孩子健康和学校成功--面板分位数回归经典例子

The relation between children's health and academic achievement
Eric R.Eide a ,⁎,Mark H.Showalter a ,Dan D.Goldhaber b
a Brigham Young University,Department of Economics,Provo,Utah,84602,United States
b
University of Washington,Center on Reinventing Public Education,2101N.34th Street,Suite 195,Seattle,WA 98103-9158,United States
a b s t r a c t
a r t i c l e i n f o Article history:
Received 4June 2009
Received in revised form 25August 2009Accepted 26August 2009
Available online 3September 2009Keywords:Child health
Academic achievement Quantile regression
We investigate the relation between a variety of health conditions and test scores for children and adolescents using data from the Child Development Supplement of the Panel Study of Income Dynamics.In addition to estimating how health conditions are associated with test scores ‘on average,’our statistical methodology estimates this association at different points of the conditional test score distribution.Such information could be crucial for policy purposes because the relation between health and academic achievement may be different for students at the bottom and top of the test score distribution.We find that several health conditions are highly negatively correlated with math and reading test scores,both on average and at different points of the achievement distribution.Given the current education policy environment where schools are shifting resources to conform to state and federal requirements on test scores and other outcomes,the results suggest caution in cutting resources from the traditional role of schools in monitoring a wide set of health outcomes.
©2009Elsevier Ltd.All rights reserved.
1.Introduction
Children with poor health have lower educational attainment,lower social status,worse adult health outcomes,and a higher like-lihood of engaging in risky behaviors than their healthy peers (Case,Lubotsky,&Paxson,2002;Case,Fertig,&Paxson,2005;Jones &Lollar,2008).A particularly potent conduit through which childhood health is linked to adult outcomes is education.Poor health impedes edu-cational progress because a student with health problems is not pre-pared to fully engage in or take advantage of learning opportunities at school or at home (Hanson,Austin,&Lee-Bayha,2004).
Schools have long recognized the relation between student health and educational progress,and have played a role in diagnosing and treating student health conditions related to vision,hearing,and speech impairments,as well as asthma,mental disorders,and more recently obesity (Council of Chief State School Of ficers,1998).Research from the medical community con firms that common health conditions can have negative consequences on children's ability to learn.Vision problems in children are associated with developmental delays and often require special education and additional services beyond childhood (Centers for Disease Control,2004).Children with asthma miss more days of school than children without asthma,and experience restrictions in other daily activities,such as play and sports (Newacheck,2000).Signi ficant hearing loss among children can interfere with phonological and speech perception abilities required for language learning,which subsequently
can lead to low academic performance,especially in reading (National Institutes of Health,1993).Children with speech impairments score lower on reading tests than children in non-impaired comparison groups (Catts,1993).
Further research from social scientists and others,using a variety of data sets and statistical methodologies,con firms the findings from the medical community.Spernak,Schottenbauer,Ramey,and Ramey (2006)find that,among former Head Start children,those with poor general health have signi ficantly lower achievement scores than children in good general health in third grade,but no differences in achievement scores in kindergarten.Sigfúsdóttir,Kristjáansson,and Allegrante (2007)explore the relation between health behavior and academic achievement in Icelandic school children.They find body mass index (BMI)was most strongly associated with academic achievement,followed by diet and physical activity.Datar and Sturm (2006)and Datar,Sturm,and Magnabosco (2004)find that being overweight is associated with lower test scores in elementary school.In contrast,Grossman and Kaestner (2008)find that in general,children who are overweight or obese have test scores that are about the same as children with average weight.1Sabia (2007)and Ding,Lehrer,Rosenquist,and Audrain-McGovern (2006)both find a neg-ative correlation between being overweight and grade point average.Currie and Stabile (2006)find that Attention De ficit Hyperactivity Disorder (ADHD)has large negative effects on test scores and
Children and Youth Services Review 32(2010)231–238
⁎Corresponding author.Tel.:+18014224883;fax:+18014220194.
E-mail addresses:eide@ (E.R.Eide),showalter@ (M.H.Showalter),dgoldhab@ (D.D.Goldhaber).
