The Impact of Childhood Events on Educational Achievement: A Sibling Study

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(1)The Impact of Childhood Events on Educational Achievement: A Sibling Study Fung-Mey Huang. . In this study we reexamine the association between childhood events and children's later educational achievement by constructing a sibling data set from the Panel Study of Income Oynamics (PSID) survey. Fixed effects models with sibling data are used to control for the unobserved characteristics that drive the outcomes of both childhood events and children's later educational achievements and the correlation among siblings. There are several differences in the ndings of conventional estimations and xed effects estimations. The results from the xed-effects estimations show that: (1) Children who experienced parental separation and lived extensively in single-parent families had substantially lower educational achievement. Children with a parent who had remarried had substantially higher educational attainment than those with a single parent who did not remarry. (2) Children of working mothers exhibited statistically no difference in educational achievements compared with children whose mothers did not work. (3) The number of siblings and location moves had no signicant impacts on children's educational achievements. The correlation between these events and unobserved family heterogeneity might be the causes of the differences. Keywords:. childhood effects, educational achievement, xed effects, semi-parametric estimation J10, J20. JEL classication:. Assistant Research Fellow, Institute of Economics, Academia Sinica. I would like to thank two anonymous referees and the managing editor for helpful comments and suggestions. Any remaining errors are entirely my own responsibility.. %d (Taiwan Economic Review), 28:4 (2000), 425 450 % | lename: le284-3, 2-25-2003].

(2) 426. Fung-Mey Huang. 1 Introduction Over the last ten years there have been many studies using household longitudinal data sets to investigate how family and neighborhood characteristics when children grow up inuence their later achievements. They found that living in a non-intact family has adverse consequence and a working mother has benecial consequence for children's later educational outcomes. However, those ndings are questioned by two econometric problems arising in those investigations. First, most of previous literature (except Manski, 1992) overlooks that some unobserved family factors might jointly drive the family and neighborhood events and their children's outcomes. Without taking into account the impacts from those unobserved parental characteristics, previous research may not be able to estimate the true effects of family events on their children's later educational achievements. Second, the household longitudinal data sets usually contain a large number of siblings. Without controlling for the unobserved parental characteristics that are common among siblings, the distributions of disturbance terms will not be independent among siblings. The estimates of the causal relationship between family events and children's outcomes in previous studies will then be biased and inconsistent. As regard the rst problem mentioned above, for example, parents who are less committed to their families may be more likely to divorce and may also provide less guidance and emotional support to their children. Behavioral and/or medical problems such as alcoholism, depression, drug addiction, anxiety, or low self-esteem may make a person more likely to divorce and less effective as a parent (Manski 1992). Similarly, working mothers may be, as the empirical evidence suggests, benecial for their children. However, it may be that some unobserved maternal characteristic results in such benecial consequences, but not working per se. For example, mothers who have behavioral, health, drug, and/or medical problems may be less likely to work and also provide less guidance to their children with regard to human capital accumulation. Mothers who have desirable observed characteristics (e.g., higher education) and unobserved characteristics (e.g., a stronger desire for higher achievement) may be more likely to work outside of the household and may be more effective in choosing a good educational environment for their children. The positive relationship between mother's working and children's later educational outcomes in previous studies may capture the positive interaction between the working and some unobserved maternal characteristics. Clearly, without controlling for the unobserved maternal characteristics, the true effect of a working mother on children's later educaet al.. et al..

(3) The Impact of Childhood Events on Educational Achievement. 427. tional outcomes will not be obtained. Concerning the second problem, if we selected children aged 0 to 6 in 1968 from PSID data and traced them until they were aged 20 to 26 in 1988, more than 60 percent of the sample would have grown up in overlapping families. The unobserved parental characteristics would then be the same or highly correlated among siblings, and the error terms in the previous studies will not be independent across siblings. Obviously, the use of ordinary least squares in a linear model or probit or logit in a probability model gives biased and inconsistent estimates of the causal relationship between the explanatory variables and the outcome. In this study we carefully reexamine the association between family events during the childhood period and children's later educational achievement. By doing so, we rst construct a sibling data set from PSID survey and incorporate a substantial observation period of childhood circumstances. Second, we adopt the xed-effects models by using sibling data to deal with the econometric problems that previous research confronted.1 Fixed-effects models take into account the correlation between the unobserved family characteristics (mainly parental) and the family events and also the correlation of unobserved family characteristics among siblings. The paper is organized as follows. Section 2. provides a selective review of the economic and sociological literature that focuses on the relationship between educational attainment and family structure and their parents' work pattern when they grew up. Section 3. describes the xed-effects models and the estimation methods that we use for this study. Three indicators of educational attainment are studied: the years of schooling, high school graduation, and college entry. Section 4. describes the data from the 1992 Panel Survey of Income Dynamics survey and the variables we have chosen. The empirical results and conclusions are presented in Sections 5. and 6. respectively.. Since we are examining the effects of several family events, the estimation model will become intractable if, for each family event, we add one more equation to describe the process of each family event. In the xed-effects model, the unobserved xed factor ( xed-effect) can be correlated with the explanatory variables. In a pioneer paper (Mundlak 1963), the production behaviors of a panel of farms were examined. The unmeasured xed input reecting soil quality and other characteristics of the farm's location. The explanatory variables, the measured production inputs such as the quantities of seeds and fertilizer, clearly interacted with the soil quality (the unmeasured xed input). See also Chamberlain (1984) and Hsiao (1986). 1.

