differential growth rates across different subpopulations of students. Random effects models such as the growth model shown in equation (2) produce a precision-weighted least-squares estimate that depends on within- and between-student variance components (σe2 and σu2, respectively) and the average number of periods per student (T). In a generic panel regression of y on x, both sides of the equation are quasi-demeaned with a weighting parameter, λ:yit-λyi=β01-λ+β1xit-λxi+(eit-λei), where (3)λ=1-σe2σu2+Tσe2 (4)As σe2→0, λ→1 and the random effects estimate converges toward the fixed effects estimate, discussed below. As σu2→0, λ→0 and the random effects estimate converges toward the pooled OLS estimate ADDIN EN.CITE <EndNote><Cite><Author>Wooldridge</Author><Year>2003</Year><RecNum>67</RecNum><DisplayText>(Wooldridge 2003)</DisplayText><record><rec-number>67</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">67</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Wooldridge, Jeffrey M.</author></authors></contributors><titles><title>Introductory Econometrics: A Modern Approach</title></titles><edition>2nd</edition><dates><year>2003</year></dates><pub-location>Cincinnati, OH</pub-location><publisher>South-Western College Publishing</publisher><urls></urls></record></Cite></EndNote>(Wooldridge 2003). Typically 0<λ<1, with the random effects estimate falling between the pooled OLS and the fixed effect estimates. The coefficient of interest in this model is β3, the average effect of classroom poverty on achievement across grades three to eight. Parameters estimated with model (2) are unbiased and efficient assuming that given the covariates, the random effects and the student-level residual, εti, are normally distributed with zero mean, are independent of one another, with the random effect independent across subjects and εti independent across subjects and occasions. The growth model produces an unbiased estimate of the effect of classroom poverty on test score growth if classroom poverty is uncorrelated with the random effects, if Z and the variables in XT are exogenous, and if family background is adequately controlled and well measured. As with the cross-sectional model, omitted variable bias could produce inconsistent parameter estimates, which could threaten the validity of this model. Although multilevel models can increase efficiency due to the use of both within and between variance, such models provide no solution for this type of confounding bias. If the between-student effects of classroom poverty are large relative to the within-student effects, it is possible that the omission of student and family background characteristics could bias estimates of classroom poverty contextual effects. In thinking about bias, it is helpful to return to our explanations of classroom poverty effects: contagion, relative deprivation, collective socialization, and institutions. Classroom effects can emerge either because students affect each other or because adults in schools affect students. The former pertains to contagion and relative deprivation explanations; the latter to an institutional or collective socialization explanation. In either case, the validity of inferences about contagion or institutional effects depends on removing the confounding effects of student and family background. We address the threat of adverse selection based on time invariant family and student background characteristics with a student fixed effects specification. Student Fixed Effects ModelWe estimate a student fixed effects model to control for fixed unobservables such as innate ability, mother's IQ, and early childhood experiences that might confound the effect of classroom poverty on test score. The fixed effects formulation uses each student as his/her own baseline, which holds constant all observable, unobservable, and mismeasured time-invariant student and family background characteristics. This approach eliminates all time-invariant between-student confounding in the classroom poverty effect and produces consistent parameter estimates when there is no within-student confounding of the classroom poverty effect. The student fixed effects model is specified as: Ati=β0+β1Gradeti+β2Gradeti2+β3Zti+θXTti+αi+εti (5)Here we treat the subject-specific intercept as a fixed unknown parameter to be estimated, with αi representing the deviation of subject i’s intercept from the mean intercept β0 with i=1Iαi=0. This model is often estimated by “demeaning” both sides of the equation by the subject’s panel mean, which removes between-student confounding by using only within-subject variation to estimate parameters. Omitted from equation (5) are time invariant covariates because these have no within-subject variance and are therefore not estimable with this approach (though their effects are subsumed into the subject-specific intercept). The student fixed effects approach requires within-student variation on classroom poverty to identify parameters and is relatively inefficient relative to the random effects models. Due to its large sample size and the six-year panels within it, however, our data are well suited to this approach. We identify the classroom poverty effect from year-to-year variation in the poverty composition of students’ classrooms. This changes due to school mobility and due to variations in the poverty compositions of student’s assigned classrooms as they progress through grade levels in the same school. Because classroom poverty rates vary more between schools than within schools, school movers are somewhat more likely to experience a change in classroom poverty than students who remain in the same school. Nearly the entire sample makes some sort of school move during their panel: 85% of students make a structural move (e.g., moving from elementary to middle school), 35% of students make a non-structural move (e.g., moving due to residential mobility), and 91% of students make either a structural move or a non-structural move or both. The evidence suggests that across time variation exists to analyze for both school stayers and school movers, but that a larger portion of the variation that is analyzed appears to come from movers. In total, about two-thirds of students either move into or out of a high poverty classroom at least once during their panel. About 17% of students make a change into or out of a high poverty classroom during the 3rd to 4th, 4th to 5th, 6th to 7th, or 7th to 8th grade transitions, whereas 20% of students make one of these changes during the 5th to 6th grade transition (a shift from elementary to middle school for most students in the sample). These changes are evenly split: 52% are changes into a high poverty classroom and 48% are changes out of a high poverty classroom. On average, the changes into