The Intergenerational Transmission of Parental schooling and Child Development New evidence using Danish twins and their children.

Transcription

1 The Intergenerational Transmission of Parental schooling and Child Development New evidence using Danish twins and their children Paul Bingley The Danish National Centre for Social Research Kaare Christensen University of Southern Denmark Vibeke Myrup Jensen Aarhus School of Business, Aarhus University, Denmark PRELIMINAY VERSION PLEASE TO NOT QUOTE April 2008 Keywords: Ability Bias, Twin data, Education, Intergenerational Mobility JEL classifications: I12, I20, J62 Understanding the causal relation between parental schooling and child development is important to create polices raising schooling level. We use unique Danish administrative data with information on identical twins and their children to estimate the causal effect of parental schooling on both short-run and long-run outcomes. By applying within twin fixed effect techniques we are able to take heritable endowments transmitted from parent to child into account. Further as an important reference point to the general population we do a parallel study on a sample of same sex DZ twins. We find that endowments counts for a substantial part of the correlation between parents schooling and child development. Father s schooling increases children s length of schooling, but decreases 9th GPA. Mother s schooling increases birth weight and the probability of high school completion. We find gender differences, but no stronger link between parents and children of same gender. 1

2 I INTRODUCTION Society has long been interested in the role of parents in their children s outcomes. In 2002 Behrman & Rosenzweig (hence B&R) shook the economic literature by rejecting the conventional wisdom that mother s schooling increases the schooling of their children. In fact, their evidence even went so far to suggest that maternal schooling has a negative effect on children. But is this relationship real? In the aftermath followed a long list of publications with focus on estimating the causal relationship between parental schooling and different stages of children s development. However, the literature is still inconclusive. In this paper we follow the innovative intergenerational strategy of B&R (2002), where pair of monozygotic (MZ) i.e. identical twins (who are mothers or fathers) are used to difference out any heritable traits transmitted from parent to child, when estimating the effect of parental schooling. We add to the literature by estimating average effects of parental schooling on both short and long term outcomes such as birth weight, fetal growth, hospitalization, academic achievement, and length of schooling. The former which no articles to date has covered. We use high quality data from the Danish administrative registers, which doubles the sample size used by B&R and provides us with the flexibility to make estimations on the basis of observable differences by gender of the child and to some extend background information of the grand parents. The literature on estimating the causal relation between parental schooling and child outcome has generally moved in tree different directions. One direction is the use of adopted children as a natural experiment. Given adopted children are genetically unrelated to the families that raise them, the effect of family environment and the genetic component is perfectly separated. Plug (2004) estimate the effect of parental schooling on children s length of schooling using American adoption data, and finds similar results to B&R. To some extend so do Björklund, Lindahl & Plug (2006) using rich Swedish data 1. Although the strong intuition behind adoption studies they have in particular been criticized for non-random placement of adoptions, leaving room for post and prebirth relations to bias the results (Scarr & Weinberg 1994). Björklund, Lindahl, & Plug (2006) test this (among other) implication indirectly by using additional information on the biological parents, and find that their estimates are robust (at least economically) to this selection effect. 1 When controlling for the schooling of the spouse. Extending the analysis to non-linear effects they also find mother s with a university degree to increase the probability of university degree for their adopted children. 2

3 Second, a recent popular strategy is policy induced variation in parental schooling. Black, Devereux, & Salvanes (2005) and Chevalier (2004) are two examples of using elementary schooling policy changes to estimate the effect on children s schooling. At the lower end of the schooling distribution both find some evidence of maternal schooling to increase the schooling of their children. Carneiro, Meghir & Parey (2007) study the effect of parental schooling on cognitive achievement among other outcomes and find parental schooling to increase cognitive achievement at age 7-8, (but not at age 13-14). Several studies use same strategy to estimate the impact of parental schooling on infant s health. Currie & Moretti (2003) use US college openings as an instrument and find that mother s schooling decreases the probability of low birth weight. Chevalier & O Sullivan (2007), Doyle, Harmon & Walker (2007), and Lindeboom Llena-Nozal & van der Klaauw (2006), all use changes in elementary schooling leaving age in UK and estimate the effect of mother s schooling on various infant and child health outcomes and find some but not consistent evidence of parental schooling affecting short run outcomes 2. Despite the popularity of the instrumental variable strategy its nature of estimating local average treatment effects encounters limitations when discussing general policy implication, (Imbens & Angrist 1994). Third, as a reaction to B&R s provocative results, Antonovics and Goldberger (2005) replicate their study using exact same data as B&R. With small modifications, they found no negative or positive effect of maternal schooling. In total the literature provides some evidence of the effect of parental schooling on child s development. Although even when using similar strategies, the results are mixed making it difficult to paint a consistent picture. Given the general criticisms of twin fixed effect estimates in terms of measurement errors attenuating the estimates and endogeneity in schooling upward biasing twin pair estimations (Bound & Solon 1999; Griliches, 1979; Neumark 1999), we extend the empirical strategy suggested by B&R in two ways. First, the high quality administrative data create a substantial reduction in measurement errors, because data not in the same way are infected by misreporting or recall bias or as selfreported measures. Further, given some measurement errors in the administrative reports, we are 2 Lindeboom, Llene-Nozal, & van der Klaauw (2006) and Doyle, Harmon, & Walker (2007) find no effects of mother s schooling on infant s and early childhood health. Chevalier & O'Sullivan (2007) find mother s schooling to increase the average birth weight using same legislative changes as Lindeboom, Llene-Nozal, & van der Klaauw (2006), though only by differentiating by grand parents social class. 3