(4) 428. Fung-Mey Huang. 2 Selective Literature Review The determinants of educational achievement have long been extensively studied by both economists and sociologists. Recently, due to the availability of a substantial observation period of family circumstances from longitudinal data sets, the impacts of family circumstances on children's later educational attainments are investigated. In this section, we selectively review some literature that is closely related to our study. For an extensive survey, please see Haveman and Wolfe (1995). At the heart of the human capital model, economists view education as an investment of current time and money for future consumption. When children are young, parents decide the family's current consumption and investment in order to raise their children's future income as adults. They thereby maximize the family's utility subject to budget constraints, time constraints, and the constraint of the children's educational production function (Becker 1981 and Becker and Tomes 1986). If investment in children is a normal good, the theory of consumer behavior implies that lower prices of education, the reduced cost of time (leisure), higher income, higher preferences for investment, and higher technology of investment raise the amount that parents invest in their children. In this way, they increase their children's future income as adults. In recent empirical analysis, a number of studies have used longitudinal survey data to investigate the relationship between the family's living arrangements and economic circumstances when the children grew up, and the children's later educational achievements. McLanahan (1985), for example, utilized longitudinal data taken from the PSID to address the question of why offspring who have grown up in female-headed households are more likely to drop out of high school. Four hypotheses regarding the effect of a father's absence were tested: the no-effects hypothesis, the economic-deprivation hypothesis, the fatherabsence hypothesis, and the family stress hypothesis.2 Among whites, eco2 In the sociology literature, there are several hypotheses concerned with the negative associations between single-parent families and their children's attainments. (1) The economicdeprivation hypothesis states that poor families' economic circumstances in single-parent families are associated with the smaller investment in their children and consequently result in the children's lower attainments (McLanahan 1985). (2) The family-stress hypothesis states that parents' marital disruptions create stress for parents and for their children which involves lack of supervision on the part of parents and also role changes these may result in behavior problems and subsequently in lower attainments (Hetherington 1981 McLanahan 1985). (3) The no-effects hypothesis states that the absence of one parent has no direct consequences for the attainments of the children. The lower attainments among children in single-parent families are hence deemed to be due to race, lower parental education, or lower parental occu-.

(5) The Impact of Childhood Events on Educational Achievement. 429. nomic deprivation and the stress associated with family disruption account for nearly all of the negative effects of family structure on the offspring's attainment, whereas among blacks the results are more mixed. This study's strength lies in the test design for those hypotheses. Its weakness lies in (1) the short length of the observation period and (2) the method used, which did not take into account the potential interaction between the unobserved family heterogeneity and the family events. All of the family circumstances were measured only when the child was 17 years old. Manski, Sandefur, McLanahan, and Powers (1992), in using another longitudinal data set the National Longitudinal Survey of Youth (NLSY)- sought to interpret the association between family structure and high school graduation based on the consideration that some unobserved process may jointly determine family structure and children's outcomes. They developed alternative estimation methods based on different assumptions about the actual process in generating family structure and high school outcomes. All of the results consistently strengthen the evidence that children living in an intact family have a higher probability of graduating from high school. The strength of their analysis lies in the robustness of the results obtained by alternative estimation methods. The weakness of their study lies in the observation period's short length. The family structure was only measured when the child was aged 14. The study by Haveman, Wolfe, and Spaulding (1991) investigated the effects of a variety of childhood events and circumstances on high school graduation by using a richer longitudinal data set taken from the PSID. They traced the family and individual information for each child from ages 04 in 1968 to ages 1923 in 1988. Their estimates suggest that parental education is a positive and signicant determinant of a child's high school completion. Having a working mother while the child is a teen also has a signicant and positive association with high school completion, the inuence being smaller when the child is younger. 3 Other family events such as being persistently poor and on welfare, and moving one's residence as a child, have signicant negative impacts on high school completion. The effects of some family stress and economic events differ depending on the child's age when they occur. The strength of this study lies pation. 3 A mother's work seems to have two offsetting effects. On the one hand, the mother's work contributes income to the family and also provides information or connections related to the job market. Such resources may translate into increased children's attainments. However, on the other hand, the loss in parental time spent with children associated with the mother's market work is viewed as fostering developmental problems in children and reducing their later attainments. The hypothesis yields no unique prediction..