a high poverty classroom are a grade-to-grade increase of 22% in peer poverty and the changes out of a high poverty classroom are a grade-to-grade decrease of 28% in peer poverty. Students who do not change on the binary high poverty classroom variable on average have a grade-to-grade decrease of 1.4% in peer poverty.Estimates from model (5) can be considered causal assuming that selection into high poverty classrooms is based only on time-invariant unobservables. The model does not adjust for unobserved time-varying exogenous factors that could be related to attending a high poverty classroom. We must assume strict exogeneity, that for each t, the expected value of the idiosyncratic error given the explanatory variables in all time periods and the student fixed effect is zero: Eεti|Xi,αi=0, where X is a vector containing all variables appearing on the right hand side of equation (5). Marginal Structural ModelBoth the multilevel and fixed effects models outlined above are vulnerable to the threat of time-varying confounding, which arises when there is a time varying variable that is affected by prior treatment and is associated with subsequent treatment and the outcome. For example, consider the causal diagram in figure 1. In this diagram, X is a time-varying control variable, Z is treatment (high poverty classroom), Y is outcome (test score achievement), the subscript 0 represents baseline variables, 1 the subsequent time period variables, and U is an unobservable that affects both X1 and Y1. The variable in the shaded box, X1, is a time varying confounder (e.g., assignment to gifted or special education), because it predicts future treatment, Z1, and is associated with future outcome, Y1, via U and directly ADDIN EN.CITE <EndNote><Cite><Author>Robins</Author><Year>2000</Year><RecNum>24</RecNum><DisplayText>(Robins, Hernan and Brumback 2000)</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robins, James M.</author><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author></authors></contributors><titles><title>Marginal Structural Models and Causal Inference in Epidemiology</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>550-560</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>(Robins, Hernan and Brumback 2000). Because X1 is affected by prior treatment through the prior outcome (i.e., endogenous), standard models will produce biased treatment effect estimates. Time-varying confounding presents a dilemma: X1 is a confounder for later treatment and thus must be controlled, but may also be affected by earlier treatment and thus cannot be controlled ADDIN EN.CITE <EndNote><Cite><Author>Robins</Author><Year>2000</Year><RecNum>24</RecNum><DisplayText>(Robins, Hernan and Brumback 2000)</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robins, James M.</author><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author></authors></contributors><titles><title>Marginal Structural Models and Causal Inference in Epidemiology</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>550-560</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>(Robins, Hernan and Brumback 2000). 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ADDIN EN.CITE.DATA (Cole et al. 2010; Greenland 2003; Hernán, Hernández-Díaz and Robins 2004). Marginal structural modeling (MSM) fit using inverse-probability-of-treatment (IPT) weighting can account for time-varying confounding and produce asymptotically consistent estimates of treatment effects in longitudinal analysis. This approach involves first computing IPT weights from each subject’s probability of having their own treatment history and second estimating an IPT-weighted regression model. Our MSM is a weighted version of the growth model shown in equation (2).Following standard practice, we compute stabilized weights which have lower variance than non-stabilized weights ADDIN EN.CITE <EndNote><Cite><Author>Robins</Author><Year>2000</Year><RecNum>24</RecNum><DisplayText>(Robins, Hernan and Brumback 2000)</DisplayText><record><rec-number>24</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">24</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Robins, James M.</author><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author></authors></contributors><titles><title>Marginal Structural Models and Causal Inference in Epidemiology</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>550-560</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>(Robins, Hernan and Brumback 2000): IPTWti= k=0tP[Zk=zZk-1,Z0,Y0,X0,GkPZk=zZk-1,Z0,Yk-1,Y0,Xk-1,X0,Gk](6) where t indexes time, i indexes student, Zk=z is treatment actually received (classroom poverty exposure), Y is outcome, X is a vector of time-invariant and time-dependent confounds, and G is grade level, variables subscripted with a 0 represent baseline values, and variables subscripted with k-1 are one period lags. In X we include student background characteristics (race/ethnicity, gender, family poverty status, parental education), school mobility variables, and academic classifications (gifted, special education, Limited English Proficiency, and grade retention). The denominator is, informally, a student’s conditional probability of receiving her own observed treatment up to time t, given past treatment, outcome, covariate history, and grade level. The numerator is, informally, a student’s conditional probability of receiving her own observed treatment up to time t, given past treatment, baseline outcome, baseline covariates, and grade level. This technique is a generalization of propensity score methods for longitudinal data. Rather than weighting inversely proportional to the probability of receiving treatment (Z=1), we instead weight inversely proportional to the probability of the treatment status actually received (Z=z). We truncate weights at the first and ninety-ninth percentiles by recoding observations above the 99th percentile to the 99th percentile weight and recoding observations below the 1st percentile to the 1st percentile weight ADDIN EN.CITE <EndNote><Cite><Author>Cole</Author><Year>2008</Year><RecNum>28</RecNum><DisplayText>(Cole and Hernán 2008)</DisplayText><record><rec-number>28</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">28</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Cole, S.R.</author><author>Hernán, M.A.