1
It is not clear why some studies find a negative correlation between overweight/obesity and test scores,while others do not.Reconciling these results is beyond the scope of this paper,and is an area for further
research.
0190-7409/$–see front matter ©2009Elsevier Ltd.All rights reserved.doi:
10.1016/j.childyouth.2009.08.019
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schooling attainment,while Ding et al.(2006)find that depression can lead to a substantial decrease in grades.As schools invest in their students'health through the diagnosis and treatment of these health conditions,students'educational achievement can likely be improved.
In recent years education policy makers have focused on accountability-based education reforms that are intended to improve student educational outcomes.Most prominent among these educa-tion reforms is The No Child Left Behind Act(NCLB),which requires all traditional public school students,including defined sub-groups (e.g.race/ethnicity),to reach academic proficiency by the2013–2014 school year.Progress is tracked by state-wide standardized tests to all students,and schools must demonstrate improvement towards minimum competency targets,or Adequate Yearly Progress,in test scores.Schools that do not improve test scores are subject to a variety of sanctions,including in the most extreme cases restructuring or closure.In principle the threat of sanctions against the school pro-vides incentives for failing schools to improve(Springer,Houck,and Guthrie,2008).
While accountability-based education reform as described above is intended to raise student achievement,it could actually lead to unanticipated negative health consequences for children,which in turn may lower future levels of achievement.When faced with the possibility of sanctions for inadequate progress on standardized tests, schools have an incentive to devote more resources towards core academic instruction and may therefore devote fewer resources to-wards costly non-academic pursuits,such as health care.For exam-ple,schools in the U.S.spend over$2billion a year on school nurses (approximately56,000full-time school nurses with a median salary of$36,000),who play an important role in assessing student health conditions and promoting health at the school(Horovitz&McCoy, 2005),and recent reports suggest some schools have indeed scaled back health programs in order to devote more resources towards improving student test performance(Costante,2002;Deutsch,2000; Hanson et al.,2004).In a related line of inquiry,Chomitz et al.(2009), in summarizing other studies,report that14%of school districts have decreased physical education(PE)time to accommodate more time for math and English,and that the percentage of students participat-ing in PE has fallen from41.6%in1991to28.4%in2003.These authors furtherfind a statistically significant relationship betweenfitness and academic achievement,although the mechanisms underlying the relationship are not clear.For instance,there may be another variable not included in the analysis,such as family socioeconomic status or neighborhood poverty,that may be influencing both physical health and academic achievement.
In this paper we estimate how a variety of student health con-ditions are related to performance on standardized math and reading tests.The health conditions we study are asthma,speech impairment, hearing difficulty,vision problems,ADHD,and being either under-weight or overweight.We use a two-fold estimation approach.First, we use Ordinary Least Squares(OLS)to estimate the relation between the health conditions and the conditional mean of the test score distribution.This tells us,on average,what the relation is between a health condition and test scores.However,just estimating the relation at the mean of the test score distribution may mask differences in the association between health conditions and test scores at other points in the test score distribution,for example at the10th percentile(0.10 quantile)or the90th percentile(0.90quantile).For policy reasons it is important to understand the broader relation between health con-ditions and test scores because the policy response may differ de-pending on the type of student that is most affected.
The second part of our estimation approach uses a statistical technique called quantile regression to account for these possible differential relations between health conditions and test scores. Quantile regression estimates the effect of explanatory variables on the dependent variable at different points of the dependent variable's conditional distribution(that is,conditional on the other explanatory variables).2Our paper is thefirst to explore the relation between health conditions and academic achievement in such a broad way, accounting for both numerous specific health conditions and how those conditions are related to student achievement across the full distribution of achievement.
2.Data
We base our analysis on the Child Development Supplement(CDS) of the Panel Study of Income Dynamics(PSID).The PSID is a nationally representative panel of individuals and their families.3Begun in1968, sampled individuals and families provide information on family com-position,wealth,earnings,expenditures,employment,and a variety of other data.In1997,the CDS was initiated by supplementing the PSID with additional information on families with children ages0–12. The intent was to gather information to add to our understanding of the early formation of knowledge and skills.The CDS includes nu-merous variables describing the home and learning environment of the child:test scores in multiple subjects,behavioral assessments, learning resources,time use,and health status are a few examples. The CDS also gives detailed information on the primary caregiver.
