面板分位数

合集下载

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 achievementEric R.Eide a ,⁎,Mark H.Showalter a ,Dan D.Goldhaber ba Brigham Young University,Department of Economics,Provo,Utah,84602,United StatesbUniversity of Washington,Center on Reinventing Public Education,2101N.34th Street,Suite 195,Seattle,WA 98103-9158,United Statesa b s t r a c ta r t i c l e i n f o Article history:Received 4June 2009Received in revised form 25August 2009Accepted 26August 2009Available online 3September 2009Keywords:Child healthAcademic achievement Quantile regressionWe 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.IntroductionChildren 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 subsequentlycan 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 andChildren 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).1It 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 furtherresearch.0190-7409/$–see front matter ©2009Elsevier Ltd.All rights reserved.doi:10.1016/j.childyouth.2009.08.019Contents lists available at ScienceDirectChildren and Youth Services Reviewj o u r n a l h om e p a g e :w w w.e l sev i e r.c o m /l o c a t e /c hi l d yo u t hschooling 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.DataWe 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)231–238the 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 estimationTo 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.Table1Sample means of main analysis variables.Boys GirlsA.Dependent variablesMath score0.010.01(1.02)(0.97) Reading score−0.060.08(1.01)(0.97)B.Health measuresUnderweight0.050.05(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 environmentFamily 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 a12821280The 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 Section5.233E.R.Eide et al./Children and Youth Services Review32(2010)231–238Because 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.Results4.1.OLS math estimatesWeﬁrst 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.Table2Mathachievement 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)231–238The 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 estimatesThe 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 estimatesThe 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 estimatesThe 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.235E.R.Eide et al./Children and Youth Services Review32(2010)231–238。

面板分位数回归模型

面板分位数回归模型面板分位数回归模型是一种用于分析什么因素会影响某个特定变量的统计模型。

它主要应用于面板数据分析中，旨在解释某个因变量在所研究个体之间的差异，以及这种差异如何随着独立变量的变化而改变。

本文将详细介绍面板分位数回归模型的相关概念、假设、解释和应用，帮助读者了解并运用这一模型。

什么是面板数据？面板数据（panel data）顾名思义，就是由多个时间点和多个个体组成的数据。

每个时间点，我们会针对同一组个体（如公司、城市、家庭等）观测它们的某些属性（如收入、投资、人口等）。

这就像一组交叉的时间序列数据，以时间为独立变量、以不同个体为分组变量。

面板数据有很多优点，比如可以避免交叉截面数据的选择偏差，同时可以对个体和时间进行深入分析，从多个角度突出数据中的趋势和变化。

什么是分位数回归？分位数回归是针对因变量分布的不对称性问题，采用分位数的思想进行统计分析的方法。

它在传统回归的基础上，拓展了解释变量和因变量之间的关系，不仅关注均值，还能反映其它分位数点的差异。

这点对于非线性关系、异方差的回归模型而言，具有更广泛的适用性。

例如：如果我们用年收入来预测房价，直接拟合一个经典的线性回归模型可能效果并不好，因为一部分收入较低的人很难买得起较贵的房子，也存在一些高收入者低房价的情况。

如果我们使用分位数回归模型，我们可以更好地理解收入与房价之间的关系，因为我们能够在不同收入分位数下，看到收入与房价之间的具体关系。

面板分位数回归模型（Panel Quantile Regression, PQR）结合了面板数据和分位数回归两者的优点。

它是一种同时考虑时间和空间对一组个体差异进行分析的方法。

通过对每个个体在不同分位数下的条件分布函数建立模型，可以刻画出因变量随着独立变量的不同取值范围的变化规律。

像传统的面板数据模型一样，PQR模型也需要考虑固定效应和随机效应。

固定效应意味着个体之间差异和时间的差异是不同的，这些固定属性与模型中的控制变量一起被引入回归模型中。

面板分位数回归stata命令

面板分位数回归stata命令
面板分位数回归是一种广泛使用的统计方法，它可以用于探究面板数据中的因变量和自变量之间的非线性关系。

Stata软件也提供了一种方便的命令来执行面板分位数回归分析，即xtqreg命令。

xtqreg命令的基本语法如下：
xtqreg depvar indepvars, q(qnum) fe/ re/ be (fixed/ random/ between) cluster(cluster_variable)
其中，depvar是因变量名称，indepvars是自变量名称（多个自变量之间用空格隔开），qnum是分位数的位置（例如q(0.1)代表求解10%位数），fe/re/be是固定效应、随机效应和区间效应的类型（默认为固定效应），cluster_variable是聚类变量名称（用于处理面板带有聚类的数据）。