</author></authors></contributors><titles><title>Constructing Inverse Probability Weights for Marginal Structural Models</title><secondary-title>American journal of epidemiology</secondary-title></titles><periodical><full-title>American journal of epidemiology</full-title></periodical><pages>656</pages><volume>168</volume><number>6</number><dates><year>2008</year></dates><publisher>Oxford Univ Press</publisher><isbn>0002-9262</isbn><urls></urls></record></Cite></EndNote>(Cole and Hernán 2008). Our MSM models also adjust for possible bias due to selective attrition ADDIN EN.CITE <EndNote><Cite><Author>Hernan</Author><Year>2000</Year><RecNum>27</RecNum><DisplayText>(Hernan, Brumback and Robins 2000)</DisplayText><record><rec-number>27</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">27</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hernan, Miguel Angel</author><author>Brumback, Babette</author><author>Robins, James M.</author></authors></contributors><titles><title>Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-positive Men</title><secondary-title>Epidemiology</secondary-title></titles><periodical><full-title>Epidemiology</full-title></periodical><pages>561-570</pages><volume>11</volume><number>5</number><dates><year>2000</year></dates><urls></urls></record></Cite></EndNote>(Hernan, Brumback and Robins 2000). We compute a stabilized censoring weight as:CWti= k=0tP[Ck=0Ck-1=0,Zk,Zk-1,Z0,Y0,X0,GkPCk=0Ck-1=0,Zk, Zk-1,Z0,Yk-1,Y0,Xk-1,X0,Gk](7) where t, i, Z, Y, X, and G are defined above, and Ck is an indicator for student became censored at time t (i.e., last observation in student’s panel). To adjust for both the inverse of the probability of treatment and censoring, the weight used in the MSM models is the product of the IPT and censoring weights (IPTWti* CWti). The IPT weighted version of the model shown in equation (2) produces a consistent estimate of treatment effect under the assumption of no unmeasured confounders or sequential strong ignorability (that treatment assignment is conditionally independent of the current and future potential outcomes given the measured past). ResultsWe begin by discussing descriptive analysis of the difference in the medians and distribution of test scores by grade and classroom poverty composition. We then summarize results from cross-sectional models which show substantial associations between classroom poverty and student test score, especially in the middle school grades. Following this, we present random coefficient growth model estimates and two alternative specifications with student fixed effects and inverse-probability-of-treatment weighting for our three measures of classroom poverty: exposure to high poverty classroom, cumulative exposure, and continuous classroom poverty. We then present a summary table of effect sizes and confidence intervals for all results. Figure 2 displays a box plot of the distribution of math test scores by grade level and the high poverty classroom measure. The plot shows a general upward trend in scores and a reduction in the inter-quartile range for both groups as students increase in grade level. The gap in median test scores between students in high and low poverty classrooms in third grade is six points; by eighth grade it is seven points. The slight widening of the gap is more noticeable among eight graders always and never exposed to a high poverty classroom (the cumulative exposure measure), with the gap in median test scores growing from six points to ten points between third and eighth grade (results not shown, but available from authors upon request).Cross-Sectional Estimates of Classroom Poverty and Cumulative ExposureWe produce cross-sectional estimates from the students-within-classrooms multilevel random intercept model shown in equation (1), which control for (but do not display) race, gender, parental education, family poverty status, gifted, special education, limited English proficiency status, grade retention, and structural and non-structural school mobility. We estimate models separately by grade level. Net of controls, the third grade cross-sectional effect of attending a high poverty classroom is -.877 scale points, or a standardized effect size of -.082σ (-.877/10.74=.082). Between fifth and sixth grade, this effect jumps from -.133σ to -.233σ. By eighth grade this estimate has grown to -.280σ. If causal, these results could reflect the differentiation of math curriculum in middle school ADDIN EN.CITE <EndNote><Cite><Author>Hallinan</Author><Year>1992</Year><RecNum>77</RecNum><DisplayText>(Dauber, Alexander and Entwisle 1996; Hallinan 1992)</DisplayText><record><rec-number>77</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">77</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hallinan, Maureen T.</author></authors></contributors><titles><title>The Organization of Students for Instruction in Middle School</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>114-127</pages><volume>65</volume><number>2</number><dates><year>1992</year></dates><urls></urls></record></Cite><Cite><Author>Dauber</Author><Year>1996</Year><RecNum>78</RecNum><record><rec-number>78</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">78</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Dauber, Susan L.</author><author>Alexander, Karl L.</author><author>Entwisle, Doris R.</author></authors></contributors><titles><title>Tracking and Transitions through the Middle Grades: Channeling Educational Trajectories</title><secondary-title>Sociology of Education</secondary-title></titles><periodical><full-title>Sociology of Education</full-title></periodical><pages>290-307</pages><volume>69</volume><number>4</number><dates><year>1996</year></dates><urls></urls></record></Cite></EndNote>(Dauber, Alexander and Entwisle 1996; Hallinan 1992) and the growing influence of peers for young adolescents PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5CdWNobWFubjwvQXV0aG9yPjxZZWFyPjIwMDI8L1llYXI+
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ADDIN EN.CITE.DATA (Buchmann and Dalton 2002; Furman 1982; Veronneau and Dishion 2011), or the cumulative nature of cognitive disadvantage through the life course of children and young adolescents. Replacing the high poverty classroom variable in equation (1) with the our cumulative exposure variable produces even larger point estimates, with the estimate growing from -.082σ to -.429σ between third and 8th grade (not shown, but results available from authors upon request). In summary, we find substantively large cross-sectional associations of high poverty classroom and cumulative exposure to high poverty classrooms that increase with grade level and become especially large by eighth grade, suggesting that test score trajectories may widen over time between students exposed to higher versus lower poverty classrooms. As we have argued above, however, a growth model is a more appropriate model to estimate the gap between higher and lower poverty classrooms than a cross-sectional one. A random coefficients growth model produces precision-weighted trajectories, which provide much more convincing evidence of the effect of context on student achievement than a point-in-time estimate. Growth Model Estimates of High Poverty ClassroomTable 3 