The initial sampling of the CDS selected2705families from the PSID.2394families participated(88%),providing information on3563 children ages0–12.The information from this initial survey is known as CDS-I.A follow-up survey was conducted in2002–2003(CDS-II)on the CDS-I families.2017families(91%)were successfully interviewed, including2908children or adolescents ages5–18.For this study,we use the results from the CDS-II data,along with some background in-formation that was gathered in the CDS-I round of ing the CDS-II gives us the largest sample size possible with these data because the majority of respondents were enrolled in school.We also incor-porate family background variables from the2001PSID interviews.
Our dependent variables are math and reading scores that we stan-dardized to have a mean of zero and a variance of one.This standard-ization allows us to interpret the regression coefficients in standard deviation units.The test scores are the Woodcock–Johnson Revised Tests of Achievement(WJ-R),Form B(Woodcock&Johnson,1989).Our math score comes from the Applied Problems subtest and our reading score comes from the Passage Comprehension subtest.4We use stan-dardized math and reading scores as dependent variables because they are reasonable measures of how much students are learning in school, and therefore suggest how much worse off children with health con-ditions may be in terms of learning relative to their healthy peers.
The set of student health conditions that we use are chosen because they represent the types of health issues that schools typically try to diagnose and assist in treating.We include binary variables that equal one if the child's doctor or health professional diagnosed the child with asthma,speech impairment,hearing problems,serious vision pro-blems,or ADHD(or hyperactivity or ADD).To be clear about what these health variables are measuring,in Appendix A we provide the wording of the health condition questions in the CDS questionnaire. Because these are binary variables,they measure the presence or absence of a particular condition,and do not measure the extent or seriousness of the condition.We also include binary variables for whether the child is in the10th percentile of the age–gender specific BMI distribution,and if the child is at or above the90th percentile of 2See Koenker and Hallock(2001)for an excellent overview of quantile regression. See Eide,Showalter,and Sims(2002)for an example of a paper using quantile regression to study education issues.
3See for more information on the PSID.
4Since the WJ-R can be used for respondents from ages2to90years,items in the WJ-R are arranged by difficulty for all persons between those ages.The easiest questions are presentedfirst and the items become increasingly difficult as the respondent proceeds through the test.The interviewer starts testing at the appropriate starting point based on education level of the child or youth as the general guideline. For additional details see /CDS/cdsii_userGd.pdf.
232 E.R.Eide et al./Children and Youth Services Review32(2010)231–238
the age–gender specific BMI distribution.These variables are intended to capture the correlation of being underweight or overweight with student achievement.5We provide a correlation matrix of the student health variables in Appendix B.
In choosing home environment variables we rely on measures that have been shown in economics and education research to be correlated with student achievement(Hanushek,1986;Rice& Schwartz,2008).Including these variables in the regressions allows us to distinguish the influence of the health conditions from ob-servable family background circumstances.We include quantitative measures for family income in2001,the head of household's years of schooling,the mother's score on a standardized IQ test,and binary variables for whether the family size is greater thanfive,and for whether the child eats breakfast.These control variables are reported in the estimation tables.We provide further definitions of these variables in Appendix C.Also included in the regressions but not included in the tables are binary variables for child's race/ethnicity (black,Hispanic,and other,with white omitted),region of the country where the child lives(north–central,south,and west,with north–east omitted),and quantitative measures for the child's birth weight (measured in ounces),age(measured in months),grade in school, height(measured in inches),and weight(measured in pounds).6 These variables cover many of the characteristics of a student's home environment that are correlated with academic achievement. There is always the possibility,however,that there are unobserved (to the researcher)variables that may influence both the likelihood of being diagnosed with a health problem and test scores.The possi-bility that unobserved variables could bias ourfindings is addressed explicitly in Section3.
To be included in the sample,children must have available data on the test scores and the health indicators,and not be diagnosed with a severe learning disability.7Low income and minority children are overrepresented in the sample due to the sampling strategy of the PSID;however,we condition on family income and race/ethnicity in the regressions so the estimates should not be affected by the sample composition.