除了基本语法之外，还有一些可选参数可以根据具体需要进行设置，例如nquantiles（分位数数量）、robust（健壮标准误）等。

在使用xtqreg命令进行面板分位数回归分析时，需要先检验自变量和因变量之间的关系是否存在非线性效应，一种常用的方法是绘制自变量和因变量的散点图并进行观察。

如果存在非线性效应，则可以考虑使用xtqreg命令进行拟合，进一步研究二者的关系。

总的来说，xtqreg命令是一种方便且实用的工具，可用于处理面板数据中的非线性关系问题。

固定效应面板分位数回归常数

固定效应面板分位数回归是一种统计学方法，用于研究面板数据中的异质性效应。

通过控制个体和时间固定效应，固定效应面板分位数回归能够更准确地估计不同分位数的效应。

这种方法在经济学、社会学、政治学等许多领域都有广泛应用。

在固定效应面板分位数回归中，常数项是模型的截距项，它代表了不考虑自变量和时间变量时，因变量的平均水平。

在某些应用中，常数项可能代表了某些个体或时间的基本特征，这些特征对因变量的影响是固定的，不会随着自变量的变化而变化。

在解释固定效应面板分位数回归结果时，需要考虑不同分位数的效应。

这意味着我们需要考虑因变量在不同分位点上的变化，以及这些变化与自变量之间的关系。

通过控制固定效应，我们可以更准确地估计不同个体或时间的基本特征对因变量的影响，并更好地理解这些特征在不同分位点上的作用。

此外，固定效应面板分位数回归还可以用于研究异质性效应。

异质性效应是指不同个体或时间之间的差异，这些差异可能由许多因素引起，包括政策变化、经济环境、文化背景等。

通过固定效应面板分位数回归，我们可以更好地了解这些异质性效应在不同个体或时间上的表现，并据此制定更有效的政策或干预措施。

总之，固定效应面板分位数回归是一种重要的统计学方法，用于研究面板数据中的异质性效应。

通过控制个体和时间固定效应，该方法能够更准确地估计不同分位数的效应，并更好地了解基本特征和异质性效应在不同个体或时间上的表现。

在许多领域中，固定效应面板分位数回归具有广泛的应用价值，有助于我们更好地理解复杂现象并制定更有效的政策或干预措施。

我国碳金融市场中碳交易价格的影响因素分析——基于面板分位数模型

我国碳金融市场中碳交易价格的影响因素分析——基于面板分位数模型我国碳金融市场中碳交易价格的影响因素分析——基于面板分位数模型摘要：碳交易作为实现低碳经济转型的重要手段之一，其交易价格的波动对于我国碳金融市场发展和碳减排的有效实施具有重要影响。

本文针对我国碳金融市场中碳交易价格的影响因素展开研究，采用面板分位数模型对影响因素进行分析并给出结果，为进一步完善碳金融市场体系和提高碳交易价格稳定性提供参考。

关键词：碳交易价格；碳金融市场；影响因素；面板分位数模型一、引言随着全球气候变化问题的日益严重，低碳经济已经成为全球各国共同关注和努力的目标。

而在实现低碳经济转型的过程中，碳交易作为一种市场化手段正在逐渐被引入并发展起来，而碳交易价格的波动对于碳金融市场的稳定运行和碳减排的有效实施具有重要的影响。

二、碳交易价格的基本特征碳交易价格是碳金融市场中最具影响力的指标之一，它的波动程度和趋势可以直接反映市场参与者对碳减排的期望和改变。

本节首先对碳交易价格的基本特征进行介绍。

1. 碳交易价格的波动性碳交易价格具有较高的波动性，这是由于碳交易市场的特殊性和碳减排政策的调整频率较高所致。

碳减排政策的变化和市场预期都会对碳交易价格产生重要影响，因此碳交易价格的波动也是合理的。

2. 碳交易价格的季节性变化碳交易价格在不同季节会出现不同程度的变化。

一方面，季节性能源需求的变化会导致碳交易价格在不同季节呈现出不同的走势。

另一方面，碳减排政策的执行和监管也会随着季节的变化而有所差异，从而对碳交易价格产生影响。

三、碳交易价格的影响因素碳交易价格的波动和变化受到诸多因素的影响。

本节主要分析了一些重要的影响因素，并通过面板分位数模型进行量化和分析。

1. 宏观经济因素宏观经济因素对碳交易价格具有重要的影响作用。

经济增长水平、人均收入水平、产业结构等因素都会对碳交易价格产生影响。

通过分析宏观经济变量与碳交易价格的相关性，可以更好地理解宏观经济对碳交易价格的影响。

基于面板分位数回归的甲状腺癌患者住院费用影响因素探析

基于面板分位数回归的甲状腺癌患者住院费用影响因素探析查清汪卓赟［摘要］　目的　分析甲状腺癌患者住院费用影响因素，为医院合理控制甲状腺癌患者住院费用，降低患者疾病经济负担提供依据。