(6) 430. Fung-Mey Huang. on very rich information regarding childhood events. The impacts of different stages of development (ages 47, 811, and 1215) on high school completion are investigated. Their results, again, might be biased due to ignoring the potential interaction between unobserved family characteristics and childhood events and circumstances. In this study, we reexamine the association between family structure and parental work patterns when children are young and the children's later educational achievement. We use the very rich information regarding childhood events from the PSID data set and also employ sibling data and xed effects models to take into account the interaction between the unobserved family factors and childhood events.. 3 Econometric Model and Estimation of the Fixed Effects. Models. The xed-effects models (the xed effects Tobit model and the xed effects Logit model), where the xed effects measure the impacts of unobserved genetic heritage and family characteristics commonly shared by siblings on sibling's educational outcomes, were implemented. Given the similarities of family characteristics among siblings, if the differences among siblings in experiencing family events during childhood years lead to the differences in their later educational outcomes, we are more condent of the associations between the childhood events with educational achievement. The differences of experiencing family events during ages 615 among siblings come from the years of younger and adolescent ages.4 The xed effects Tobit model is used for the years of schooling, and the xed effects Logit model is used for either high school graduation or college entry. Assume a linear relationship between the educational achievement and the observed and unobserved attributes. The xed-effects model can then be written as E ij D 0 X i j C i C "i j i D 1 N I j D 1 Ji (1) where E ij is a latent variable representing the educational achievement of sibling j in family i and X i j is a vector of observed family events and background For example, if sibling 1 was 6 years old and sibling 2 was 1 year old in 1968, the childhood information from ages 6 15 collected includes those events from 1968 to 1977 for sibling 1 and those from 1973 to 1982 for sibling 2. They share the same family information during 1973 1977. The different family information among siblings comes from 1968 1972 for sibling 1 (ages 6 10) and 1978 1982 for sibling 2 (ages 11 15). 4.

(7) The Impact of Childhood Events on Educational Achievement. 431. variables of sibling j in family i . The terms i represents the unobserved family factors commonly shared by all siblings in family i and "i j are the unobserved individual factors, which are assumed to be independent of X i j and of i . In the xed effects model, i are allowed to be correlated with X i j . It is well known that, for large N and xed J (e.g. a sibling model, in which the number of families N is large and the number of siblings in each family Ji is xed and generally small), the estimate of the xed effect i is inconsistent (Anderson 1970). When the estimators of the structural parameters and are functions of the incidental parameters i , this inconsistency carries through to the estimates of and . The indicators of educational achievement analyzed in this study are either binary variables (high school completion and college entry) or a censored variable (years of schooling, which is upper censored for those individuals who are still in school in 1988). The estimation methods for these indicators are described in the following subsections. 3.1 Years of Schooling. Let the observed variable E i j denote the years of schooling completed. If the individual is not enrolled as either a part-time student or a full-time student in the last sample year, we assume that he/she has completed his/her education. In this case, the years of schooling observed ( E i j ) is equal to his/her educational achievement ( E ij ). However, in the sample, 106 out of 1,013 individuals are still enrolled in school in the last sample year. The educational attainments of enrolled individuals are thus censored and their educational achievements are not fully observed instead, the years of schooling completed in the last sample year are observed. Let K i j be the years of schooling completed in the last sample year if censored. The relationship between the observed years of schooling and educational achievement in (1) can then be written as follows. Ei j. D. E. ij. Ki j. if E ij K i j if otherwise. (2). where the error term "i j has an iid normal distribution with mean 0 and variance 2. To deal with the incidental parameters, i , Honore (1992) proposed a semiparametric estimation of censored regression models- trimmed least squares estimation for the case where the panel is short. It is proven that the trimmed least squares estimators are consistent and asymptotically normal under suitable regularity conditions. Also, it is not necessary to maintain parametric assumptions on the error terms to obtain this result. Let Yij D K i j ; E ij , and Yi j D K i j ; E i j ..

(8) 432. Fung-Mey Huang. Then Yi j D maxf0 Yij g. The trimmed least square estimators for are dened by minimizing the following objective function: Tn .b/ D. X n. i D1. .maxfYi 1 1 X i bg ; maxfYi 2 ;1 X i bg ; 1 X i b/2. 2 1fYi 1 < 1 X i bg.1 X i b ; Yi 1 /Yi 2 C2 1fYi 2 < ;1 X i b g.;1 X i b ; Yi 2 /Yi 1 C. X n. D. i D1. where. .z1 z2 / D. (3). .Yi 1 Yi 2 1 X i b/. 8 z2 <1 : .zz21. 2z1.;z2 ; / for ;z2 z2 ; /2 for ;z2 < < z1 for z1 : 2 C 2 z 2 . ; z 1 / C. ;. The trimmed least square estimators O are, thus, satised the sample analogs of following rst order condition. E .1f.Y1 Y2/ 2 A1 g.Y1 ; Y2 ; 1 X/ ; 1f.Y1 Y2/ 2 A2 g .Y2 ; maxf0 ;1 X g/ C 1f.Y1 Y2 / 2 B1 g.Y1 ; Y2 ; 1 X / C1f.Y1 Y2 / 2 B2 g.Y1 ; maxf0 1 X g// 1 X ] D 0 (4). where 1fg represents the indicator function, A1 D f.Yi1 Yi2 / : Yi1 > 1 X , Yi2 > Yi1 ; 1 X g, A2 D f.Yi1 Yi2 / : Yi1 1 X Yi2 > 0g, B1 D f.Y Y / : Y i1 i2 i 1 > 1 X 0 < Yi 2 < Yi 1 ; 1 X g, and B2 D f.Yi 1 Yi 2 / : Yi1 > 1 X Yi2 0g for the case of 1 X 0. For the purpose of comparison, the parametric estimation of censored regression model with xed effects, model (1) and (2), are also presented.5 In order to ensure that the algorithm updates the parameters in a direction that increases the log likelihood, model (2) is re-parameterized by dividing through by . Let For the parametric estimation (years of schooling), it is not possible to devise estimators of and that are not functions of the incidental parameters . Heckman and MaCurdy (1980), however, argue that Monte Carlo results for the multivariate probit model with xed effects suf ciently reassure that the incidental parameters problem appears to be practically unimportant. It is intuitively plausible that the unvariate Tobit estimator should be even better behaved because it combines the linear regression model with the probit model. Moreover, less than 10 percent ((106 14)/999) of our sibling samples are censored and K s' (the years of schooling completed in the last sample year if censored) are very close to their eventual years of schooling.. 5. i. ij.