4 more confident that these would be classical and not mean revering. We can therefore assume that using a instrumental variable strategy is valid to take measurement errors and endogeneity into account (Ashenfelter & Krueger 1994). Second, following the economic twin literature in financial returns to schooling (e.g. Behrman, Rosenzweig, & Taubman 1994; Miller, Mulvey, & Martin 2004) we also provide estimates for a sample of same sex DZ twins (ssdz). They serve as a reference point to the population at large, because ssdz twins only share half of their heritable endowments like siblings in general but on other characteristics resemble pair of MZ twins. Differencing within ssdz pair should therefore remove some endowment differences but contain same share of e.g. measurement errors. Using the sample of ssdz twins we in line with the conventional wisdom find positive effects of parental schooling; however using the sample of MZ twins we, as B&R (2002), find endowments to count for a substantial part of the correlation between parents schooling and child development. Further we find father s schooling to increase length of schooling, but to decrease 9th grade GPA, whereas mother s schooling increases the chances of infant s birth weight and high school completion. We also find substantial gender differences but no evidence of a stronger gender link between parents and child of same gender. The rest of this paper is as follows. In section II we describe our identification strategy; in section III we describe the Danish education system and our data. In section IV we discuss our results from infant s health to labor market outcomes. In section V we address some of the criticism to twin studies and deal with these by applying some robustness checks and finally we conclude in section VI. 4

5 II IDENTIFICATION STRATEGY Recent studies of the intergenerational transmission of human capital use a standard reduced-form intergenerational mobility model. A model consistent with household resource allocations models, where both parents have an effect on their child s outcome. This can be expressed as: c Y = δ S + δ S + Γ h + Γ h + γx + ε c m f m f (1) j 1 j 2 j 1 j 2 j j j Where c Y j denotes the outcome of the child c where subscript j indexes the family in which the S j m f child is born and raised. is the schooling of the mother, the schooling of the father. The h s are the unobserved heritable endowments genetically transmitted from parent to child. is a vector of family specific variables (such as fertility decision indicators like mother s age at birth and total household size) and important child demographic variables (e.g. gender and birth year of the c child) and ε j is the idiosyncratic error term of the child in family j. Considering the effect of mother s schooling on child s outcome; then δ 1 captures the net effect of mother s schooling on the quality and quantity of time and goods the mother devote to her children. However, because we must assume the effect of unobserved heritable endowments Γ 1 ( ), to be uncorrelated with mother s schooling (including effects of assortative mating) or at least have a 0 effect on child outcome ( c Y i S j ), cross sectional estimation of equation (1) will in general lead to upward bias estimates of mother s schooling. Following B&R s (2002) strategy; taking the difference in schooling between pairs of female MZ twins, who per definition are identical in their heritable endowments (h)- but different length of schooling eliminates by assumption the unobserved endowment effects transmitted from mother to their biological children. This leads to: (2) c j Y δ1 m = + δ S 2 +Γ f S 2 f h + γ x j + ε c Differencing between pair of MZ female twins take observed and unobserved heritable endowments along with rearing abilities that both twins share by growing up together. Although, f we are still left with bias from the unobserved endowment effects of the father ( h ) and because of assortative mating we expect this to upward bias the effect of mothers schooling. However, given assortative mating, correlation between spouses length of schooling are relatively high within twin pairs (32 percent). Further heritable endowments are proven correlated with schooling x j 5