方法　收集2018年1月1日至2022年12月31日中国人民解放军海军安庆医院收治的共1 464例甲状腺癌患者住院费用信息，采用分位数回归模型，以住院费用的不同分位数为基准，划分为低、中、高分位组，分析患者在3个分位组住院费用影响因素。

结果　1 464例甲状腺癌患者人均住院费用为11 949.38元。

分位数回归模型显示是否手术、淋巴结转移和住院天数在3个分位组均正向影响（β＞0）住院费用；年龄、性别负向影响（β＜0）低分位组住院费用；患者为首次入院负向影响（β＜0）中高分位组住院费用。

结论　甲状腺癌患者住院疾病经济负担较高，需从费用结构、住院时长和临床路径等途径切入，进一步降低住院费用。

［关键词］甲状腺癌；住院费用；分位数回归doi:10.3969/j.issn.1000-0399.2023.09.023Exploration of factors influencing hospitalization cost of thyroid cancer patients based on panel quantile regression ZHA Qing 1，WANG Zhuoyun 21.Department of Nuclear Medicine ， Anqing Hospital of the Chinese People's Liberation Army Navy ，Anqing 246001，China2.Department of Tendering and Procurement Office ，the Second Affiliated Hospital of Anhui Medical University ，Hefei 230601，China Funding project:Health soft science Research Project of Anhui Medical Association （2020WR02017）Corresponding author:WANG Zhuoyun ，***********************[Abstract ] Objective To analyze the influencing factors of hospitalization expenses for thyroid cancer patients ，and provide a basis forhospitals to reasonably control the hospitalization expenses of thyroid cancer patients and reduce their economic burden of disease. Methods A total of 1 464 thyroid cancer patients' hospitalization expenses were collected from a hospital in Anhui Province from January 1, 2018 to De‐cember 31, 2022. Using the Quantile regression model, the hospital expenses were divided into low, medium and high quantile groups based on different Quantile of hospitalization expenses, and the factors affecting the hospitalization expenses of patients in the three quantile groups were analyzed. Results The average hospitalization cost for 1 464 thyroid cancer patients was 11 949.38 yuan. The Quantile regression model showed that whether surgery, lymph node metastasis and hospital stay all had positive impact on hospitalization expenses of the three quantile groups (β＞0). Age and gender had negative effects on hospitalization expenses of low percentile group (β＜0). First admission for patients had negative impact on hospitalization expenses for the middle and high percentile groups （β＜0）.Conclusions The economic burden of hospital‐ization for thyroid cancer patients is relatively high and it is necessary to further reduce hospitalization costs through approaches such as coststructure, length of hospitalization, and clinical pathway.［Key words ］ Thyroid cancer ；Hospitalization costs ；Quantile regression甲状腺癌是一种常见于头颈部的内分泌系统恶性肿瘤，主要表现为颈部结节或肿块。