(9) 433. The Impact of Childhood Events on Educational Achievement. h D 1= , b D = , amd ci D i = . Dene an indicator i j equal to one if h E ij hK i j and equal to zero otherwise. The log-likelihood function for the sample can now be written as follows: LD. X .1. i D N j D Ji. ;. i D1 j D1. . i j / log 1 ; 8.hK i j. log h ; i j .h E i j. C ij. ;. ;. b 0 X i j ; ci /. . . b0 X i j ; ci /2 =2. (5). where 8 is a standard normal distribution function. In this model the parameter set to be estimated includes h , K elements of b, and N elements of c (see Appendix). Note that if all the family's siblings were censored, to maximize the log-likelihood function (5), the xed effect ci would be innite and would make no contribution to the log-likelihood function. The observations of such groups (14 individuals) are discarded during the estimation. In total, 999 siblings from 416 families are analyzed in the xed effects Tobit model. 3.2 High School Completion or College Entry The realizations of either high school completion or college entry are as follows: Ei j. D. 1. if E ij 0 0 if otherwise. (6). where E i j D 1 if the child completed high school and E i j D 0 otherwise in the high school completion model and "i j has a logistic distribution.6 In the college entry model, E i j D 1 if the individual entered college and E i j D 0 if the individual has not entered college, but has completed high school. The individuals used in estimating college entry are those children who have completed high school. To deal with the incidental parameters, i , Chamberlain (1980) suggested a conditional logit approach for the binary model.7 This conditional likelihood function does not depend upon the incidental parameters. Therefore, the conditional ML estimator of is consistent, provided that the conditional likelihood In the case of a limited dependent variable, the ML estimation of the xed effects model with large N and small T gives inconsistent estimates of the parameters. Andersen (1970) and Chamberlain (1980) demonstrate this for the logit model and suggest a conditional likelihood approach. In the logit model one can obtain consistent estimates using the conditional ML method (conditioned on the xed effects). Such conditioning is not possible with the probit model. 7 The key idea is to base the likelihood function on the conditional distribution of the data, which is conditioned on a set of suf cient statistics for the incidental parameters . 6. i.

(10) 434. Fung-Mey Huang. function satises regularity conditions, which impose mild restrictions on i . These restrictions constrain the rate at which the sequence of i 's is allowed to become unbounded (Anderson, 1970). The conditional ML estimate of can be obtained from a standard ML binary program. Chamberlain (1980) also showed that the standard errors obtained by the usual conditional logit programs can be used as the asymptotic standard errors for the conditional ML estimator of . Because of this, if either E i j D 1 or E i j D 0 for all j in family i , the observations in such groups do not affect the ML estimate of and are discarded during the estimation. For computational simplicity, J D 2 is xed for each family unit. In the high school completion model, 272 siblings from 136 families are included to estimate the xed effects model. In the college entry model, only 230 siblings from 115 families are studied.. 4 Data and Childhood Characteristics The analysis in this study is based primarily on the data from the 1992 tape of the University of Michigan's Panel Study of Income Dynamics (PSID). The individuals selected from the 1992 tape are those who were 6 years old or younger in 1968, and who still responded in the survey sample in 1988 as young adults aged 20 to 26. The children selected in each survey year were of different ages (e.g., ages 06 in 1968, and ages 2026 in 1988). To make the childhood experiences comparable across the six different ages in each survey year, all information is transformed from a time-indexed format to an age-indexed format. For monetary data, all dollar values are expressed in 1976 constant prices. After adjustment, there are 1,013 children in the sibling sample.8 In addition to the basic PSID data, a second source - the University of Michigan Time Use Data Set - was utilized to collect the information for the amount of time that parents spent in childcare activities. The time-use data was constructed from time diaries lled out in 1975-1976, in which respondents entered the amount of time spent in various activities in a typical day. The variable time spent in childcare was constructed by adding the times spent in ac8 We discarded the observations that had missing information for at least two continuous years and had no information on education for the entire 21 years. For observations with one year of missing data (17 observations), the missing data were lled in as follows. If the individual's sibling was still living with the same family in the year with the missing data, then the observation's family information was lled in using the sibling's family information (10 observations) otherwise, the missing data were lled in by averaging the data for the two years contiguous to the missing year (7 observations)..