Table1presents descriptive statistics of the main analysis vari-ables.The means and standard deviations of the standardized math and reading scores are close to zero and one,respectively.They are not exactly zero and one because the test scores are standardized based on the full sample,and because some observations are dropped when we estimate the regression models(e.g.if data on a health condition is missing)the means and standard deviations based on the estimating samples deviate a bit from zero and one,respectively.The percentage of girls and boys with each health condition is similar in most cases, although somewhat more boys than girls have been diagnosed with speech impairment and ADHD.For both boys and girls the most common health condition is overweight,with31%of boys and27%of girls having this condition.The home environment variables are similar for boys and girls.Average family income(in2001dollars) is around$60,000–$65,000,12–13%of students have a family size greater thanfive,average head of household education is about 13years,and over80%of students eat breakfast.The mother's IQ score is standardized to have a mean of zero and a variance of one.
3.Methodology and estimation
To study the relation between student health and academic achievement,wefirst use OLS to estimate how student achievement changes,on average,as a function of the health conditions and home environment.Second,we use quantile regression to measure the as-sociation between the explanatory variables and test scores at dif-ferent points in the conditional test score distribution.We estimate the quantile regressions at the0.10quantile(or10th percentile),the 0.50quantile(or median),and the0.90quantile(or90th percentile).8 The difference between OLS and quantile regression is that quantile regression explores the relation between the explanatory variables and test scores at any point in the conditional test score distribution, whereas OLS estimates these correlations only at the conditional mean of the test score distributions.Research suggests that there may be differences between boys and girls in how they perform on math and reading tests(boys tend to perform better in math and girls better in reading);therefore,all models are estimated separately for boys and girls(LoGerfo,Nichols,and Chaplin,2006).
5We also estimate our models using the official Centers for Disease Control definitions for underweight(bottom5th percentile),overweight(85th percentile or above),and obese(95th percentile or above)and the results are qualitatively the same.We choose our BMI cut-offs in order to measure being in the tails of the BMI distribution generally,and to assure large enough samples in the tails.Because we include variables for child's height and weight in the models,the BMI dummies measure how being in the tails of the BMI distribution is related to performance, separate from the actual height and weight.
6We do not include school-level variables in the models because our sample contains students from all levels of K-12schooling,and so the school-level variables are not comparable across students.
7After merging data from the CDS II with family background variables from the 2001PSID,we have a sample of2644observations.From that sample there are103 observations missing for the reading score,and19observations missing on the math score.Missing observations on the health variables results in the loss of59 observations for the reading score sample and63observations in the math score sample.To account for the missing values on the home environment and other control variables,we include in the regressions dummy variables that equal one if the data on the particular variable is missing,and equal zero otherwise.We also set the missing values of the explanatory variables to zero.Table1
Sample means of main analysis variables.
Boys Girls
A.Dependent variables
Math score0.010.01
(1.02)(0.97) Reading score−0.060.08
(1.01)(0.97)
B.Health measures
Underweight0.050.05
(0.22)(0.22) Overweight0.310.27
(0.46)(0.44) Asthma0.180.14
(0.39)(0.34) Speech0.090.03
(0.28)(0.18) Hearing0.020.01
(0.14)(0.11) Vision0.050.06
(0.23)(0.23) ADHD0.110.03
(0.31)(0.18)
C.Home environment
Family income60,17865,074
(65,877)(93,674) Family size greater than50.120.13
(0.33)(0.34) Head of household education12.7712.80
(2.65)(2.66) Mother's standardized IQ score0.010.00
(0.99)(1.01) Eats breakfast0.860.82
(0.34)(0.38) Observations a12821280
The health measures in Panel B,“Family size greater thanfive”and“Eats breakfast”in Panel C are all binary variables.Standard deviations are in parentheses.
a Samples used in math models.Reading models have1236observations for boys and 1246for girls.
8Quantile regression at the0.50quantile is also known as“median regression”or “least absolute deviations regression.”More detail on this technique,and its comparison to OLS,is provided in Section5.