基于面板数据的分位数回归及实证研究

基于面板数据的分位数回归及实证研究《基于面板数据的分位数回归及实证研究》近年来,分位数回归技术已被广泛应用于经济学、行为经济学和金融学中。

它引入了一个新的参数,称为“分位数”,它可以用来捕捉数据的分布特性,用于信息提取。

近年来,面板数据回归是一种非常有用的统计模型,它包含一个面板数据集和一个自变量。

然而,到目前为止,尚不清楚面板数据集与分位数回归技术的关系。

本研究旨在探讨基于面板数据的分位数回归及其应用。

首先,本文将介绍面板数据回归模型及其特点。

面板数据回归模型是一种多元回归模型,旨在研究一组观察单位上的一项或多项变量的关系。

面板数据回归的定义可以分为两类:平面和时间面板数据回归。

平面面板数据回归模型包括固定效应模型、描述性统计模型和混合效应模型。

一般来说,平面面板数据回归模型可以提供有关多个观察单位之间指定变量关系的重要信息。

另一方面,时间面板数据回归模型可以捕捉面板数据中时间序列变量之间的关系,并可以计算观测时间内因变量的变化。

然而,平面和时间面板数据回归模型都存在一定的局限性,例如不能很好地处理数据的变成断点特性。

其次,本文将介绍分位数回归模型。

分位数回归是一种具有非常强大拟合功能的多元回归分析方法。

它的基本原理是引入一个新的参数,将模型参数分离,以捕捉分布特性。

另外,分位数回归模型具有良好的信息提取功能,因此,它可以用来预测模型中变量的分布情况。

本文还研究了分位数回归模型的优化方法,例如最小二乘法,贝叶斯估计法和最大似然估计法。

最后,本文将探讨基于面板数据的分位数回归技术应用。

一般来说,分位数回归技术可以有效地处理面板数据中的空间和时间变量,从而捕捉和提取面板数据的分布特性。

来自德国的一项研究表明,基于面板数据的分位数回归可以有效地捕捉数据特性,它能够准确描述数据的分布特性,并可以提供有关多个观察单位之间指定变量关系的重要信息。

此外,在很多应用中,如金融学、宏观经济学和行为经济学等领域,基于面板数据的分位数回归技术可以提供更加完整的结果。

基于面板分位数回归的住宅价格影响因素分析

金和地价在大都市区之间差异的最重要因素% 5QCIHT 和 _;H9!&"'"$研究了美国人口结构的变化对住宅市场的影响"认为二战后 )婴儿潮*时期出生的一代进入购房阶段是 $% 世纪 A% 年代美国房地产价格上涨的主要原因&$'%5QCCHCV!&"'"$利用美国 "?个大都市地区&"'%年的数据估计了住宅价格模型"实证结果表明适宜的气候对住房价格有正的影响并且在统计上是显著的 % &!' fSHV9;]!&"""$用 &"'>+&""?年?&个大都市地区的数据研究了住房价格与住房开工率 (人口总数 (收入及失业率等之间的关系"结果表明经济基本面因素的相关指标能够在一定程度上解释住宅价格的变化&?'%,;UQYI !$%%#$研究了明尼苏达州的公立学校和住宅价值" 研究发现在那些学生能够进入更好学校的社区"住宅的价值更高&#'%KSD 和 _HCI9;G!$%%$$考察了美国&!%个大都市统计区的房价动态"发现房价主要受人口增长率(实际收入(建筑成本(股票价格以及地理位置的影响 % &>' 5H99;G和 LHQCV!$%%>$选取美国$$A个大都市统计区的数据"并利用 P.,2) 模型和面板 7., 模型研究了美国住宅价格波动和经济变化 (收入变化的关系 "结果表明居民收入变化对于住宅价格波动存在显著的影响 &A'%)QSGHC!&"">$ 使用多个大都市统计区的数据"在享乐住房价格框架下 "研究房价的决定因素 "发现公立学校的质量对于所在城市的住宅价格有显著的影响 % &''