(11) The Impact of Childhood Events on Educational Achievement. 435. tivities which were classied as childcare, and then expanding that information to an annual basis. Two separate regressions of this childcare time variable using the time-use data set were regressed on family characteristics, income, and other variables which were comparable over the PSID data and the time-use data. The imputed estimates of the childcare time variables were then calculated for every family each year based on those coefcients and the values of the corresponding variables each year in the PSID. Table 1 accordingly presents the mean statistics of family background and childhood variables for three sub-samples of youth high school dropouts, high school graduates, and college entrants. Signicant differences appear among the groups (Table 2). On average, high school dropouts grew up in families with the lowest parental education and having the largest number of siblings, while college entrants grew up in families with the highest parental education and having the fewest siblings. The children's educational achievements are found to be monotonically decreasing with the number of years living with one parent and the family stress faced during the childhood period. High school dropouts lived much longer in single-parent families than other groups of youth. On average, high school dropouts lived 2.71 years with only one parent high school graduates lived 1.61 years and college entrants lived 1.09 years with only one parent from the ages of 6 to 15. High school dropouts also experienced almost twice as many location moves as high school graduates and college entrants. In relation to parental work patterns, college entrants grew up in families where the father and mother worked more, while high school dropouts had parents who worked less. Similarly, high school dropouts experienced more unemployment hours of the household head. Family incomes are high among the families of college entrants, and low among the families of high school dropouts. It is not surprising that the families of high school dropouts were heavily dependent on welfare. High school dropouts experienced an average of 1.32 years on welfare, while college entrants on average experienced only 0.207 years on welfare. Finally, high school dropouts received more childcare time than other groups of youth during ages 615. This result may be due to the measurement error associated with the variable for childcare time. The childcare time variable here cannot represent the quality of childcare time in the production function of human capital..

(12) 436. Fung-Mey Huang. 1: The Sub-sample Means of Some Family and Childhood Variables High School High School College Dropouts Graduates Entrants Demographic variables: Non-white 0.24 0.17 0.13 Father's education 10.2 12.0 13.2 Mother's education 10.4 11.7 12.8 Number of siblings 1.77 1.62 1.31 Living arrangements and family stress: Number of years living in a singleparent family, ages 615 2.71 1.61 1.09 Number of parental separations, ages 615 0.27 0.17 0.13 Number of parental remarriages, ages 615 0.20 0.17 0.10 Number of location moves, ages 615 2.15 1.39 1.12 Number of years living in SMSA, ages 615 6.13 6.77 7.23 Employment and unemployment status: Mother worked, ages 615: Number of years 5.51 5.81 5.90 Average annual working hours 692 736 734 Father worked, ages 615: Number of years 7.12 8.28 8.87 Average annual working hours 1,811 2,083 2,262 Average annual unemployment hours of household head, ages 615 83.6 60.5 35.2 Family economic circumstances: Average annual welfare ratio, ages 615 2.26 3.04 3.81 Number of years receiving AFDC, ages 615 1.32 0.56 0.21 Child care time: Average annual childcare time, ages 615 976 907 817 Sample size 395 830 464 Note: (1) All the means were calculated by using 1988 weights. (2) All of the father's and mother's information were calculated only when they were present..

(13) 437. The Impact of Childhood Events on Educational Achievement. 2: The LR Test of the Equality of Sub-sample Means High School Dropouts vs. High School Graduates Demographic Variables: Non-white 2:93 Father's Education ;8:88 Mother's Education ;8:89 Living arrangements and family stress: Number of years living in a single -parent family, ages 6 15 5:38 Number of parental separations, ages 6 15 3:58 Number of parental remarriages, ages 6 15 1:13 Number of location moves, ages 6 15 6:85 Number of years living in SMSA, ages 6 15 ;2:36 Employment and unemployment status: Mother worked, ages 6 15: Number of years ;1:39 Average annual working hours ;1:07 Father worked, ages 6 15: Number of years ;5:28 Average annual working hours ;5:03 Average annual unemployment hours of household head, ages 6 15 2:75 Family economic circumstances: Average annual welfare ratio, ages 6 15 ;6:93 Number of years receiving AFDC, ages 6 15 6:16 Child care time: Average annual childcare time, ages 6 15 3:75 Note: Signi cant at 10% level, two-tailed test. Signi cant at 5% level, two-tailed test.. High School Dropouts vs. College Entrants 4:24. ;13:8 ;15:6. High School Graduates vs. College Entrants 1:94. ;6:86 ;8:48. 7:57. 3:06. 4:65. 1:69. 3:85 8:52. 3:06 2:90. ;3:68. ;1:83. ;1:60 ;0:91 ;7:88 ;7:93. ;0:43 ;0:05 ;3:68 ;3:91. 6:16. 3:79. ;11:1. ;6:41. 8:43. 4:14. 8:60. 5:51. 5 Results In order to compare the results from the xed effects model with most previous results in which standard Tobit or standard logit and probit were used, table 3.

