## Abstract

Using the British Household Panel Survey, we investigate if family size and birth order affect children’s subsequent educational attainment. Theory suggests a trade-off between child quantity and “quality” and that siblings are unlikely to receive equal shares of parental resources devoted to children’s education. We construct a new birth order index that effectively purges family size from birth order and use this to test if siblings are assigned equal shares in the family’s educational resources. We find that the shares are decreasing with birth order. Ceteris paribus, children from larger families have less education, and the family size effect does not vanish when we control for birth order. These findings are robust to numerous specification checks.

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## Notes

Their measure of relative birth order is \( {\left[ {{{\left( {\phi - 1} \right)}} \mathord{\left/ {\vphantom {{{\left( {\phi - 1} \right)}} {{\left( {N - 1} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {N - 1} \right)}}} \right]} \), where

*φ*is birth order and*N*the number of children in the family.Iacovou (2001) included dummy variables for the younger of two children, the middle of three children, the younger of three children, the middle of four children, the youngest of four children, the middle of five children, the youngest of five children, the middle of six or more children, and the youngest of six or more children.

There is clearly a need to disentangle birth order effects from parental cohort effects. Some mothers have their first born when they are teenagers, whereas others have their first birth in their late thirties. As we discuss later, these maternal age differences might translate into different inputs of time, energy and experience, which may affect children’s educational attainment quite distinctly from birth order effects.

Ejrnaes and Portner (2004) hypothesise that parental fertility choices induce a birth order effect quite separate from the above hypotheses, owing to an optimal stopping calculus based on heterogeneity in degrees of parental inequality aversion. Booth and Kee (2006) use the 2003 wave of the BHPS to investigate intergenerational patterns of fertility in women’s origin and destination families, controlling for birth order.

Capital market imperfections may affect family resources devoted to education. In Britain, primary and secondary schooling is paid for by the state, and a grants and loans system is in place for higher education (although not further education). British children are, thus, more likely to become independent from their parents, and their educational choices might be less constrained by parental resources and birth order than in developing countries without such a long-established system of subsidised education.

Bjorklund et al. (2004) find, using administrative data, separate effects of birth order and family size on young adults’

*earnings*in Norway, Finland and Sweden.These variables are retrospective, and with retrospective data, there are always issues about potential recall error. However, the variables in which we are interested relate to attributes that are unlikely to be forgotten; it is hard to imagine that anyone within our sample of interest, 28- to 55-year-olds, would be likely to forget the number of siblings or their own birth order.

The highest educational attainment measure is ordered as follows: (1) No defined qualification; (2) Vocational or low-level academic qualification(s) (e.g. commercial or clerical qualifications, CSE grades 2–5, apprenticeship); (3) One or more Ordinary level or equivalent qualifications taken at age 16 at end of compulsory schooling (and forming the selection mechanism into Advanced-level courses); (4) One or more Advanced level qualifications (or equivalent) representing university entrance-level qualification typically taken at age 18; (5) Teaching, nursing or other higher qualifications (e.g. technical, professional qualifications); (6) University first or higher degree.

All respondents were initially asked Question D107: “Have you ever had any brothers or sisters who lived in the same household as you as a child? DO NOT INCLUDE STEP OR FOSTER SIBLINGS.” For those who answered “yes” in D107, respondents were then asked question D108 and D108+1. Because of the construction of this question, we obtain the information only on natural siblings. Hence, we are unable to control for the effect of mixed families arising from remarriages.

Unfortunately, the BHPS does not provide information about the age gaps between siblings.

Black et al. (2005) had the entire Norwegian population in their dataset and were therefore able to estimate the effects of birth order separately for each family size. We are unable to do this across all birth orders owing to very small cell sizes, as illustrated in Table 2. However, as reported later in this paper, we did experiment with this form of specification up to birth order of seven and above.

Respondents were asked: “Thinking about the time from when you were a baby until the age of ten, which of the following statements best describes your family home: There were a lot of books in the house; There were quite a few books in the house; There were not very many books in the house; Don’t know.” We constructed dummy variables for “a lot of books in the house” and “quite a few books in the house”. The base in the regressions is “not many books in the house”.

The precise question about area of residence was: “Please look at this card and tell me which best describes the type of area you

*mostly*lived in from when you were a baby to 15 years.” Responses are described in Table 13 Appendix A. The base for the regressions is “lived in a suburban area”.These seven cases were individuals whose mothers were aged less than 45 at the interview date. Of course, there might still be subsequent births of half brothers and sisters if the father has re-partnered, but we cannot do anything about this possibility. However, we do control for parental birth cohorts in addition to child cohorts. This is potentially important, as—controlling for child cohort—the parents of first-born children are likely to be younger than parents of third or fourth born.