displays coefficients from time-nested-within-student random coefficient growth models for math (see equation 2, above). Column 1 shows an unadjusted effect of high poverty classroom of -2.249. Including grade and grade2 reduces the classroom poverty effect by about 70%. The coefficient shrinks from -2.249 to -.683 due to the fact that including grade level (a within-student parameter) greatly reduces unexplained within-student variation (σe) while leaving between-student variation (σu) essentially unchanged. As discussed above, when within-student variation falls between models 1 and 2, λ increases, which pulls the classroom poverty effect closer to the fixed effect estimate, which as we will see below, is quite close to zero. At the average of grade, the average student has a math test score of 352.5, an instantaneous growth rate of 4.166, and a negative curvature parameter of -0.651, which indicates that students' rate of change in test score growth declines over time. Including covariates in column 3 further reduces the classroom poverty effect from -.683 to -.413, suggesting that the classroom poverty effect is due in part to compositional differences across classrooms. Most control variable coefficients conform to expectations, with negative effects for minorities, males, and poor students, and positive differences for students with highly educated parents. The classroom poverty effect indicates that the predicted gap between students in high and low poverty classrooms across grades three through eight is -.413 scale points, or .035σ. In column 4, we include interactions between all student background controls and grade and grade.2 Allowing the effects of student background to vary with grade level does not significantly alter our treatment effect estimate. Table 4 shows these same models with reading test score as the outcome. Similar to the effects on math, the coefficient drops from -2.275 scale points in the unadjusted model to -0.399 scale points (.031σ) in the fourth model.Fixed Effect and MSM Growth Model Estimates of High Poverty ClassroomGrowth model estimates are unbiased assuming all confounders are controlled. A student fixed effects model controls for fixed pre-baseline unobservables such as innate ability, early childhood experiences, and mother’s IQ that might confound the effect of classroom poverty on test scores. By using only within-student variation in classroom poverty, this approach eliminates all time-invariant between-student confounding and produces unbiased parameter estimates when all time-varying confounders are controlled. The strength of the student fixed effects model is adjustment for time-invariant unobservables. A weakness of both the growth model and the student fixed effects specification is that neither appropriately adjusts for time-dependent confounding. A marginal structural model (MSM) with inverse-probability-of-treatment weighting (IPTW) is designed to address time-dependent confounding. Table 5 presents in column 1 estimates from the primary coefficients of interest from the random effects growth model shown in tables 3 and 4, model 3, student fixed effects estimates in column 2 (see equation 5), and MSM with IPTW estimates in column 3 (the random effects growth model in column 1 estimated with the weights computed by equations 6 and 7). In both math and reading, the absolute values of the student fixed effects estimates and the MSM estimates are much smaller than the random coefficients estimates. The effect of high poverty classroom on math in the MSM model is not statistically different from zero and the effect on reading is only significant at the p<0.05 level. Both of these alternative specifications produce estimates that are less than one percent of a standard deviation in effect size in both math and reading. Growth Model Estimates of Cumulative Exposure to Classroom PovertyTo address the concern that our estimates presented thus far could potentially underestimate the effect of classroom context by ignoring the cumulative nature of such effects, in table 5 we present growth model estimates with cumulative exposure to high classroom poverty as the explanatory variable. The random effects growth model predicts a -2.037 point gap in math between students who up to a point in time were always and never exposed to high poverty classrooms. This represents 0.172σ of the math test score, a fairly large effect, which is due in part because it is an average of effects across grades three through eight. As shown in the cross sectional results, the effect of cumulative poverty in third grade are much smaller than effects in eighth grade. (By eighth grade, an always-exposed student has been in a high poverty classroom for six years, whereas an always-exposed student in third grade has been exposed only once.) The student fixed effects model, on the other hand, produces only a -0.192 point gap (0.016σ) in math between students who up to a point in time were always and never exposed to high poverty classrooms. The difference in the two estimates suggests that the large effect produced by the random coefficients model is largely due to baseline differences in students who become exposed to particularly high and low levels of classroom poverty. The MSM model produces a high poverty classroom gap of that is not significantly different from zero (0.0267), suggesting that time-dependent confounding is downwardly biasing the estimate in column 1. The pattern in reading is largely the same with a large negative effect from the random effects growth model (0.161σ) shrinking closer toward zero in the fixed effects (0.023σ) and MSM specifications (0.022σ). The unexpected result is that the sign of the cumulative poverty effect is positive in the fixed effect and MSM specifications rather than negative.Growth Model Estimates of Continuous PovertyFor consistency with prior research that uses continuous measures of poverty context, we present the effect of a standardized measure of continuous classroom poverty (measured as percent of classroom that is on free or reduced priced lunch) in table 7. We present estimates from the random coefficients and fixed effects models. In column 1, a one standard deviation increase in classroom poverty produces a 0.297 decrease in math test score (-.025σ). The estimate from a student fixed effects model produces an effect with the opposite sign, but much smaller in absolute value (+.003σ). In reading, the signs of the effects from the random coefficients and fixed effects specifications are also opposite signed, and both are approximately the same size, producing effect sizes of -.002σ and +.017σ, for a one standard deviation increase in classroom poverty. Effect Size Summary with 95% Confidence IntervalsMost of the reported effects are statistically