(14) 438. Fung-Mey Huang. presents both standard Tobit (standard logit) estimates and xed effects Tobit (xed effects logit) estimates. Three educational indicators are analyzed. The years of schooling reveal the overall educational achievements, and among that, we consider whether a child completes the compulsory education (high school completion) and whether he/she goes beyond (entering college).9 In previous studies, variables, such as parental education, unemployment rate, and the percentage of adults having college degree in the county, were interested in and included to capture the genetic factor and economic environment which affect the child's education and also relates to the family structure and parental work patterns. Those variables are included in our standard Tobit and logit estimations, but not in xed effects model except parental education. In order to examine whether having different levels of parental education during ages 615 makes signicantly different educational attainments later on in xed effects models, we average the parental education over age 615 for each individual. The variation for averaging parental education during ages 615 among siblings come from the years of younger and adolescent ages. The variables no parents in 1968 and one parent in 1968 are used to control for the missing values for parents' education.10 In the xed effects models, those variables having very little variation among siblings are excluded, such as race and whether the father and the mother graduated from college. Again, differences in experiencing parental education and family events during ages 615 among siblings come from the years of younger and adolescent ages. Table 3 presents the impacts of childhood circumstances on children's later years of schooling (the rst four columns), high school graduation (columns 5 6), and college entry (the last two columns). For years of schooling, the estimates from the xed effects linear model are also presented where the years of schooling in the last survey year for those who still enrolled in school ( K i j ) are treated as We only consider siblings who have completed high school in the college entry model. Otherwise, we mix up high school graduation behavior with college entry behavior. 10 The estimates of the effects over various time periods (6 9, 10 12, and 13 15 years of age), which were also emphasized in Haveman's study (Haveman et al. 1991), are not considered here. The reasons are following. First, the xed-effects estimator is the within group estimator. In order to have reliable estimates, the variations of the childhood events within siblings need to be suf cient. If we divide the child's childhood years into three three-year periods (5 9, 10 12, and 13 15 years of age), the variations in terms of experiencing family events in each period within siblings will be very small. The results might not be reliable. Second, the trends of single-parent family structure and parents' work patterns are increasing. Individuals in their adolescent years are more likely to experience their parents' breakups and mothers' working than in their younger years. The results are therefore likely to be signi cant during the adolescent years. The rst reason is the main reason. 9.

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(18) 442. Fung-Mey Huang. being observed as eventual schooling instead of censored. A xed effects model is one of the econometric models that correct for the omitted variable bias if omitted variables (such as unobserved family characteristics in our study) interact with observed explanatory variables. The bias contains the interactions between the unobserved family heterogeneity and childhood events and the inuence of the unobserved family heterogeneity on children's educational outcomes in which we assume to be positive (The omitted variable problem, please see Goldberger 1991, pp.189191). That is, the higher the unobserved family characteristics are, the higher the children's educational attainments would be. The sign of the bias would then be determined by the interactions between the unobserved family heterogeneity and childhood events. The childhood events in both the standard models and the xed effects models are discussed here. Regarding the impacts from family structure, three variables are considered: number of years living with a single parent, number of parental separations, and number of parental remarriages during ages 615. In the standard Tobit and logit models, parental separations had ambiguous but insignicant signs and parental remarriages had a substantial and negative association with children's educational achievements. In the xed effects models, however, the results showed that within a family, the sibling who experienced more parental separations or lived longer in a single-parent family (usually female-headed) than the other siblings during his/her younger or adolescent years had signicantly and substantially lower educational attainments. On the other hand, the sibling who experienced parental remarriages than the other siblings who did not during their childhood periods had substantially higher educational attainments. These xed effects ndings were consistently shown across various indicators of educational achievements. The unobserved family characteristics might be negatively correlated with the number of parental remarriages, which caused the different ndings between the standard models and the xed effects models. If the family had higher unobserved family characteristics, the parents tend to be less likely to separate and remarry and the family is more likely to be intact. The family who frequently moved its location when children were young was found to adversely and signicantly in inuence their children's educational attainments in previous studies (Haveman 1991). Our xed effects results, however, show signicantly positive or insignicantly negative associations with children's years of schooling and positive but insignicant association with children's high school graduation and college entry behaviors. The result may suggest that the negative effect of family moves in previous studies captured the et al..

(19) The Impact of Childhood Events on Educational Achievement. 443. negative association between the number of moves and unobserved family factors. That is, the higher the unobserved family characteristics were, the less frequently the family would move. Moving per se, in fact, might be an optimum choice based on the family's current situation and expectations of future events. Mother's work was positively and signicantly associated with children's educational attainments in previous ndings. Their positive effects then became insignicant in the xed effects model. The xed effects results indicate that within a family the siblings' educational attainments do not vary signicantly with the amount of work the mother did during their younger or adolescent years. The positive association between the mother's work and the children's educational outcomes found in the standard Tobit and standard logit models might be due to the positive association between these two variables and some unobserved family heterogeneity. When families have higher values of unobserved family factors, their mothers tend to work more. Similarly, families having higher values of unobserved family characteristics tend to raise fewer children (i.e. fewer numbers of siblings). The signicantly adverse effects of number of siblings on children's later educational outcomes found in previous studies mixed up the negative association between number of siblings with unobserved family heterogeneity. Siblings experiencing a different number of siblings do not have a signicant difference in their educational attainments. The family welfare ratio (i.e. family income / poverty line) and parental education was consistently found to have substantial and positive effects on children's education.11 Our standard Tobit and logit estimates also suggest that children's years of schooling, the probability of high school graduation, and the probability of college entry increased substantially with both the mother's and the father's schooling. In the xed effects model, the signicance disappears for many parental education variables, except for father having some college degree and the mother completing high school and having some college degree. The estimates imply the existence of a strong positive association between parents' education and family unobserved characteristics, such as gene, attitudes in learning and schooling. The higher the unobserved family characteristics are, the higher the parental education is and the higher the children's education will be. Given the same genetic and environmental factors, however, if siblings experienced differences in mother's high school graduation, they would have substantial and significant difference in their years of schooling, the probability of high school graduation, and the probability of college entry. The mother who completed high 11 In the xed effects model, the average father's and mother's education during ages 6 15 was used to capture differences among siblings in terms of experiencing parental education..