6 (Björklund, Lindahl & Plug 2006; Plug 2004). We therefore assume heritable endowments between spouses to be correlated. Using father s schooling as a proxy for endowments and differencing between (non-twin) fathers schooling will therefore partially eliminate the effects of unobserved rearing and heritable endowments from the father when estimating the effect of mother s schooling. II.A Same sex DZ twins as reference group DZ twins only share one-half their genetic endowments and are therefore as genetic similar as regular siblings. Although, compared to regular siblings they, if reared together, have the virtue of being influenced by same observed and unobserved family effects at same point in time (e.g. shocks like divorce or parental salary increase), just like MZ twins. Within the economic twin literature comparisons between samples of same sex DZ twins and MZ twins has widely been used to back out differences between genetic and endowment 3 effects when estimating financial returns to schooling (Behrman & Taubman 1989; Behrman, Rosenzweig, & Taubman 1994;Miller, Mulvey, & Martin 1997), used as reference point to the population at large ((Miller, Mulvey, & Martin 2006; Miller, Mulvey, & Martin 2004) or to investigate if zygocity information is needed when taking endowments in to account 4 (Black, Devereux, & Salvanes 2007a; Isacsson 1999; Isacsson 2004) In this paper we primarily use the sample of ssdz twins as a reference group for the population at large. Further in terms of twin estimates sensitivity to measurement errors, we assume that the bias induced by measurement errors is the same for the sample of MZ and ssdz twins. Intuitively this means that as long as estimates on the sample of ssdz twins are in line with the conventional wisdom of positive associations of parental schooling and child outcome, we are confident that results given by the sample of MZ twins are not solely due to measurement errors. 3 In line with the traditional epidemiological twin design (Stachan & Read 2004) 4 The tradeoff being a larger sample when pooling MZ and DZ same sex twins compared to a more homogenous group of twins, when estimating the effects separately. Plomin, DeFries, & McClearn (1990), Goldberger & Karmin (1998) and Stachan & Read (2004) all discuss how samples of MZ and DZ twins besides their share of genetic similarity can differ. E.g. that MZ twins could be treated more similar than same sex DZ twins. 6

7 III INSTITUTIONS & DATA III.A. The Danish Education System In Denmark Elementary School consists of 9 years (grades) of compulsory schooling corresponding to primary and lower secondary school and an optional 1 year 10th form 5. Education is a requirement from August the year the child turns 7 until completed 9 years of schooling at age Upon completing elementary school in percent of this cohort left the education system. There are two branches of secondary education (ISCED97 level 3): general upper secondary education and vocational upper secondary education. Both forms take typically 3 years to complete but especially within vocational upper secondary education the length can vary between 1.5 years to 5 years of training. General upper secondary education is the primary academic branch, which gives direct access to tertiary education. We translate this academic track of upper secondary education to high school and use this term through out the paper. The alternative, vocational upper secondary education can be divided into two forms of training. First the 3 year vocationally-oriented general upper secondary program of business or technical college, which also gives direct access tertiary education. Second the basic vocational training prepares students to proceed directly to the labor market as skilled workers (e.g. carpenters, bricklayers or hair dressers) percent of those who left elementary school in 2003 leave the education system with vocational education (Danish Ministry of Education and Research 2005). Tertiary education (ISCED97 level 5) in Denmark is normally classified into three levels of education: short-cycle, medium-cycle or long-cycle higher education. In 2005 respectively 44.5 of the students who left elementary school in 2003 were expected to enter the labor market with tertiary education. Admission criteria s are primarily based on meritocratic principles - GPA from upper secondary education. There are no tuition fees or other direct costs for either of these types of education (Danish Ministry of Education and Research 2005). Short-cycle higher education is in many aspects similar to vocational education, because this education provides courses at middle technician s level and takes around 2 to 3 years to complete. The medium-cycle higher education comprises partly of professional BA programs such as nurses 5 61 percent of 9th grade students in 2002/2003 chose to continue in the 10th grade. 6 After completing the first 7, 8 or 9 years of elementary schooling the pupils can choose to take the last forms in continuation school, which typically are private boarding schools. In 1990 respectively 3, 8 and 21 percent of a given year cohort chose to do this (Danish Ministry of Education and Research 2001). 7

8 (3.5 years) and partly of general BA courses, which make up part of the long-cycle higher education courses (3 years). Long-cycle higher education contains of 2 year MA degree, and finally the student can choose to take the PhD-program (ISCED97 level 6). These courses are mostly a 3 years period that builds on the MA-degree 7. III.B. Data description We use high quality administrative data managed by Statistic Denmark in combination with data from the Danish Twin Registry, a survey based dataset from University of Southern Denmark. In total we have 7,524 (12,140) MZ (ssdz) twins, who are born between 1935 and 1977 and parents to at least one child. The variables, we use from Statistic Denmark, are from five different administrative databases, the Danish Civil Registration System, the Medical Birth Register, National Patient Register, the Integrated Student Register, and the Integrated Database for Labor Market Research. The unique identifying number for each individual in the Danish Civil Registration System allows us (i) to combine information from the administrative registers, (ii) establish family relations, birth order, household size 8, and marital status, and (iii) link information from the registers to the individual responses from the twin surveys. Begun in 1954, the Danish Twin Registry is the Worlds oldest survey-based twin registry. It comprises more than twin pairs born from 1870 through present (Skytthe et al. 2002). Zygocity classification for all same sex twins is constructed on the basis of four survey questions about twin similarity. A method validated to an overall accuracy of 96 percent (Christiansen et al. 2003). Given zygocity information is only valid for those who completed the survey questionnaire (approximately 70 percent of all twins), we discuss sample selection issues in section V. We study the following outcomes: Infant s health status is found in the medical birth register, where data is collected directly at the medical records in the hospitals. We use information from all children born of twins between 1978 and 2001 on birth weight, birth length and gestation. As birth weight measure we use 7 In recent years it has also become possible to do enter a 5 year Ph.D. program directly after the undergraduate degree. This varies from institution to institution. 8 Information on family relations before the official starting point of this register- comes from the last national census held in Here families are defined as everyone living at the same address. A validation study of the Danish Civil Registration System concludes that all children of mothers born from 1935 and onwards are observed in the registers. Among fathers almost all children are observed from this date, but not before 1945 complete fertility of the father is observed (Pedersen et al. 2006). 8