For a one-child family, average birth order

*A*= 1, for a two-child family,*A*= 1.5, for a three-child family*A*= (3 + 1)/2 = 2, and so on, up to a total value for the ten-child family of*A*= (10 + 1)/2 = 5.5.It is well known that the children of wealthy parents receive more and better quality schooling than children of poorer families and that the family environment is also important (see inter alia the survey by Bowles and Gintis 2002; Hauser and Sewell 1985; Hauser and Kuo 1998; Kaestner 1997 and Kessler 1991). Our goal here was additionally to look at

*intra-family*differences while controlling for family wealth and the family environment.To illustrate, concider four family types: one-child, two-child, three-child and ten-child. For the only child from a one-child family, B

_{11}= 1, where the first subscript denotes birth order and the second family size. Now concider the first-born child from a two-child family. Her index is*B*_{12}= 1/1.5 = 0.666. For the second-born child,*B*_{22}= 2/1.5 = 1.333. Next, take a three-child family. The first born has*B*_{13}= 0.5, the second born has*B*_{23}= 1, while the third born has*B*_{33}= 3/2 = 1.5. Finally, consider a ten-child family. Here, the first born has*B*_{1,10}= 1/(5.5) = 0.182, the second born has*B*_{2,10}= 2/(5.5) = 0.364, the third born has*B*_{3,10}= 3/(5.5) = 0.545, the ninth born has*B*_{9,10}= 9/(5.5) = 1.636, while the tenth born has*B*_{10,10}= 10/(5.5) = 1.818.This is analogous to fixed-effects estimation in that the birth order effect is estimated as deviations from the within-family-size mean of unity. Thus, in, for example, a ten-child family, half of the observations will be above the mean and half below the mean. Deviations from the mean yield the birth order effect.

For example, in a three-children family with

*β*< 0, the first born will receive the biggest share, the second born the second biggest share and the third born the smallest share. If*β*> 0, the ordering is reversed. A practical way of ascertaining the monotonicity of a given function*y*=*f*(*x*) is to check whether the derivative*f*′(*x*) always adheres to the same algebraic sign for all values of*x*. See for example Chiang (1984).We also experimented with including a dummy variable taking the value one if the child lived with both biological parents from birth to age 16. As this was insignificantly different from zero, we dropped this from our reported models in Tables 5 and 6. Children who grew up with both parents are no different in terms of educational attainment from those who did not for our sample of British children.

The only exception is the dummy variable for mother aged between 21 and 25 years old at the respondent’s birth.

We also reestimated all the specifications on separate older and younger subsamples. The first comprised individuals aged 42–55, and the younger subsample comprised individuals 28–41. Our results were robust to this reestimation. Hence, in the interests of space, we do not report them here.

To avoid throwing out cases with missing information on family background variables, we constructed dummy variables for missing information for each relevant variable. It is possible, e.g. that children whose mother had a low-level qualification might be less likely to know what it was, and we control for this. Thus, for the maternal highest educational qualification, the respondent was first asked if they knew their mother’s qualification. If they did not, we included a dummy reflecting this. The respondent was then—conditional on knowing their mother’s qualification—asked what it was. We therefore constructed another dummy for this. We do not, however, report the coefficients to these missing information variables in the tables in the interests of space. Note that all the variables for parental qualifications and numbers of books in the house are conditional on reporting information, and the coefficients should be interpreted in line with this. There is, however, no missing information for area of childhood home.

As family size is potentially endogenous (see inter alia Cigno and Ermisch 1989, and Barmby and Cigno 1990), we also estimated two additional separate equations for each of Specifications [3] and [4] in which we dropped family size and included only the birth order index. These are essentially reduced form equations. We find that the estimated coefficients of the birth order index changed slightly, from −0.263 in Specification [3] and −0.260 in Specification [4] to −0.272 and −0.262 in Specifications [3] and [4], respectively. Both coefficients remained statistically significant at the 1% level.

In this smaller subsample of 7,105 observations, the simple correlation between family size and the EP index is 0.27, while the simple correlation between family size and our own birth order index is just 0.07.

We also reestimated the model on a subsample of larger families (with at least three children and above) to test for family size non-monotonicity. We find that our results are very similar under this new stratification. This suggests that our result is not simply picking up a size effect from family size of two and above.

We also experimented with estimating this model using the entire sample of 7,722 cases. Here, the children from only-child families are included in the base group (as their birth order index takes the value 1). The estimates from this specification were that

*γ*_{1}> 0, but that*γ*_{2}is insignificantly different from zero. This was the case regardless of how we specified family size (i.e. as linear or inverse). These results suggest that ‘only children’ may do worse than the first or high born in multi-children families, a result that Iacavou (2001) also found. This could arise if sibling input matters. But if so, it matters asymmetrically across family members.To test the suitability of our instruments, a regression with family size as the dependent variable and the instruments as explanatory variables was estimated. We found that the instruments are statistically significant as a group in explaining family size.