面板数据分位数回归及其经济应用

面板数据分位数回归及其经济应用面板数据分位数回归是一种多变量回归方法，在经济学中具有广泛的应用。

它通过使用面板数据集，考虑个体和时间的异质性，可以更准确地估计经济变量在不同分位数的变化。

面板数据是指对同一组个体（例如家庭、企业或国家）进行多个时间观察的数据集。

与传统的横截面数据或时间序列数据相比，面板数据具有更多的信息，可以提供更准确的估计结果。

面板数据分位数回归将这些数据应用到经济学研究中，以分析变量在不同分位数下的影响和变化。

面板数据分位数回归的基本思想是将依变量和解释变量的关系扩展到不同的分位数。

传统的回归模型通常使用一个条件的均值作为衡量标准，而忽略了分布的其他信息。

而面板数据分位数回归通过分析不同分位数下的条件均值，可以确定变量对于不同个体和时间的异质性的影响。

面板数据分位数回归在经济学中有许多重要的应用。

首先，它可以用于研究不同收入群体的收入差距。

通过将个体收入与其他解释变量的关系扩展到不同收入分位数，可以更好地理解收入分配的变化和影响因素。

这对于制定公共政策和减少贫困具有重要意义。

其次，面板数据分位数回归可以用于研究教育、健康和劳动力市场等领域的不平等问题。

通过分析不同分位数下的教育水平、健康状况和工资收入等变量，可以揭示不同个体和时间的异质性，并提供政策建议。

此外，面板数据分位数回归还可以用于分析企业和产业的效率和生产力的变化。

通过将生产率和利润等变量与其他解释变量在不同分位数下的关系进行比较，可以对企业和产业的差异进行深入研究，为企业管理和政策制定提供参考。

总之，面板数据分位数回归是一种重要的经济学方法，它能够更准确地分析经济变量在不同分位数下的变化。

它在研究收入差距、教育和健康不平等、企业效率等方面具有广泛的应用前景。

通过利用面板数据的丰富信息，我们可以更好地理解经济现象，为公共政策和管理决策提供科学依据。

stata面板数据分位数回归代码

Stata 是一个流行的统计软件，它提供了丰富的功能用于数据分析和回归分析。

面板数据分位数回归是一种常用的统计方法，可以用来研究不同分位数下自变量和因变量之间的关系。

在 Stata 中，可以通过简单的代码实现面板数据分位数回归分析。

本文将介绍如何使用 Stata进行面板数据分位数回归分析，并给出相关的代码示例。

二、面板数据分位数回归介绍面板数据分位数回归是一种利用面板数据进行分位数回归分析的方法。

在面板数据中，每个观测对象都有多个时间点的观测值，可以用来研究因变量在不同分位数下与自变量之间的关系。

与传统的 OLS 回归相比，分位数回归能够更好地反映数据的分布特征，对异常值具有更好的鲁棒性。

在 Stata 中，可以使用 quantreg 命令进行分位数回归分析。

该命令可以指定分位数水平，还可以对面板数据进行分析。

三、面板数据分位数回归代码示例以下是一个简单的面板数据分位数回归代码示例：use panel_data, clearquantreg y x1 x2, tau(0.25 0.5 0.75)```以上代码首先加载面板数据集 panel_data，然后使用 quantreg 命令进行分位数回归分析。

在该命令中，y 是因变量，x1 和x2 是自变量，tau(0.25 0.5 0.75) 指定了分位数水平，这里分别为 0.25、0.5 和 0.75。

四、代码解释在上面的代码中，quantreg 命令表示进行分位数回归分析。

y 表示因变量，x1 和 x2 分别表示两个自变量。

tau(0.25 0.5 0.75) 指定了分位数水平，可以根据实际需求进行调整。

五、结果解释运行以上代码后，Stata 会输出每个分位数水平下的回归结果。

可以得到每个自变量的系数估计值、标准误、t 值和 p 值等统计量。

还可以得到残差项的统计量和回归模型的 R-squared 值等信息。

六、总结面板数据分位数回归是一种常用的统计方法，可以用来研究不同分位数下因变量和自变量之间的关系。

4.面板分位数回归模型

本文使用似然比检验来检验零假设β=0和
（25）
3 研究过程——竞争模型及评价方法
经济上的评价：一般地，最优投资组合的有效边界的构建有两种等同的方式：（1）不同水平的投资组合风险价值下的期望收益最大化。（2）不同水平的投资组合期望收益下的风险价值最小化。
（26）
3 研究过程——竞争模型及评价方法
3 研究过程——竞争模型及评价方法
原始的计算VaR的参数方法：
（17）
投资组合的波动率：
（18）
因此我们可以计算给定投资组合的风险价值比率（%VaR）：
（19）
（20）
（21）
3 研究过程——竞争模型及评价方法
统计上的评价：对于绝对表现的评价本文采用CAViaR检验，定义“hit”：
（22）（23）（24）
3 研究过程——仿真研究
样本内拟合：下表展示了三个模型在经济角度看最重要的四个分位数5%、 10%、90%、95%的估计结果（Monte-Carlo模拟）：
显著显著，但系数小于上面的
系数跟PQR-RV基本一样系数小且不显著
3 研究过程——仿真研究
样本外表现（无条件覆盖的测量和CAViaR检验）：
CAViaR检验无条件覆盖的测量
红框内的是各分位数上平均偏差最小的值，除了50%以外，PQR和UQR在各分位数上的平均偏差基本上是最小的。这几个模型除了50%以外，平均偏差均是接近0的，表明没有模型是systematically misspecified的。
3 研究过程——仿真研究
样本外表现（Diebol-Mariano检验）：
（2）另外一个吸引点是维度的减少，因为估计参数的数量总是小于或等于k+n（k是回归量，n是资产的数量）。

地方政府债务对区域金融发展的影响——基于面板分位数的研究

(１．兰州财经大学金融学院,甘肃兰州７３００２０;２．西南财经大学金融学院,四川成都６１００７４)
摘要:防控地方政府债务风险是守住不发生系统性金融风险的重中之重,地方政府债务对区域金融安全的影响不容忽视.本文基于２００７~２０１６年省级面板数据,采用面板分位数回归方法实证检验了地方政府债务与区域金融发展的关系.研究结果表明:地方政府举债融资会显著促进地区金融发展,有利于实现金融资源优化配置,但在不同金融发展水平的分位数上影响系数存在显著差异;金融发展相对落后地区的地方政府在举债融资过程中处于劣势,地方政府债务带动金融资源配置的效果较弱.金融发展落后地区必须着力改善金融生态环境 ,提高金融资源配置效率 ,方能增强地方政府债务的资源配置效率 .
１０５
地方政府债务与金融发展的关系并把握二者的发展态势 ,才能积极应对地方政府债务对区域金融安全可能造成的影响.
二、文献述评
虽然理论界关于地方政府债务与金融发展关系的研究起步较晚,而关于地方政府行为与金融发展关系的研究则较为丰富,这些文献为本文研究工作提供了有益借鉴.与本文内容相关联的有如下三方面文献.
关键词 :地方府债务 ;分位数回归 ;金融发展 ;资源配置效率中图分类号 :F８１２．５文献标识码 :A 文章编号 :１００３Ｇ５２３０(２０２０)０１Ｇ０１０５Ｇ０９