9 actual birth weight in 10 gram intervals 9 and a dummy for low birth weight using the WHO threshold at 2500 grams. Birth length is measured in centimeters, and we convert this measure into Ponderal index (PI). [not reported] PI is a measure of the relationship between length and weight and mimics the more conventional measure of Body Mass Index, although assumed to be more accurate to predict future obesity. PI is determined by the ratio of the cube root of weight (in grams) divided by length (in cm), multiplied by 100 (Murphy et al 2006). We use gestation measured in days, which we convert into a binary variable for preterm birth (PTB), using WHO definition at less than 37 full weeks. Although according to the Preterm Birth and Genetics Alliance, an international epidemiological association with focus on the causes and consequences of preterm birth, the most serious complications and highest risk of death in the developed world occur when child is born at less than 32 weeks 10. Therefore we also investigate the effect of mother s schooling on early preterm birth (EPTB) [not reported]. Finally we measure fetal growth as birth weight in grams divided by weeks of gestation to account for complex interaction effects between birth weight and length of gestation. We only estimate the impact of mother s length of schooling on infant s health, because we consider these as measures of mother s prenatal health care. Indicators for early childhood health are found in the National Patient Register from Information in this dataset also comes directly from the medical journals and follow all admissions for each individual. As indication of the health status during childhood, we use a measure of days spent at the hospital and calculate the total number of days until age 1 and up until age 6. To some extend admission at a hospital can reflect both poor health and the actions of worried parents, making the assumed negative correlation between parental schooling and admission less clear. We therefore use overnight stays spent at the hospital and not the number of contacts with the hospital service because the health of the child needs to be evaluated critical enough for overnight observation. Academic achievement as teens and young adults are found in the Integrated Student Register, were reports about grades, enrollment and drop outs for each individual are collected at each educational institution. We use two measures of academic achievement. The first one is 9 th grade GPA available for equivalents to birth cohorts , a score important for enter- 9 The register goes back to 1973, although from 1973 until 1977, birth weight is measured in 250 gram intervals. We restrict the sample to maximize variation. 10 Information on this association can be found at 9

10 ing upper levels of secondary education. Most students take the final exams when they are 16 years old, although some enter school early, late or complete 9 th grade as adults. Because we only observe 9 th grade academic achievement in a 5 year window, at best we observe 87% of a birth cohort with a 9 th grade GPA. Second measure is High school GPA for the selected sample of individuals graduating from high school , a score important for entering university. Most Danish High school students are between 18 and 20 years old when graduating (90 %), although as 9 th grade students some graduate earlier or return at a later point to graduate. We therefore restrict the sample to individuals completing high school between age 18 and 20 equivalents to the birth cohorts. Schooling measured as length of schooling for both parents and children are found in the Integrated Database for Labor Market Research, which contains labor market data for individuals in the time period 1980 to Information is collected for everyone born after 1920 up until today and still alive and living in Denmark in We use length of schooling measured in months to maximize within twin-pair variation, but recalculate the estimates into years in the presented tables. For the dependent variables of infant s health and early childhood health, parental schooling is measured the year of the dependent variable is observed. Children s length of schooling are measured the last year, they are observed in the dataset (for most 2004) and exclude individuals who have not turned 25 in 2004 equivalents to birth cohorts 1956 to Further given the broad age window and most children in Denmark complete education in late 20 s we also estimate length of schooling at age 30. For children born we create a binary variable for High school completion, measured as whether or not having a GPA score in the age of equivalent to the High School GPA measure. Given the wide age range of the outcomes, for each child we are not able to estimate the effect of parental schooling on both short and long term outcomes. Instead we use different cohorts for different outcomes. Therefore we cannot rule out possible cohort effects even though we do control for children born in different cohorts. Further analysis on more sufficient data will reveal if this is the case. III.C. summary statistics Table I presents basic summary statistics. The table is broken down to samples of ssdz twins (column 1 and 2) and MZ twins (column 3 and 4), females and males respectively. 10