significant, yet small in substantive terms. Our claim that the contextual effects found in this study are small would fail if confidence intervals contain values that could be considered large. Due to the large sample size used in this study, however, confidence intervals are quite narrow (table 8). For example, in panel A of table 8 we show that 95% confidence interval of standardized fixed effects high poverty classroom estimates (0 to 1 contrast) lie between -.009 and -.002 in math and .005 and .012 in reading. The MSM confidence intervals are also tightly arranged around zero. Panel B shows that the fixed effect cumulative poverty effects (0 to 1 contrast) in math and reading lie within the range of -.026 (lower bound for math) and .033 (upper bound for reading); the MSM results for the cumulative poverty effect lie between -.006 and .031. For continuous classroom poverty we report effects from two contrasts: a one and two standard deviation increase in classroom poverty. To put these contrasts into perspective, in our sample 32% of students experience no more than one instance of an increase in classroom poverty of 25%, which represents about one standard deviation in classroom poverty. A two standard deviation change represents a much more rare event. Only five percent of students have no more than one instance of an increase in classroom poverty of 50%. The effects for a one standard deviation effect from the random coefficient and fixed effects specifications lie within the range of -.027 to +.019, whereas the effects for a two standard deviation effect from these two specifications lie within -.054 to +.039. Given that most effects reported from the student fixed effects and MSM models are smaller than .04σ in absolute value, we conclude that the contextual effects of classroom poverty on cognitive achievement are very small. Conclusion For decades scholars from a variety of disciplines have been debating the evidence of contextual effects on youth outcomes. What do we add to this rich literature? This study moves beyond a conception of contextual effects as correlations estimated on young people at one point in time to context shaping youth development over time. This study is designed to test the hypothesis that classroom contexts with high levels of poverty harm student achievement. Our findings challenge previous research based on cross-sectional designs which tend to report negative effects of peer poverty on student achievement. With cross-sectional models, we replicate past research by establishing that exposure to high poverty classrooms is negatively associated with math test score, with the strength of the association becoming quite large as students increase in grade level. The growth model evidence presented, however, shows very small negative effects of exposure to a high poverty classroom and continuous classroom poverty on math and reading test scores. The effects on cumulative exposure to a high poverty classroom, though, are larger (one-sixth of a standard deviation). Models with student fixed effects, which control for time-invariant student background unobservables, and with inverse-probability-of-treatment weighting, a method to properly adjust for observable time-dependent confounding, produce negligible effects of all three measures of classroom poverty on math and reading achievement. That exposure to classroom poverty has a strong association with test score in the cross-section, but has very small effects in models with weaker assumptions for causal inference, strongly suggests that selection bias is present in the cross-sectional estimates reported in studies based on point-in-time designs. The question of whether the effect of school poverty is causal or simply a function of either omitted variable bias or endogenous self-selection is a critical conceptual and empirical matter for both the theory of school effects and policies that seek to integrate students by socio-economic background ADDIN EN.CITE <EndNote><Cite><Author>Duncan</Author><Year>1999</Year><RecNum>53</RecNum><DisplayText>(Duncan and Raudenbush 1999)</DisplayText><record><rec-number>53</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">53</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Duncan, Greg J.</author><author>Raudenbush, Stephen W.</author></authors></contributors><titles><title>Assessing the Effects of Context in Studies of Child and Youth Development</title><secondary-title>Educational Psychologist</secondary-title></titles><periodical><full-title>Educational Psychologist</full-title></periodical><pages>29-41</pages><volume>34</volume><number>1</number><keywords><keyword>MULTILEVEL</keyword><keyword>MODEL</keyword><keyword>NEIGHBORHOODS</keyword><keyword>CRIME</keyword></keywords><dates><year>1999</year><pub-dates><date>Win</date></pub-dates></dates><isbn>0046-1520</isbn><accession-num>ISI:000078527000004</accession-num><urls><related-urls><url><Go to ISI>://000078527000004 </url></related-urls></urls><research-notes>Times Cited: 87</research-notes></record></Cite></EndNote>(Duncan and Raudenbush 1999). This study has important implications for both research and public policy. These findings suggest that standard estimates and prevailing theories about social influence among pre- and early-adolescents may not hold for test score achievement, one of the most important educational outcomes. This suggests that simply mixing students by poverty level and not altering important institutional resources such as high quality instruction and teacher expectations may not have the intended effect of increasing achievement because achievement is not simply a function of poverty context but of student and family background. The policy goal of mixing students by race-ethnicity or social background has been a mainstay in educational policy since the Brown vs. Board decision. Since the 1980s, school desegregation orders have been vacated by an increasingly conservative judiciary. The changing legal landscape has contributed to a resegregation of American schools PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5PcmZpZWxkPC9BdXRob3I+PFllYXI+MTk5NjwvWWVhcj48