分位数面板门槛回归模型

分位数面板门槛回归模型英文回答：Quantile regression is a statistical technique that allows us to estimate the relationship between a set of independent variables and different quantiles of the dependent variable. It is particularly useful when the distribution of the dependent variable is not symmetric and we are interested in understanding how the relationship between the variables changes across different parts of the distribution.Panel data refers to data that is collected over time on multiple individuals or entities. In the context of quantile regression, panel data can be used to estimate the quantile regression coefficients for each individual or entity over time.The threshold regression model, also known as the quantile regression with threshold effects, is an extensionof the quantile regression model that allows for non-linear relationships between the independent variables and the dependent variable. It assumes that the relationship between the variables changes at a certain threshold value. This threshold value can be interpreted as the point at which the relationship between the variables switches from one quantile to another.To estimate the quantile regression coefficients in a panel data setting, we can use a fixed effects or random effects approach. The fixed effects approach controls for individual-specific characteristics that do not vary over time, while the random effects approach allows for individual-specific characteristics that vary over time.For example, let's say we are interested in understanding the relationship between income and education level on different quantiles of happiness. We have panel data on individuals over a period of 10 years. We can estimate the quantile regression coefficients using the fixed effects approach to control for individual-specific characteristics that do not change over time. This wouldallow us to understand how the relationship between income and education level varies across different quantiles of happiness for each individual over time.中文回答：分位数回归是一种统计技术，可以用来估计自变量与因变量不同分位数之间的关系。

面板数据门限分位数回归模型及应用

足括号内的条件时，I (×) = 1 ，否则 I (×) = 0 。
1.2 参数估计
PTQR 模型的参数估计可通过优化式（2）得到：
( ) θ̂1(τ)θ̂ 2(τ)θ̂ 3(τ)γ̂ 1(τ)γ̂ 2(τ)
( ) =
arg
θ1
min
θ2 θ3 γ1
γ2
S
(θ1
τ
θ2
åå ( ( | )) N T
(
τ
)
θ
3(
τ
)
γ1(
τ
)
γ
2(
τ
))
=
arg
θ1
min
θ2 θ3 γ1
γ2
i
=
1
t
=
1
ρ
τ
yit - Qyit
τ
xit
（2）
其中，S(θ1(τ)、θ2(τ)、θ3(τ)、γ1(τ)、γ2(τ)) 为目标函
数；ρτ(u) 为非对称损失函数，满足：
{ ρτ(u) =
τu, u ³ 0
(1 - τ)u, u < 0
二个门限值 γ̂ 2(τ) 是基于第一个门限值 γ̂ 1(τ) 确定存在的
条件下获得的，具有一致性；但估计的第一个门限值是基
于假定无门限的条件下，利用加权的绝对偏差和最小获得
的，不具有一致性。因此，需对第一个门限值 γ̂ 1(τ) 进行重新估计。选取集合 Γ1 中小于第二个门限估计值 γ̂ 2(τ) 的
（1）
( | ) 其中，τ(0 < τ < 1) 为分位点；Qyit τ xit 表示给定 xit 条
件下 yit 的第 τ 条件分位数；γ1(τ) 和 γ2(τ) 为门限值，α(τ)

面板分位数

分位数回归（Quantile Regression）的思想最早是由科恩克和巴塞特（1978）提出的，它是对古典条件均值模型为基础的最小二乘的拓展。

普通最小二乘法（OLS）是利用因变量的条件均值来建模，通过使残差平方和达到最小值来获得对回归参数系数的估计值；分位数回归则利用因变量的条件分位数来建模，通过最小化加权的残差绝对值之和来估计回归参数，它又可以称之为“加权的最小一乘回归法”。

两种方法相比较，分位数回归模型具有多方面的优势：首先分位数模型特别适合存在异方差性的模型；其次在对条件分布的刻画方面更为细致，能给出条件分布的大体特征；在模型假设方面，OLS法要求满足经典假设的多个条件，而分位数回归法只要求符合扰动项e_i~F_i的条件下F_i^(-1) (τ)=0；在估计方法上，不同于OLS方法通过使残差平方和最小得到参数估计，QR法通过使加权误差绝对值之和最小得到参数估计，这种方法得到的结果不易受异常值影响，决定了其估计具有较强的稳键性。