The question takes the form: “Did you live with BOTH your biological mother AND biological father from the time you were born until you were 16?”

This control is not ideal, as it does not account for the possibility of living with other stepsiblings that arise from parents’ re-marriages. In other words, we still cannot rule out the possibility that parents might tend to invest more resources in their biological children rather than stepsiblings from remarriages.

The simple correlation coefficient between mother working and mother with a degree is quite low at 0.1206.

Of course, there are considerable losses in experience capital—representing a form of switching cost—for women who make these transitions. This would suggest there would be a band of inaction.

Iacovou (2001) also found, using British data from a 1958 birth cohort, that children from larger families have lower levels of educational attainment at ages 7 to age 23 and that there is an additional negative birth order effect.

The correlation coefficient between family size and birth order is 0.7047, while the correlation coefficient between family size and our birth order

*index*is just 0.0697, as discussed in Section 4.1.Conley and Glauber (2005) employ instrumental variable estimation to control for endogenous family size using a sex-mix instrument. We do not have this information in our data. Using 1990 US Census data for children still living in the parental home, they find that children from larger families are less likely to attend private school, more likely to be held back in school, and that there is a birth order effect.

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## Acknowledgements

We are grateful to Tim Hatton for very helpful discussions, and to the Editor Alessandro Cigno, two anonymous referees, John Ermisch, Paul Miller and seminar participants at the Australian National University and Melbourne University for their comments. We also thank Margi Wood and Jeta Vedi for data assistance. The data were made available through the UK Data Archive and were originally collected by the ESRC Research Centre on Micro-social Change at the University of Essex, now incorporated within the Institute for Social and Economic Research. Neither the original collectors of the data nor the Archive bear any responsibility for the analyses or interpretations presented here. Part of this research was funded by the ARC under Discovery Project Grant No. DP0556740.

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## Appendix

### Appendix

### 1.1 Appendix A: The British educational system

The brief summary below covers England, Wales and Northern Ireland. It was obtained from: http://www.essex.ac.uk/ip/aclife/british.htm British education system (note that the system in Scotland differs slightly).

Education in Britain is compulsory between the ages of 5 and 16 (11 years of schooling). Before 1972, the minimum school leaving age was 15 years, and we have allowed for this when constructing our measure of years of completed schooling. At the age of 16, students wishing to continue academic study take examinations in a number of subjects in the General Certificate of Secondary Education (GCSE). Following GCSE, students take two further years of study, following between two and four subjects (usually three). The number of subjects is small, and the range of disciplines followed is generally narrow. It is common for example to take either all arts-based subjects or all science-based subjects. It is less common to mix them. Each subject is studied to a high level of specialization, and coursework and examinations involve a considerable amount of essay writing. At the end of this 2-year period, students take the examinations for the Advanced level of the General Certificate of Education (‘A’ levels).

Students in the United Kingdom have therefore normally completed 13 years of full-time education before entering university. This is 1 year more than most US high school students have on entering a US college. Admission to universities in the United Kingdom is competitive, and around 35% of the age group now normally expect to go on to higher education. Universities in Britain are autonomous bodies, empowered under their Charters or other acts of incorporation to award their own degrees. Undergraduate degrees normally take 3 years—1 year less than most Bachelor degree schemes in the United States. Although the two systems are not completely comparable, the following table provides a useful comparison.

### 1.2 Appendix B: Variance of birth order index *B*

It is interesting to see if the predicted means and variances of *B* for each family size are similar to what we find in the sample. The following table gives the actual mean and variances of *B* and the predicted variances by family sizes. Note that the predicted means and variances are based on the assumption that all children in each family appear in the data, which does not happen in the sample.

Generally, we find that the actual means and variances in our sample are very close to the predicted values. Notice also the actual variances are less than the predicted variances in most cases.

The predicted variances were calculated as follows. The general formula for variance is \( \sigma ^{2} = \frac{{{\sum {{\left( {X_{i} - \overline{X} } \right)}} }^{2} }} {{N - 1}} \), where \( \overline{X} \) is the mean, and *N* is the number of scores.

In Section 4.1, we noted that by construction, the mean of birth order index is \( \overline{B} = 1 \) across and within all family sizes. The variance of *B* can be obtained by plugging the value of *B* into the above formula. To illustrate, for example:

Repeat this exercise for all the family sizes (up to ten) in our sample; the rest of the variances of *B* can be summarised as follows:

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Booth, A.L., Kee, H.J. Birth order matters: the effect of family size and birth order on educational attainment.
*J Popul Econ* **22**, 367–397 (2009). https://doi.org/10.1007/s00148-007-0181-4

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DOI: https://doi.org/10.1007/s00148-007-0181-4