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ADDIN EN.CITE.DATA (Orfield, Eaton and Desegregation 1996; Reardon and Yun 2005; Rumberger and Palardy 2005). These trends are likely to continue given that in the 2007 case of Parents Involved v. Seattle School District No. 1, the Supreme Court ruled that school districts may not use race in assigning students or granting transfers to achieve or maintain school integration. In response to increases in school racial segregation and the Supreme Court’s prohibition on the use of race in making school assignments, some advocate for integrating students based on socio-economic background ADDIN EN.CITE <EndNote><Cite><Author>Kahlenberg</Author><Year>2001</Year><RecNum>15</RecNum><DisplayText>(Kahlenberg 2001)</DisplayText><record><rec-number>15</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">15</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Kahlenberg, Richard D.</author></authors></contributors><titles><title>All Together Now: Creating Middle-Class Schools Through Public School Choice</title></titles><pages>xv, 379 p.</pages><keywords><keyword>Educational equalization United States.</keyword><keyword>Education Economic aspects United States.</keyword><keyword>Public schools United States.</keyword></keywords><dates><year>2001</year></dates><pub-location>Washington, D.C.</pub-location><publisher>Brookings Institution Press</publisher><isbn>0815748108 (alk. paper)</isbn><call-num>Jefferson or Adams Bldg General or Area Studies Reading Rms LC213.2; .K35 2001
Jefferson or Adams Bldg General or Area Studies Reading Rms LC213.2; . K35 2001</call-num><urls></urls></record></Cite></EndNote>(Kahlenberg 2001), which is constitutionally permissible. Kahlenberg ADDIN EN.CITE <EndNote><Cite ExcludeAuth="1"><Author>Kahlenberg</Author><Year>2001</Year><RecNum>15</RecNum><DisplayText>(2001)</DisplayText><record><rec-number>15</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">15</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Kahlenberg, Richard D.</author></authors></contributors><titles><title>All Together Now: Creating Middle-Class Schools Through Public School Choice</title></titles><pages>xv, 379 p.</pages><keywords><keyword>Educational equalization United States.</keyword><keyword>Education Economic aspects United States.</keyword><keyword>Public schools United States.</keyword></keywords><dates><year>2001</year></dates><pub-location>Washington, D.C.</pub-location><publisher>Brookings Institution Press</publisher><isbn>0815748108 (alk. paper)</isbn><call-num>Jefferson or Adams Bldg General or Area Studies Reading Rms LC213.2; .K35 2001
Jefferson or Adams Bldg General or Area Studies Reading Rms LC213.2; . K35 2001</call-num><urls></urls></record></Cite></EndNote>(2001) argues that the best way to ensure the presence of high standards, highly qualified teachers, and less crowded classes is to ensure a critical mass of middle class families to advocate for these resources. Various forms of SES integration have been implemented in more than 50 districts across the U.S., including Lacrosse, WI; Wake County, NC; Cambridge, MA; and San Francisco, CA. The findings of the present study suggest that simply mixing students by social background may not have the intended effects, unless such mixing can garner increased resources and support for proven teaching practices that can increase student achievement in impoverished contexts. There are some limitations to this study that point the way for future work on school and classroom poverty effects. Although North Carolina is racially and economically diverse, the study covers only the public school students from one state, which limits the generalizability of our findings. Using population-level administrative data, we have pursued an identification strategy that privileges reduction of bias over national representativeness. The external validity of these results will hinge on cross-state replications using administrative data, and large nationally representative surveys with rich contextual information and interval metric test scores designed to measure growth over time. We must be careful to stress that we use a research design that reduces, but may not entirely eliminate, bias from unobservables. For example, our inability to account for time-varying student or school unobservables could prove these estimates to be biased. Future work should carefully theorize and measure time-varying factors that predict test scores. We cannot empirically examine whether changes in classroom poverty correspond to substantial differences in micro-level interaction between students and between students and teachers. An important next step for school contextual effects research is to examine the effect of school or classroom poverty on test score growth. Although these models suggest negligible effects of classroom poverty on average test score achievement across students' third through eighth grade panels, it is possible that school or classroom poverty negatively deflects students' growth rates. Moreover, contextual effects may vary by a number of demographic characteristics such as race, individual poverty status, or gender ADDIN EN.CITE <EndNote><Cite><Author>Clampet-Lundquist</Author><Year>2011</Year><RecNum>84</RecNum><DisplayText>(Clampet-Lundquist et al. 2011; Legewie and DiPrete 2012)</DisplayText><record><rec-number>84</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">84</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Clampet-Lundquist, Susan</author><author>Edin, Kathryn</author><author>Kling, Jeffrey R.</author><author>Duncan, Greg J.</author></authors></contributors><titles><title>Moving Teenagers Out of High-Risk Neighborhoods: How Girls Fare Better Than Boys</title><secondary-title>American Journal of Sociology</secondary-title></titles><periodical><full-title>American Journal of Sociology</full-title></periodical><pages>1154-1189</pages><volume>116</volume><number>4</number><dates><year>2011</year></dates><urls></urls></record></Cite><Cite><Author>Legewie</Author><Year>2012</Year><RecNum>85</RecNum><record><rec-number>85</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">85</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Legewie, Joscha</author><author>DiPrete, Thomas A.</author></authors></contributors><titles><title>School Context and the Gender Gap in Educational Achievement</title><secondary-title>American Sociological Review</secondary-title></titles><periodical><full-title>American Sociological Review</full-title></periodical><pages>463-485</pages><volume>77</volume><number>3</number><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>(Clampet-Lundquist et al. 2011; Legewie and DiPrete 2012). Finally, test scores may be mostly impervious to the influence of peers and socialization processes. Other outcomes such as pregnancy, drug use, school completion, and college attendance, may be more amenable to these factors than a test score, which is a discrete cognitive task rather than a behavioral event. Much of the existing research base on contextual effects has examined the experiences and outcomes of high school students. This study represents one of the first sociological examinations of contextual effects among elementary and middle school students. Despite this contribution, it may be that by third grade, the earliest time point in this study, early childhood experiences have largely determined a student’s potential for achievement. If test score gaps among socioeconomic groups are essentially stable by third grade and variations in school quality have little effect on these gaps over time ADDIN EN.CITE <EndNote><Cite><Author>Heckman</Author><Year>2006</Year><RecNum>86</RecNum><DisplayText>(Heckman 2006)</DisplayText><record><rec-number>86</rec-number><foreign-keys><key app="EN" db-id="vdfta2z26tx9fhewt5vp99ftdr50ee5rs5zt">86</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Heckman, James J.</author></authors></contributors><auth-address>Heckman, JJ