分位数可按如下定义：设随机变量Y的分布函数为F(y)=P(Y≤y)，则Y的τ分位数为F^(-1) (τ)=inf⁡{y:F(y)≥τ}以下再以数学公式的形式简要介绍分位数的回归思想。

对于Y的一组随机样本{y_(1,) y_(2,)…,y_n }，样本均值是min∑_(i=1)^n▒(y_i-μ)^2 的最优解。

样本中位数是最小化残差绝对值和的解，即F^(-1) (1⁄2)=arg⁡min┬(τ∈R)⁡∑_(i=1)▒〖|y_i-τ|〗对于其他的第θ分位数,我们可以求解下式，我们可以通过求解以下表达式得到：〖min〗_(β∈R^p ) [∑_(i∈{i:y_i≥τ})▒〖θ|y_i-τ|+〗∑_(i∈{i:y_i<τ})▒(1-θ)|y_i-τ| ]上式可等价表示为：min┬(τ∈R)⁡∑_(i=1)▒〖ρ_θ (y_i-τ) 〗其中ρ_θ (z)=θzI_*0,∞)┤(z)-(1-θ)zI_((-∞,0) ) (z)，该式中I(∙)为示性函数。

基于面板数据的分位数回归及实证研究

基于面板数据的分位数回归及实证研究
分位数回归是近20多年分析和建模技术、计量经济学研究一个重要的分支，它可以有效地捕捉“分位数函数”变量（如消费者市场上的价格和消费量等）受到观测结果所影响的大小和变化，并用于追踪它们受外生决定因素影响的变化。

本文基于面板数据，将介绍分位数回归的一般使用方法及实证研究。

面板数据，学名叫做多维时间序列数据，可以有效地捕捉观测结果所影响的单位，以及时间和特定文化、政治或社会因素的变化。

分位数回归可以用来检查分位数和自身的联系，情形可以多种多样，也可以进一步探索一类分位数变量如消费量受观测结果影响的程度，以检查它们是否可以反映外生决定因素对该类变量的影响。

在应用分位数回归对消费量进行实证研究时，必须定义一个表示消费量的变量，同时还需要定义一个或多个表示外生决定因素的变量，例如价格、收入水平和消费税等，考虑各个变量之间的相互作用，最后得到拟合模型。

通过识别回归中出现的分位数，模型可以更好地表达消费者在购买行为中感受到的价格和税收影响，并以分数形式表示，比如税收所占价格比例是多少，以及存在什么样的高或低价格范围。

本文介绍了基于面板数据的分位数回归方法及实证研究，它具有良好的可扩展性，可以用来检查外生决定因素（如收入水平、价格和税收）对消费量的影响。

本文介绍的方法可以为研究者提供更好的研究数据和方法，可以作为为决策制定民意调查、财经预测或其他研究的有力参考。

面板数据分位数回归模型的参数估计与变量选择

研究了分位回归模型及其估计．王新宇［３］系统地介绍了分位数的基本模型及其扩展、分位数回归模型的经典统计推断．Ｔａｎｇ等【］研究了加权复合分位数ｆＷＣＱ）与随机截尾线性回归模型．在这个模型中，提出了可变选择的自适应惩罚程序，并证明了一致性和渐近正态性．Ｗａｎｇ和Ｙｉｎ【ｌ研究了无界意义下的在线变化分位数回归算法．分位数回归模型中的变量选择问题一直受到广泛的关注．Ｓｈｏｗｓ等［０】针对一种多元线
性模型，提出了对随机删失数据的白适应Ｌａｓｓｏ加权ＬＡＤ（ＡＷＬＡＤ）变量选择方法．Ｗａｎｇ等［７］提出了ＢＩＣ调整参数选择方法，证明了这种方法能够辨别出真模型，并在模拟中验证了理论的有效性．Ｗｕ等（Ｊ研究了惩罚分位数回归，在一些较弱的条件下得到了ＳＣＡＤ和自适应Ｌａｓｓｏ惩罚分位数回归的Ｏｒａｃｌｅ性质．Ｚｏｕ［９】提出了分位数回归模型的自适应Ｌａｓｓｏ的变量选择方法，也得到了其Ｏｒａｃｌｅ性质．吕亚召等［１ｏ］研究部分线性单指标复合分位数回归
收稿日期：２０１５ — ０９．２６接收日期：２０１６ — ０２．２５
基金项目：国家自然科学基金资助（１１２０１３５６）．作者简介：何晓霞（１９７９一），女，湖北大悟，副教授，主要研究方向：数理统计