11 TABLE I HERE In general differences between the group of MZ and ssdz twins are small. Age at firstborn child is between years old for female and two years older for male twins. Average length of schooling is and years for MZ and DZ female twins. For fathers we find similar differences, although male MZ twins have on average years of schooling whereas male DZ twins have years of schooling 11. The fraction of MZ or DZ twins having boys is the same across the groups, however small differences are found in household size. The tendency is a higher proportion of female MZ twins having two children (50.10 percent compared to percent for female DZ twins), whereas female DZ twins in turns have more than two children (42.69 percent) (37.95 for female MZ twins). Same differences are not found in the sample of male MZ and DZ twins. For all groups the proportion of married parents is large (around 72 percent). The sample construction partly explains this, because valid information on both parents is needed to take endowments from both parents into account 12. However from 1957 to 2001, the same time period as our sample, the proportion of children born out of wedlock in the total Danish population did not exceed 20 percent before 1975 and reached 30 percent in The 72 percent married couples in our sample therefore also reflect a general high marital rate at birth of the child 14. Children s outcomes of mothers who are MZ or DZ twins are very similar. There is only a 5 gram differences in birth weight, less than 2 grams per week in fetal growth, and less than half a day in hospitalization at age 6. The largest differences are found in length of schooling were children of female MZ twins on average have 1.5 month longer schooling than children of female DZ twins. Further, a t-test at the 5 percent significance level reveals that the means of hospitalization and length of schooling are significantly different in the sample of children of MZ twins compared to the sample of children of ssdz twins. TABLE II HERE! 11 For both samples of male and female twins, mean length of schooling for the sample of MZ twins is significantly higher at a 5 percent level. 12 For each dependent variable we do mean comparison between the group of children where we observe both parents and the group where we only observe one of the parents (primarily the mother). The t-tests in general show a significant positive sample selection; although economically the differences are small. However the selection process follows the same patterns within the groups of singletons, DZ same sex twins and MZ same sex twins, which reduces the issues connected to this selection. 13 After 1985 the proportion is stabile at around 45 percent. However it is quite common in Denmark, not to get married before the children are born. We include cohabitants in married after 1980 where this information is available. 14 Data available from the dynamic statistics, Statistic Denmark at 11

12 Table I showed minor differences between MZ and DZ twins and even smaller differences between the children of MZ and DZ twins indicating DZ twins to be a valuable reference group for the sample of MZ twins. Table II reports within twin-pair and within-cousin variation; the cornerstone of the identification strategy. 56 percent of female MZ twin pairs have different length of schooling and percent of male MZ twin pairs have different length of schooling. The fractions are similar to that found in previous economic twin studies (Ashenfelter & Krueger 1994; Isacsson 1999; Miller, Mulvey, & Martin 2004). In comparison percent of female DZ twins and percent of male DZ twins have different length of schooling, which do imply more variation within the sample of ssdz twins. For the share of twin pairs with variation in length of schooling, the average length of schooling is 8.7 months for MZ twins and 12.5 months for ssdz twins. The high proportion of twin pairs with same length of schooling are not in the same extend carried over to the next generation. In general the within cousin variation in the outcomes of twins offspring is around 90%. The exception is hospitalization were only percent of children of MZ twins and percent of children of DZ twins have different number of days spent at the hospital. IV RESULTS We now turn to the estimations of parental schooling on short and long run outcomes, where we compare the OLS with the twin fixed effect estimations. Table III presents these outcomes for both the samples of MZ and ssdz twins, female and male respectively. As stated in the previous section, different cohorts are available for different outcomes; the outcomes therefore represent estimations from separate regressions. All regressions are controlled for schooling of the other parent, marital status, gender, first born, household size, mother s age at birth and child s birth year. None of these covariates are reported instead we direct the focus onto the outcomes of interest. TABLE III HERE IV.A. Prenatal and early childhood health Birth weight, low birth weight, ponderal index, preterm birth, early preterm birth, fetal growth, hospitalization during 1 st year, and hospitalization up until age 6 are our infant and early childhood health measures. With one exception the OLS estimations indicate a positive transmission of mother s schooling to each of these outcomes. Birth weight increases with 29.6 grams, the 12

13 probability of low birth weight decreases with 0.5 percentage points, PI with xxx gram/cm3, the probability of EPTB with xx percentage points and fetal growth with 0.74 grams per week for each year of mothers schooling, when mothers are MZ twins. Similar results are found within DZ female twin indicating small differences between our sample of interest and our reference group. The exception is the effect of PTB where we do not find any effect using female MZ twins, but do find a positive effect using female DZ twins. Taking mother s heritable endowments into account the average effect of her schooling on birth weight is reduced to 17.8 grams for each year of schooling, indicating a causal return to mother s schooling on birth weight. We find no causal return to any of the other infant s health measures 15. The OLS estimates also report a positive effect of mother s schooling on hospitalization at age 1 and hospitalization up until age 6 with ten years of additional schooling reducing the risk of hospitalization with half a day at age 1 and one day at age 6. Despite the interesting feature increasing risk of hospitalization by child s age, we find no evidence of a causal effect of mother s schooling on hospitalization when taking endowments into account. Further there are no effects of father s schooling on hospitalization in the cross section estimates, indicating that fathers have little impact on the early stages of children s life 16. Placing our estimates in the context of previous studies; our average results on birth weight are lower than the 0.5 percentage points decrease in the probability of low birth weight by found by Currie & Moretti (2003) in the upper end of mother s education distribution and effect of mother s schooling increasing the average birth weight with 75 grams at the lower end of mother s education distribution (Chevalier & O Sullivan s 2007). Although most of our estimates are in line with the insignificant results found in Lindeboom, Llene-Nozal, & van der Klaauw (2006) and Doyle, Harmon & Walker (2007). IV.B. 9 th grade and high school academic achievement Turning to academic achievement we estimate the effect of both mother s and father s schooling on 9 th grade GPA and high school GPA. Given GPA is standardized, cross section es- 15 We also estimate the effect on APGAR score at one and five minutes, we did not find any effects in the cross section estimates. 16 We also estimate the effect of parental schooling on observed number of accidents, which lead to contact with the hospital, diagnosis of asthma in the childhood, diagnosis of diabetes in childhood. Neither led to any proof of parental schooling related to these outcomes in the cross section estimations. This could be due to small sample sizes, since we only observe some of these variables for a 10 year period. 13