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Because our estimating sample is cross sectional and our health indicators are binary variables denoting whether or not the child has been diagnosed with a health condition,there are some limitations to ourfindings that we need to note.As previously stated,our regressions control for numerous individual and family variables.However,we are cautious about applying a“cause and effect”interpretation to the estimates because there may be some unobserved factor that is cor-related with both test scores and health conditions,and hence the mechanisms underlying the relationship are not clear.For example, when students have low test scores,teachers may try tofind a reason why the student is performing poorly.Because a health condition is a possible reason for poor performance,a teacher may be more likely to send a low performing student to the school nurse to be tested for a health problem compared to a student that is not performing poorly. Were this the case,then low performing students would be more likely than higher performing students to be diagnosed with a health condition.
In considering the potential influence of unobserved factors on our estimates,we note that such factors would have to operate in-dependently from the explanatory variables we include,e.g.family income,race/ethnicity,and education.Given our expansive set of covariates,the influence of unobserved variables is plausibly small.To be conservative in our interpretations,we consider our estimates to be a comprehensive descriptive relation between children's health and education outcomes.Additionally,due to data limitations,we do not know if a student diagnosed with a health condition has received treatment for the health condition.We also do not know how many students there are in the sample who have a health condition but who have not been diagnosed.These data limitations could potentially affect the interpretation of our estimates.
4.Results
4.1.OLS math estimates
Wefirst discuss the OLS and quantile regression results for the math achievement models,followed by the reading achievement models.The math regression results are provided in Table2,where each column represents a different regression.Columns(1)–(4)pre-sent results for boys,and columns(5)–(8)the corresponding results for girls.The rows in Panel A show the estimated coefficients for the health measures,and the rows in Panel B the coefficients for the home environment variables.Recall that the test scores are measured in standard deviation units,so the estimated coefficients are interpreted accordingly.The OLS regressions report Huber–White robust standard errors that have also been corrected for family-level clustering(i.e. multiple children from the same family).The quantile regressions report bootstrapped standard errors that have been corrected for family-level clustering.In the tables we put boxes around the statis-tically significant coefficients to make it easier to visually identify patterns across the quantiles.
Table2
Math
achievement for boys and girls.
All standard errors are corrected for family-level clustering and are reported in parentheses.OLS standard errors are robust(Huber–White)and quantile regression standard errors are bootstrapped.Significant coefficients are enclosed in boxes to aid visual identification of patterns across quantiles.
⁎Significant at10%.
⁎⁎Significant at5%.
⁎⁎⁎Significant at1%.
234 E.R.Eide et al./Children and Youth Services Review32(2010)231–238
The OLS math estimates for boys in column(1)of Panel A show that six of the seven health measures are statistically significant;only hearing impairment is insignificant.Speech impairment has the largest coefficient magnitude at−0.226,followed by vision problems and ADHD at−0.149and−0.191,respectively.The OLS coefficient for underweight is−0.124.These estimates suggest that boys who have speech impairment,vision problems,or ADHD can score up to almost one-quarter of a standard deviation lower on the math test than boys without a health condition.The coefficients for asthma and overweight are both positive.These surprising results are discussed in more detail in Section5.
The OLS results for girls in column(5)of Panel A show that only two of the health conditions are negative and statistically significant, although the coefficient sizes of those variables are large.Specifically, girls with either a speech impairment or ADHD score approximately one-quarter to one-third of a standard deviation lower on the math test than girls without one of these conditions.As with boys,girls with asthma score a bit higher on the math test.Overall,the OLS math results for boys and girls demonstrate a substantial correlation between health conditions and the conditional mean of math scores.
Consistent with a large body of empirical literature(e.g.Hanushek, 1986),columns(1)and(5)of Panel B show that the home envi-ronment variables are highly correlated with math achievement for boys and girls at the conditional mean of the math distribution.For both boys and girls,better educated heads of household raise math achievement by3%to5%of a standard deviation,and more intelligent mothers raise math achievement by between7%and9%of a standard deviation.For boys,higher family income and eating breakfast also raise math ing from a large family lowers average math achievement of boys and girls by roughly8–10%of a standard deviation.
Comparing the math OLS results in Panel A to those in Panel B illustrates that the negative coefficient sizes of the health conditions are on the whole larger in magnitude than the home environment coefficients.The takeaway from these OLS math results is that a student's health is highly correlated with math achievement on aver-age,even conditional on home environment.