(20) 444. Fung-Mey Huang. school does substantially increase her children's educational attainments. Comparing the estimates of standard models with xed effects models suggests that controlling for the unobserved genetic and environmental factors does change the parameter estimates. Correcting the censoring problem decreases the standard errors of the parameter estimates (column 2 vs. column 3).. 6 Discussion and Summary In this study we construct a sibling data set from the PSID survey with a substantial observation period of childhood circumstances to reexamine the association between childhood events and children's later educational achievements. Fixed effects models with sibling data were used to control for the unobserved characteristics that drive the outcomes of childhood events and children's later educational achievements as well as the correlation among siblings. There are several different ndings between the standard estimations and the xed-effects estimations. In the standard Tobit and logit models, parental separations had ambiguous but insignicant signs and parental remarriages had a substantial and negative association with children's educational achievements. However, when unobserved common family factors were controlled for, the results from the xed effects estimations showed that parental separation has an adverse impacts on children's educational outcomes, and given separation, parental remarriage has benecial impacts on children's educational outcomes. The unobserved family characteristics might be negatively correlated with the number of parental remarriages, which caused the different ndings between the standard models and the xed effects models. If the family had higher unobserved family characteristics, the parents tend to be less likely to separate and remarry and the family is more likely to be intact. Moreover, in the standard Tobit and logit model, the number of parental remarriages highly correlates to the number of parental separations.The large number of parental remarriages implies that there is a large number of separations preceding the remarriages. The impact of parental remarriages on children's educational outcomes might be confounded with those of parental separations. A mother's work exhibited a positive and signicant association with her children's educational outcomes in the standard Tobit and logit estimations and also in some previous studies (Haveman 1991). In our xed effects model, however, the children of mothers who worked showed lower but statistically insignicant educational outcomes than children whose mothers did not work. The positive association found in standard models might be due to the positive association between the mother's work and unobet al..

(21) The Impact of Childhood Events on Educational Achievement. 445. served family heterogeneity. Among the family background variables, parental education had a persistent and positive inuence on the children's education even after controlling for the unobserved factors. In particular, children having a mother who completed high school had a signicantly higher educational outcomes than children whose mother did not nish high school. This nding regarding the intergenerational transmission of high school graduation strengthens the argument that completing high school is a primary step towards reducing the probability of long-term dependence on welfare and of living in poverty.. Appendix Fixed Effects Tobit with Stochastic Observed Thresholds The xed effects Tobit model with observed thresholds can be parameterized as follows. Yi j. D. Yi j. D. 0 xi j. Y ij. Ki j. C. i C "i j. "i j. . I I N . 0 2 /. if Yij K i j i D 1 n j D 1 Ji otherwise. (A1). where K i j is a stochastic and observed threshold, which changes with every i and j . For the standard Tobit model, Amemiya (1973) has shown that by using the ( ) parameterization the likelihood function is not globally concave. The same result carries over to the xed effects Tobit model which is more complicated than the standard Tobit model. However, Olsen (1978) has shown that when using the (= 1= ) parameterization the standard Tobit model does result in a globally concave log likelihood function. The reparameterized version (= 1= ) of the xed effects Tobit model also results in an unique maximum with respect to the structural parameters (Huang 1993). Therefore, to ensure that the algorithm updates the parameters in a direction which increases the log likelihood, model (A1) is reparameterized by dividing through by , and the model is rewritten as follows hYi j. D. b0 x. ij C. hK i j. ci C vi j if Yij K i j otherwise. .A2/. where h D 1= , b D = , and vi j I I N .0 1/. Dene an indicator variable i j equal to one if hYij hK i j and equal to zero otherwise. The log-likelihood function for the sample can now be written.

(22) 446. Fung-Mey Huang. as LD. X .1. i D N j D Ji. ;. i D1 j D1. . i j / log 1 ; 8.hK i j. log h ; i j .h E i j. C ij. ;. ;. b0 X i j ; ci /. . . b0 X i j ; ci /2 =2. (A3). In model (A2), the parameters to be estimated include h , K elements of b, and N elements of c. Let the vector contain the parameters of the model. The Newton-Raphson step is then 1. D ;. @2L @@ 0. ;1 @ L. @. . where the derivatives are evaluated at the current estimates of . In order to simplify the computation of the step, we partition into 10 D .b0 h / and 20 D c0 , and then let the partitioned Hessian matrix be A11 D. @2L @1 @10. A12 D. @2L @1 @20. D. A021 . A22 D. @2L : @2 @20. Plugging in the formula of the inverse of the partitioned matrix (e.g. Amemiya 1985), the step of the Newton-Raphson alogrithm becomes. 1 1. 12. D. . A11 ; A12 A;221 A21 /;1.