14 timates report one year of female MZ twins schooling to increase 9 th grade GPA with 0.07 of a standard deviation and 0.05 of a standard deviation increase in high school GPA. The results are similar for the group of female DZ twins. Taking endowments into account we find no evidence of a causal effect of mother s schooling on 9 th grade GPA but we do find a significant effect of mother s schooling decreasing high school GPA with 0.04 of a standard deviation. The insignificant effects of mother s schooling resembles the findings in Carneiro, Megihr, & Parey (2007) who use an instrumental variable strategy and find no evidence of mother s schooling on children s math and reading scores, when the children are between years old 17. However we are not able to locate similar negative effect of mother s schooling on high school GPA in the literature. The negative effect we interpret as selection into high school. Compared to mother s schooling cross section estimations of father s schooling has a slightly lower impact on both 9 th grade GPA and high school GPA. OLS estimations on the sample of male MZ twins show a positive effect of father s schooling increasing 9 th grade GPA with 0.04 of a standard deviation and 0.03 of a standard deviation on high school GPA. The causal effect of father s schooling is however quite different. One year of father s schooling decreases 9 th grade GPA by 0.05 of a standard deviation and has no effect on high school GPA. As expected the fixed effect estimations on the DZ twin sample are between the OLS and MZ fixed effect estimates. IV.C. High school completion and years of schooling Our final outcomes are high school completion, length of schooling at minimum age 25, and at age 30. The OLS estimates show a significant positive effect of parental schooling on all tree outcomes. One additional year of female MZ twins schooling increases the probability of high school completion by 0.04 percentage points and 1.6 months of schooling at age 30. The OLS estimates also show the effect of father s schooling to be lower than the effect of mother s schooling. E.g. the effect of one additional year of male MZ twins schooling increase children s probability of high school completion by 0.02 percentage points, and 1.3 months of schooling. The fixed effect estimations on the sample of female MZ twins show one year of mother s schooling to causally increase the probability of high school completion by 1.4 percentage points but no evidence of a causal effect on length of schooling. Contrary we find no evidence of a 17 They also find mother s schooling to have of a standard deviation effect on math and reading scores when the children are 8 years old. 14

15 causal effect of father s schooling on high school completion (the estimate is both insignificant and small in magnitude), using the sample of male MZ twins, but do find father s schooling to increase length of schooling by one month at age 30 and 0.8 month when children at least have turned 25 years old. The causal impact of father s schooling and no impact of mother s schooling on length of children s schooling are coherent with Behrman & Rosenzweig (2005), Antonovics & Goldberger (2005) and within recent adoption studies (Björklund, Lindahl & Plug 2006). Latter find children s schooling to increase by 0.09 years for each year the adoptive father s schooling is increasing but an insignificant effect of adoptive mothers schooling 18. Plug (2004) also finds similar results on American adoption data. Although for father s schooling we, in contrast to B&R, find a substantial reduction in the fixed effects compared to the cross section estimates, indicating a consistent a substantial bias due to endowments from both mothers and fathers. It is interesting that mother s schooling affects high school completion but not length of schooling. If more schooled mothers are better at guiding appropriate educational inputs than less schooled mothers given uncertainties for future returns to education and better insight into the education system in general, we would expect mothers to influence both high school completion and length of schooling. One explanation could be that mother s schooling affects their children s schooling decisions as teens, when the children are still living at home. V ROBUSTNESS CHECKS The results suggest that mother s schooling has an effect on birth weight and high school completion, but no or a negative effect on academic achievement, and length of schooling. Contrary father s schooling has no effect at early childhood health but a positive, although minor effect on children s length of schooling. The sample of DZ same sex twin parents has provided us with validation of the MZ twin estimates, because DZ twins only share half of their innate endowments and these estimates has, as expected, been between the OLS and the MZ twin fixed effect estimates. So far we have not questioned the robustness of the model specification or the identification strategy. In this section we do so. First we investigate the model specification in terms of (a) 18 Unless measuring the probability of children getting a university degree, where they find mother s with a university degree to have a significant impact. 15