4.2.Quantile regression math estimates
The OLS results document the relation between health measures and the conditional mean of the math score distribution.It may be the case,however,that health conditions are correlated with math achievement at other points across the conditional math distribution. Indeed,quantile regressions often reveal patterns of correlations across the conditional distribution of the dependent variable that are masked by only looking at the estimates at the conditional mean(i.e. OLS).The quantile regression estimates for boys in columns(2)–(4) and girls in columns(6)–(8)provide the quantile regression estimates.
The results for boys suggest speech impairment and ADHD are negatively associated with math scores across the conditional math distribution.For speech impairment,the largest magnitude is at the0.10quantile(−0.357),with lower coefficients at the median (−0.206)and0.90quantile(−0.229).Boys with ADHD score20–25% of a standard deviation lower than boys without ADHD.These co-efficients suggest boys with speech impairments or ADHD score lower on math tests than boys without these health conditions at each point of the distribution.Moreover,the starkest difference is among the lowest performing boys(0.10quantile).Boys who are under-weight score lower than average weight boys at the median and the 0.90quantile.At the median of the math score distribution for boys, overweight is associated with higher math scores,while vision prob-lems lead to nearly a one-quarter of a standard deviation reduction in math scores.
Turning now to the math quantile regression results for girls,there are fewer significant coefficients than there are for boys.Girls with ADHD score about one-quarter to one-third of a standard deviation lower than otherwise similar girls at the0.10quantile and median, respectively.At the median,the asthma coefficient is positive and the speech impairment coefficient is negative and large(over one-third of a standard deviation).Comparing the math quantile regression estimates for boys and girls,the strongestfindings are that ADHD and speech impairment have the broadest negative correlations with math score performance.
The home environment results for boys and girls in Panel B show that head of household's education and mother's IQ score raise math achievement at multiple points of the conditional math distribution. Family income has positive coefficients for boys across the conditional distribution.
Overall,the math quantile regression estimates lend support to and shed additional light on the OLSfindings on the importance of student health conditions.Whereas the OLS estimates establish a baseline story about the average relation between student health conditions and math achievement,the quantile regression estimates clarify the baseline story by revealing for whom the health conditions matter most;that is,whether health conditions are most correlated with achievement for students who are at the bottom,median,or top of the math distribution.
4.3.OLS reading estimates
The reading results are provided in Table3,which has the same layout as Table2.Focusingfirst on the OLS results in Panel A,boys with speech impairment have lower reading achievement than boys without this condition by31%of a standard deviation.As with math achievement,boys with asthma have higher reading achievement than boys without asthma.For girls,ADHD and speech impairment lower reading achievement by35%and44%of a standard deviation, respectively.Overweight girls have somewhat higher reading achievement than girls who are not overweight.
The home environment OLS reading results in Panel B of Table3 are quite similar to the OLS math results.Higher family income (for boys),better educated heads of household,and more intelligent mothers all significantly raise reading rge family size is correlated with lower reading achievement for both boys and girls. The coefficient for boys is particularly large at nearly23%of a standard deviation.
4.4.Quantile regression reading estimates
The quantile regression results for reading are in columns(2)–(4) for boys and columns(6)–(8)for girls.A few patterns emerge.Speech impairment lowers reading scores at the top half of the conditional reading distribution for boys,and at the bottom half of the distribution for girls.These speech impairment coefficients are large,ranging between−0.235for boys at the0.90quantile and−0.657for girls at the0.10quantile.
In Panel B of Table3,mother's IQ and the head of household's education are positively correlated with reading achievement for both boys and girls across the full conditional distribution.For boys,family size is negatively correlated with reading in the bottom half of the conditional reading distribution,and for girls this relation is significant at the median.Higher family income raises reading achievement at the median for boys,and at the0.90quantile for girls.
Taken together,the OLS and quantile regression results for reading suggest that health conditions are highly correlated with reading achievement.In some cases these associations are persistent across the reading distribution.Based on the number of significant coefficients in Panel B relative to Panel A,the home environment variables overall have broader correlations with reading than do the health conditions.
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