(23). ;. ;. A;221. @L @ 2. ;. @L @ 1. ;. A12 A;221. A;221 A21 11. @L @ 2. !. :. The structural parameters, 10 , can then be estimated separately from the family effects, 20 . Dene. B. b12 b22. 11. b21. and. D. 1. D. D. A11 ; A12 A;221 A21 . @L @1. ;. A12 A;221. @L : @2. D2 Simplifying all the second derivatives and the rst derivatives with respect to 1 and 2 , the partition leads to the following formula 11 D ;. B. 11. b12. b12 b22. ;1 D. 1. D2. (A4).

(24) 447. The Impact of Childhood Events on Educational Achievement. B11 D ; b12 D. D2 D. i D1 j D1. X. i D N j D Ji i D1 j D1. b22 D ; D1 D. X. i D N j D Ji. r i j x i j yi j ;. X. i D N j D Ji i D1 j D1. X. i D N j D Ji i D1 j D1. X. i D N j D Ji i D1 j D1. ri j x i j x i j C. .ri j yi2j. i j x i j. C. N. i D1. D X i. N. i D1. ri xNi xNi 0. ri xNi yNi. i j h ;2 / C. X N. ;. X. i D1. X N. i D1. ri . yNi/2. ri xNi N i . . i j h ;1 ; i j yi j / C. X N. i D1. ri xNi N i. where ./ D standard normal pdf, 8./ D standard normal cdf, and m ./ D ./=1 ; 8./].. . ri j. D. .1 ; i j /m . Z i j / m . Z i j / ; Z i j. Zi j. D. xNi D i j. D. 12 D. . Wi j. D. hki j ; b0 xi j ; ci . ri. D. J 1X r x ri j D1 i j i j. yNi D. C. i j . i. .1 ; i j /m . Z i j / C i j Wi j . 0 1c 1 1 B 1 c 2 C B CC B B @ CA . D ;. A;221. . D. 1c N 0 N 1 BB N 12 CC. 0 x 1 B BB CC B B @ A B @ . N n. N. 0. ;. xNn. 0. @L @2. ;. y. ; N1. 0. . y. ; Nn. hyi j ; b0 xi j ; ci. X Ji. N i D. j D1. 1 ri. ri j. X Ji. j D1. ri j yi j. J 1X ri j D1 i j i. A;221 A21 11. 1 CC CC 11 A. 0. Once the estimates of b, c, and h are found which maximize the likelihood,.

(25) 448. Fung-Mey Huang. the transformation back to and is made. The standard errors for the transformed parameters are obtained with the delta-method.. Reference Amemiya, T. (1973), Regression analysis when the dependent variable is truncated normal, Econometrica, 41, 997 1016. Andersen, E.B. (1970), Asymptotic properties of conditional maximum likelihood estimators, Journal of the Royal Statistical Society, Series B, 32, 283 301. Becker, G.S. (1981), A treatise on the family. Cambridgc, MA: Harvard U. Press. Becker, G.S. and N. Tomes (1986), Human Capital and the Rise and Fall of Families, Journal of LaborEconomics, 4 (3, Part 2), S1 39. Behrman, J., Z. Hrubec, P. Taubman and T. Wales (1980), Socioeconomic Success: A Study of the Effects of Genetic Endowments, Family Environment, and Schooling, Amsterdam: North-Holland.. Bound, J., Z. Griliches and B.H. Hall (1986), Wages, schooling and IQ of brothers and sisters: do the family factors differ? International Economic Review, 27, 77 105. Chamberlain, G. (1980), Analysis of covariance with qualitative data, Review of Economic Studies, 47, 225 238. Chamberlain, G. (1984), Panel data, in Z. Griliches and M.D. Intrilligator ed., Handbook of Econometrics, 2, 1248 1318, Amsterdam: North Holland. Corcoran, M., R.H. Gordon, D. Laren and G. Solon (1992), The association between men's economic status and their family and community origins, Journal of Human Resources, 27, 575 601 Datcher, L.P. (1982), Effects of community and family background on achievement, Review of Economics and Statistics, 64, 32 41. Goldberger, A.S. (1991), A Course in Econometrics, Cambridge: Harvard University Press. Griliches, Z. (1979), Sibling models and data in economics: beginnings of a survey, Journal of Political Economy, 87, S37 64. Hauser, R.M. and R.S. Wong (1989), Sibling resemblance and intersibling effects in educational attainment, Sociology of Education, 62, 149 171 Haveman, R. and B. Wolfe (1995), The determinants of children's attainments: a review of methods and ndings, Journal of Economic Literature, 33, 1829.

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(27) 450. Fung-Mey Huang. Olsen, R.J. (1978), Note on the uniqueness of the maximum likelihood estimator for the Tobit model, Econometrica, 46, 1211 1215. Solon, G., M. Corcoran, R. Gordon and D. Laren (1991), A longitudinal analysis of sibling correlation in economic status, Journal of Human Resources, 26, 509 534.. A59K`>5. : Sibling. Y: 2%F. . dS PSID e Sibling J Fixed effect ljVh A 2 < 9Kwn(`>A 5 }!

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