16 sensitivity to the included covariates, (b) gender differences, and (c) non-linearity. Second we investigate the identification strategy by (d) measurement errors and endogeneity, and (e) twinsingleton differences. V.A. Robustness of covariates There are several channels through which the effect of parental schooling can affect the development of the child, and so far we have tried to isolate the effect of parent s length of schooling by adding a long list of family characteristics and using twin fixed effect models. In all cases we find reduced or no evidence of parental schooling. The conventional wisdom states that the channels through which parental schooling can effect the outcome of the child downward bias the general effect of parental schooling. This clearly seems to be the case in terms of endowments. However up until now we have not dealt with our covariates in a systematic way and more importantly we have not dealt with the important effect of income or earnings. In this subsection we therefore investigate how sensitive our results are to excluding the covariates and to the inclusion of father s earnings or income. For simplicity we only report estimates for birth weight, hospitalization at age 6, high school GPA, high school completion and length of schooling. For infant s and childhood health we estimate income and earnings the year we observe the outcome and for long run outcomes we create a yearly average when fathers are between 40 and 50 years old as a proxy for lifetime earnings or income 19. We use gross annual income including labor earnings, taxable sick-benefits, unemployment benefits, public pension and other taxable subsidies such as student support 20. Earnings are constructed on the basis of annual labor earnings, public pension and student support. Because we only observe earnings and income from 1980 to 2004, all estimations are based on a reduced sample. TABLE IVA. & TABLE IV.B. HERE Table IV.A. shows the twin fixed effect estimations for the effect of mother s schooling on child development whereas table IV.B. shows the twin fixed effect estimations for father s schooling on child development. Estimations in column (1) and (2) are the base specification for ssdz and MZ twins respectively (both in table V.A. and V.B.) as used in the analysis so far. Es- 19 We also tried using dummies for earnings and income disentitles. However the estimates are similar to using log earnings and log income and are therefore not reported. 20 Some of these figures might be negative. E.g. student support consists partly of a student loan one need to start paying back one year after graduation. Typically the payment plan runs over years. 16

17 timations in column (3) and (4) exclude the schooling of the other parent; estimations in column (5) and (6) exclude indicators for fertility decisions: household size and mother s age at birth of the child. Column (7) and (8) include father s log earnings and (9) and (10) include father s log income. Because some of the effect of mother s schooling is driven by how she fares on the marriage market, excluding the effect of father s schooling will increase the effect of mother s schooling (and visa versa). But also more importantly, by excluding father s schooling we also exclude the part of father s endowments, which is not picked up by mother s schooling. As expected the causal effect of mother s schooling increases when excluding schooling of the father from the model. E.g. birth weight increases from 17.8 grams to 19.9 grams, reduces the negative effect of mother s schooling on high school GPA to being insignificant and increases the probability of high school completion from 1.5 to 1.6 percentage points, although the insignificant effect of mother s schooling on children s length of schooling remains. When excluding the effect of mother s schooling the effect of father s schooling also increases, but remains within same magnitudes. A large literature claims that schooling is an important determinant for human s fertility (Birdsall 1988; Schultz 1993). Fertility indicators such as household size and timing of child birth are therefore important channels through which parental schooling affects home environment. Although recent studies have also indicated that household size has an independent effect on IQ and high school completion of the children, (Black, Devereux, & Salvanes 2007b) making parents fertility planning difficult to extrapolate from the exogenous effect of household size. Assuming that most of the effects from fertility decisions are connected to parental schooling, excluding controls for family size increases the effect of both parents schooling. For example the effect of mother s schooling on birth weight increases from 17.8 grams to 18.8 grams per year of mothers schooling. However the probability of high school completion is constant and the effect of father s schooling on children s length of schooling is also constant indicating that parental schooling through fertility decisions has larger effects on short run outcomes than long run outcomes. As stated by Black, Devereux, & Salvanes (2007b) their household size effects on IQ and education are sensitive to the cohorts being investigated, with larger results found among the youngest cohorts. Because our results also stems from different cohorts and the larger effects are found in earlier cohorts, our results may also be sensitive to the cohorts analyzed. 17

18 With one exception the effect of mother s and father s schooling is quite robust to including either father s log earning (9) or log income (10). A small proportion of the effect of parental schooling on child outcome is therefore channeled through income and earnings. This can however be a virtue of using Danish data. In Denmark there are small returns to education (3%), further schooling is a public good reducing the effect of parental budget constrains on children s schooling choices. The exception is including father s log income when estimating the effect on birth weight; the effect is reduced to only 5 grams increase per additional year of mother s schooling, (and even insignificant). In comparison the effect of mother s schooling when controlling for income, using DZ female twins instead of MZ female twins, we find results similar to the base specification. Since the primary difference between MZ and DZ twins is the similarity in endowments, this result indicates an unexplainable strong interaction effect between endowments of the mother and fathers income. In future drafts we will investigate this drop. In addition father s schooling remains the same when including indicators for his income or earnings. In general there are little changes in the causal transmission of parental schooling, when altering the model specification, indicating the effect of parent s schooling is quite robust once controlled for endowments. V.B. Gender differences in the transmission of parental schooling Several commentators have argued that a priori there may be a stronger educational link between parents and children of same gender than across genders. One explanation is parental role models serve to elicit more effort from children of same sex as the parent. Table V.A and table V.B for daughters and sons respectively show the gender differences on most outcomes. For simplicity we only present some estimations of infant s health. We also exclude the effect on 9 th grade GPA, because of small sample size. If not stated otherwise we-in the following section-only comment on the fixed effect estimations where endowments are taken into account. TABLE V.A. AND TABLE V.B. HERE Mother s schooling has no causal effect on boy s birth weight, probability of low birth weight, fetal growth, and hospitalization. Contrary we find large causal effects of mother s schooling on girls health at birth. One year of mother s schooling increases girl s birth weight by grams, decreases the probability of low birth weight by 1.5 percentage points, increases fetal growth by 1.33 grams per week, but do not have a causal effect on hospitalization. Despite the interesting differences between boys and girls, these large effects of mother s schooling on girls 18