面板分位数模型指标替代

面板分位数模型指标替代
面板分位数模型是一种常用的经济学分析工具，它可以用来研究各种经济现象和政策效果。

然而，这种模型在实际应用中存在一些问题，其中之一就是指标的选择和使用。

传统的面板分位数模型通常使用诸如收入、教育水平、就业率等指标来解释变量之间的关系，但这些指标并不一定能够准确反映真实的情况。

因此，研究者们开始尝试使用一些替代性指标，以提高模型的准确性和可靠性。

替代性指标的选择应基于以下几个原则：一是指标应该具有代表性和可比性，能够准确反映研究对象的特征和变化趋势；二是指标应该具有可测性和可靠性，能够被准确地观察和记录；三是指标应该具有解释性和预测能力，能够有效地解释模型中的变量关系和预测未来趋势。

一些常用的替代性指标包括国内生产总值、物价指数、人口结构、社会保障支出等。

这些指标可以提供更全面和准确的信息，有助于研究者们更好地了解经济现象和政策效果。

在使用这些指标时，需要注意数据来源和质量，以保证模型的可靠性和有效性。

总之，替代性指标的使用可以提高面板分位数模型的分析能力和预测能力，为经济学研究和政策制定提供更有力的支持。

- 1 -。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

分位数回归（Quantile Regression）的思想最早是由科恩克和巴塞特（1978）提出的，它是对古典条件均值模型为基础的最小二乘的拓展。

分位数可按如下定义：设随机变量Y的分布函数为F(y)=P(Y≤y)，则Y的τ分位数为
F^(-1) (τ)=inf⁡{y:F(y)≥τ}
以下再以数学公式的形式简要介绍分位数的回归思想。

对于Y的一组随机样本{y_(1,) y_(2,)…,y_n }，样本均值是min∑_(i=1)^n▒(y_i-μ)^2 的最优解。

样本中位数是最小化残差绝对值和的解，即
F^(-1) (1⁄2)=arg⁡min┬(τ∈R)⁡∑_(i=1)▒〖|y_i-τ|〗
对于其他的第θ分位数,我们可以求解下式，我们可以通过求解以下表达式得到：
〖min〗_(β∈R^p ) [∑_(i∈{i:y_i≥τ})▒〖θ|y_i-τ|+〗∑_(i∈{i:y_i<τ})▒(1-θ)|y_i-τ| ]
上式可等价表示为：
min┬(τ∈R)⁡∑_(i=1)▒〖ρ_θ (y_i-τ) 〗
其中ρ_θ (z)=θzI_*0,∞)┤(z)-(1-θ)zI_((-∞,0) ) (z)，该式中I(∙)为示性函数。

对于一般线性条件均值函数E(Y|X=x)=x^' β，通过求解β=arg⁡min┬(β∈R^p )⁡∑_(i=1)^n▒(y_i-x_i^' β)^2 得到模型的参数估计值。

而一般线性条件分位数函数为Q(θ|X=x)=x^' β(θ)，使用具体方法和工具进行求解得到模型的参数估计值
β(θ)=arg⁡min┬(β∈R^p )⁡∑_(i=1)^n▒〖ρ_θ (y_i-x_i^' β) 〗
对于任意的θ∈(0,1)，估计β(θ)即称为第θ分位数下的回归系数估计。

根据已有文献归纳，常见的分位数回归参数估计方法主要有：单纯形算法(Simplex Method)，内点算法(Interior Point Method)，平滑算法(Smoothing Method)和其他算法如adaptive method等。

面板数据分位数回归是指将分位数回归方法应用于面板数据实证分析的参数估计当中，这利益于科恩克（2004）的研究成果，他成功的将分位数回归估计思想和方法扩展运用于面板数据固定效应模型的估计中。

这一方法的创新对于面板数据的估计有着重要意义，通过引入分位数回归方法，可以更好的控制个体差异，在此前提下被解释变量条件分布在不同分位点上与各种解释变量的关系能够得到更完美的分析。

常见的面板数据模型主要有固定效应模型、随机效应模型和混合估计模型，其中混合估计模型一般被当作普通最小二乘模型进行估计；随机效应模型中不可观测的因素往往与解释变量存在相关性，所以在估计时通常采用广义最小二乘估计法。

固定效应模型的典型特点是不同的横截面或者时间序列对应着不同的截距，因此在具体估计时可通过在分位数回归中加入虚拟变量的方法得到参数估计值。

本部分将以面板数据分位数模型实证分析金融因素及其他主要变量对处在不同分位点的我国对外直接投资的影响情况。