Univ Chicago, Dept Econ, Chicago, IL 60637 USA
Univ Chicago, Dept Econ, Chicago, IL 60637 USA
Univ Chicago, Dept Econ, Chicago, IL 60637 USA
Natl Univ Ireland Univ Coll Dublin, Dept Econ, Dublin 4, Ireland</auth-address><titles><title>Skill Formation and the Economics of Investing in Disadvantaged Children</title><secondary-title>Science</secondary-title><alt-title>Science</alt-title></titles><periodical><full-title>Science</full-title><abbr-1>Science</abbr-1></periodical><alt-periodical><full-title>Science</full-title><abbr-1>Science</abbr-1></alt-periodical><pages>1900-1902</pages><volume>312</volume><number>5782</number><dates><year>2006</year><pub-dates><date>Jun 30</date></pub-dates></dates><isbn>0036-8075</isbn><accession-num>ISI:000238848100043</accession-num><urls><related-urls><url><Go to ISI>://000238848100043</url></related-urls></urls><electronic-resource-num>DOI 10.1126/science.1128898</electronic-resource-num><language>English</language></record></Cite></EndNote>(Heckman 2006), then policies to mix students by social background may be of limited utility. On the other hand, research has found neighborhood effects on birth weight and other early childhood development experiences PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Nb3Jlbm9mZjwvQXV0aG9yPjxZZWFyPjIwMDM8L1llYXI+
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Causal diagram showing a time-varying confounder (X1) on the causal pathway between treatment occasions and the outcome. Figure 2. Math Score by Classroom Poverty and GradeNote: Each box contains the 25th to 75th percentile with the white line in each box at the median. Whiskers indicate the 5th and 95th percentilesTable 1. Descriptive Statistics ObsMeanSDMinMaxDependent VariablesMath test score537,653350.7811.84303388Reading test score537,653348.0412.89303384Student BackgroundParent has high school degree or less537,6530.530.4201Parent has some postsecondary education537,6530.210.4101Parent has bachelor's degree or higher537,6530.270.4401Black student537,6530.300.4601Hispanic student537,6530.050.2201Other racial/ethnic background537,6530.050.2201Male student537,6530.500.5001Student was designated gifted537,6530.140.3501Student received special education services537,6530.110.3201Student showed Limited English Proficiency537,6530.020.1501Student was ever retained537,6530.110.3201Student received free or reduced price lunch537,6530.450.5001Student made a structural school move537,6530.160.3701Student made a non-structural school move537,6530.090.2801Classroom Poverty MeasuresHigh poverty classroom (top quintile)537,6530.240.4301Cumulative exposure to high poverty classrooms537,6530.230.3501Continuous classroom poverty (pct free/reduced lunch)537,6530.450.2601Time VariablesGrade level537,6535.341.6938Grade level ^2537,65331.4118.50964Note: Observations reported are student-year observations.Table 2. Classroom Poverty and Math Achievement: Cross-Sectional Multilevel Models, 2001-20063rd Grade4th Grade5th Grade6th Grade7th Grade8th GradeHigh Poverty Classroom-0.877***(0.0976)-0.848***(0.0819)-1.155***(0.0799)-2.088***(0.0888)-2.210***(0.0880)-2.484***(0.107)Effect Size-0.082-0.091-0.133-0.233-0.249-0.280SD (Math)10.749.348.668.958.878.86Observations97,99596,14490,90489,07184,58574,525Note: Each model controls for race, gender, parental education, individual poverty status, gifted, special education, limited English proficiency, structural school mobility, and non-structural school mobility. Each model also includes a random intercept for classroom. High poverty classroom is the top quartile of a standardized measure of percent classroom peers' poverty status. Standard errors in parentheses;* p < 0.05, ** p < 0.01, *** p < 0.001. Table 3. Classroom Poverty and Math Achievement: Random Coefficient Growth Models, 2001-2006(1) Classroom Pov(2) w/ Growth(3)w/ Student Chars(4) w/ Student Chars InteractionsHigh Poverty Classroom -2.249***(0.0413)-0.683***(0.0191)-0.413***(0.0191)-0.407***(0.0191)Grade4.166***(0.00451)4.148***(0.00453)4.142***(0.00451)Grade2-0.651***(0.00228)-0.651***(0.00229)-0.653***(0.00229)Parent Has Some Postsec Educ 0.514***(0.0174)0.419***(0.0230)Parent Has Bach Degree or More 1.057***(0.0217)0.764***(0.0265)Black-6.324***(0.0523)-6.358***(0.0538)Hispanic-3.507***(0.108)-3.661***(0.111)Other Race/Ethnicity-1.313***(0.120)-1.454***(0.122)Male-0.419***(0.0480)-0.302***(0.0490)Student Poverty-0.706***(0.0236)-0.601***(0.0275)Constant350.2***(0.0283)352.5***(0.0269)352.5***(0.0243)352.5***(0.0245)σu7.809***(0.370)7.968***(0.322)7.118***(0.268)7.175***(0.274) σe8.461***(0.160)3.722***(0.0392)3.736***(0.0397)3.733***(0.0396)SD(High Pov 5.596***1.027***0.930***0.907*** Classroom)(0.666)(0.116)(0.114)(0.112)SD(Grade)0.978***0.976***0.955***(0.00906)(0.00906)(0.00888)SD(Grade^2)0.279***0.280***0.257***(0.00251)(0.00252)(0.00246)Observations537,653537,653537,653537,653Note: Random coefficient models (see equation 2) with an unstructured covariance matrix. Covariances of random effects not shown. Model 4 includes interactions between listed student background controls and grade and grade2 (coefficients not shown). Robust standard errors in parentheses;* p < 0.05, ** p < 0.01, *** p < 0.001.Table 4. Classroom Poverty and Reading Achievement: Random Coefficient Growth Models, 2001-2006(1) Classroom Pov(2) w/ Growth(3)w/ Student Chars(4) w/ Student Chars InteractionsHigh Poverty Classroom -2.275***(0.0469)-0.727***(0.0220)-0.418***(0.0221)-0.399***(0.0220)Grade4.656***(0.00517)4.631***(0.00520)4.630***(0.00513)Grade2-0.570***(0.00260)-0.573***(0.00261)-0.570***(0.00263)Parent Has Some Postsec Educ 0.584***(0.0203)0.525***(0.0274)Parent Has Bach Degree or More 1.278***(0.0248)1.145***(0.0311)Black-6.097***(0.0550)-6.662***(0.0591)Hispanic-3.905***(0.116)-5.074***(0.123)Other Race/Ethnicity-1.769***(0.115)-2.392***(0.124)Male-1.617***(0.0481)-1.702***(0.0519)Student Poverty-0.951***(0.0271)-0.869***(0.0325)Constant347.5***(0.0303)349.6***(0.0290)349.6***(0.0259)349.6***(0.0260)σu8.237***(0.425)8.479***(0.373)7.460***(0.305)7.483***(0.310) σe9.481***(0.201)4.448***(0.0556)4.466***(0.0563)4.465***(0.0562)SD(High Pov 6.407***1.206***1.086***1.095*** Classroom)(0.829)(0.153)(0.150)(0.150)SD(Grade)1.103***1.097***1.052***(0.0121)(0.0121)(0.0117)SD(Grade^2)0.247***0.247***0.237***(0.00331)(0.00333)(0.00331)Observations537,653537,653537,653537,653Note: Random coefficient models (see equation 2) with an unstructured covariance matrix. Covariances of random effects not shown. Model 4 includes interactions between listed student background controls and grade and grade2 (coefficients not shown). Robust standard errors in parentheses;* p < 0.05, ** p < 0.01, *** p < 0.001.Table 5. High Poverty Classroom and Achievement: Comparison of Alternative Specifications, 2001-2006(1)(2)(3)Random CoefficientsStudent FE MSM w/IPTW (treatment and censoring)A. Math High Poverty Classroom-0.413***(0.0191)-0.0629***(0.0204)0.00784(0.0180) Grade4.148***(0.00453)4.154***(0.00455)4.199***(0.00466) Grade2-0.651***(0.00229)-0.655***(0.00230)-0.665***(0.00235) Constant352.5***(0.0243)352.6***(0.00654)352.3***(0.0177) Observations537,653537,653537,653B. Reading High Poverty Classroom-0.418***(0.0221)0.106***(0.0237)0.0545*(0.0212) Grade4.631***(0.00520)4.623***(0.00524)4.685***(0.00540) Grade2-0.573***(0.00261)-0.592***(0.00265)-0.589***(0.00266) Constant349.6***(0.0259)349.7***(0.00753)349.4***(0.0205) Observations537,653537,653537,653Note: Model 1 panel A is model 3 from table 3 and model 1 panel B is model 3 from table 4 (with the same covariates, though only a selection are shown here) reprinted here for comparison purposes. All models control for parent's education, race/ethnicity, gender, and poverty status; race/ethnicity and gender are subsumed into the student-specific intercept in the student fixed effects model; MSM weights also adjust for school mobility, gifted, special education, LEP, and grade retention. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.Table 6. Cumulative Exposure to Classroom Poverty and Achievement: Comparison of Alternative Specifications, 2001-2006(1)(2)(3)Random CoefficientsStudent FE MSM w/IPTW (treatment and censoring)A. Math Cumulative Pov Exposure -2.037***(0.0462)-0.192***(0.0567)0.0267(0.0487) Grade4.144***(0.00455)4.154***(0.00455)4.199***(0.00465) Grade2-0.649***(0.00229)-0.655***(0.00230)-0.665***(0.00235) Constant352.5***(0.0241)352.6***(0.00654)352.3***(0.0178) Observations537,653537,653537,653B. Reading Cumulative Pov Exposure -2.085***(0.0529)0.292***(0.0668)0.263***(0.0569) Grade4.627***(0.00522)4.623***(0.00524)4.685***(0.00540) Grade2-0.572***(0.00261)-0.593***(0.00265)-0.589***(0.00266) Constant349.6***(0.0257)349.7***(0.00753)349.4***(0.0205) Observations537,653537,653537,653Note: All models control for parent's education, race/ethnicity, gender, and poverty status; race/ethnicity and gender are subsumed into the student-specific intercept in the student fixed effects model; MSM weights also adjust for school mobility, gifted, special education, LEP, and grade retention. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.Table 7. Continuous Classroom Poverty and Achievement: Comparison of Alternative Specifications, 2001-2006(1)(2)Random CoefficientsStudent FE A. Math Continuous Classroom Pov -0.297***(0.0104)0.0328**(0.0112) Grade4.123***(0.00459)4.156***(0.00460) Grade2-0.648***(0.00229)-0.655***(0.00230) Constant352.5***(0.0242)352.6***(0.00654) Observations537,653537,653B. Reading Continuous Classroom Pov -0.260***(0.0118)0.224***(0.0131) Grade4.610***(0.00529)4.637***(0.00529) Grade2-0.571***(0.00261)-0.592***(0.00265) Constant349.6***(0.0258)349.7***(0.00753) Observations537,653537,653Note: All models control for parent's education, race/ethnicity, gender, and poverty status; race/ethnicity and gender are subsumed into the student-specific intercept in the student fixed effects model; MSM weights also adjust for school mobility, gifted, special education, LEP, and grade retention. Robust standard errors in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.Table 8. Effect Size Summary Table(1) Random Coefficients(2) Student FE(3) MSM w/ IPTWLower boundEstimateUpper boundLower boundEstimateUpper boundLower boundEstimateUpper boundA. High Poverty Classroom Math-0.038-0.035-0.032-0.009-0.005-0.002-0.0040.0000.003 Reading-0.036-0.032-0.0290.0050.0080.0120.0010.0060.009B. Cumulative Pov Exposure Math-0.180-0.172-0.164-0.026-0.016-0.007-0.0060.0000.008 Reading-0.170-0.162-0.1540.0120.0230.0330.0120.0220.031C. Continuous Classroom PovOne standard deviation increase Math-0.027-0.025-0.0230.0010.0030.005------ Reading-0.022-0.020-0.0180.0150.0170.019------Two standard deviation increase Math-0.054-0.050-0.0470.0020.0060.009------ Reading-0.044-0.040-0.0370.0310.0350.039------Note: These estimates use coefficients and 95% confidence intervals from Tables 5, 6, and 7, divided by the standard deviation of math (11.84) and reading (12.89) to provide standardized effect sizes. High poverty classroom effects represent the average difference between 0 (not in a high poverty classroom) and 1 (in a high poverty classroom) across all years. Cumulative poverty exposure effects represent the average difference between 0 (never in a high poverty classroom) and 1 (always in a high poverty classroom) across all years. MSM model for continuous classroom poverty not estimated.Appendix Table A1. Pre-Imputation Descriptive Statistics Pre-ImputationPost-ImputationObsMeanSDObsMeanSDDependent VariablesMath test score550,147350.7211.86537,653350.7811.84Reading test score548,301348.1112.91537,653348.0412.89Student BackgroundParent has high school degree or less551,9060.530.50537,6530.530.42Parent has some postsecondary education551,9060.210.41537,6530.210.41Parent has bachelor's degree or higher551,9060.260.44537,6530.270.44Black student558,3530.310.46537,6530.300.46Hispanic student558,3530.050.22537,6530.050.22Other racial/ethnic background558,3530.050.23537,6530.050.22Male student558,3530.510.50537,6530.500.50Student was designated gifted558,3530.140.35537,6530.140.35Student received special education services557,8620.120.33537,6530.110.32Student showed Limited English Proficiency557,9310.020.15537,6530.020.15Student was ever retained552,7910.110.32537,6530.110.32Student received free or reduced price lunch544,2890.460.50537,6530.450.50Student made a structural school move558,3530.160.36537,6530.160.37Student made a non-structural school move558,3530.090.29537,6530.090.28Peer PovertyHigh poverty classroom558,3530.240.43537,6530.240.43Cumulative exposure to high poverty classrooms558,3530.240.35537,6530.230.35Continuous classroom poverty558,3530.450.27537,6530.450.26Time VariablesGrade level558,3535.341.70537,6535.341.69Grade level ^2558,35331.4318.58537,65331.4118.50Note: Observations reported are student-year observations. 4,108 student year observations were dropped pre-imputation due to a student having < 50% valid math scores in their panel (1,266 for reading). ................
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