19 health at birth are upper bounds, because the OLS estimates of MZ female twin s schooling on i.e. birth weight is grams, more than 20 grams higher than the effect of DZ female s schooling. Further we find an insignificant effect of mother s schooling on infant s health when using the sample of DZ female twins. For the effect of fathers we find a causal effect of one additional year of schooling decreasing their daughter s hospitalization by 0.3 day at age 6. In table III we found a general negative effect of mother s schooling on high school GPA. This negative effect is only replicated for the boys, with one year of mother s schooling decreasing boys GPA by 0.11 of a standard deviation whereas the effect of mother s schooling on girls high school GPA is insignificant. For high school completion, one additional year of mother s schooling increases the chance of boys high school completion by 1.3 percentage points whereas there is no effect on girls high school completion. A result not consistent with the conventional wisdom but resemble the effect of mother s schooling on their son s schooling found in Black, Devereux, & Salvanes (2005). We find no evidence of gender differences in the effect of father s schooling on neither high school GPA nor high school completion. On children s length of schooling we, as in table III, find no evidence of mother s schooling having a significant effect on either boys or girls. Father s schooling also has no effect on boys length of schooling, but increases girl s schooling by 1.2 months for each additional year. In total we do find large differences in the causal effects of mother s and father s schooling between boys and girls. In fact most of the significant causal effects found in table III were only replicated in the effects of either boys or girls. Although we find little evidence of stronger links between parents and children of same gender except for the effect of mother s schooling on daughter s prenatal health. However a more sensible explanation for this relationship is that girls in general are smaller at birth and therefore more sensitive to prenatal behavior of the mother. V.C. Non-linearity and grandfathers schooling In recent studies authors have suggested non-linearity in the transmission of human capital with the conventional wisdom of higher returns to the bottom of the schooling distribution (Black, Devereux, & Salvanes; Chevalier & O Sullivan 2007, Chevalier 2004). Although stronger intergenerational associations are also found at the higher end of the education distribution (Björklund, Lindahl, & Plug 2006; Currie & Moretti 2003). This said, there is little evidence of estimations both at the lower and higher end of the education distribution for the same population. In this sec- 19

20 tion we investigate if coming from less or more human capital families, defined by the schooling level of the grandfather 21, yield different effects for the outcome of the (grand) child. Because this requires data from 3 generations, we are only able to estimate the effect on infant and early childhood health outcomes. The results are listed in table VI [not reported]. II.B. Measurement errors and Endogenous variation in twins schooling choices In 1979, Griliches raised the critiques that (i) estimates obtained from differencing in general and between MZ twins in particular, exacerbates the extent of variation driven by measurement errors, which attenuate the estimates, and (ii) the ideally assumption of MZ twin pairs being identical except for the exogenous variation in within twin pairs schooling is questionable and lead to an upward bias of the estimates. Both issues we will address in this section, although because of data restrictions we only provide error corrected estimates on high school completion and length of schooling. The classic solution to the issue of measurement errors, first stated by Ashenfelter & Krueger (1994), is to use a second measure of the variable that is measured with error. Given measurement errors in the second measure is uncorrelated with the measurement errors in the first, the second measure can be an instrument for the first measure. However as exemplified by Bound & Solon (1999) and Neumark (1999) correcting for measurement errors without any correction for omitted variable bias exacerbate the (presumably upward) bias from these omitted variables. An issue even more critical, if the classical error-in-variables assumption is not fulfilled but measurement errors instead are mean reverting. If measurement errors are mean reverting, the error correcting IV strategy breaks down and in fact leads the error corrected twin fixed effects estimates to be more (upward) biased than the original fixed effect and the OLS estimates (Bound & Solon 1999; Neumark 1999; Black, Berger, & Scott 2000). In general we would expect a minimum level of measurement errors in our schooling measure because administrative reported schooling stems directly from educational institutions, which reduces noise from e.g. recall bias. Given measurement errors in the administrative reports, for two reasons we are more confident that they are classical, first because schooling is measured in months and not to the same extend discrete as self-reported yearly schooling, and second there are 21 Estimated as > and <= 12 years of schooling, equivalent to schooling above high school. 20