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The riaht - e DONALD ROBERTSON

&JAMES SYMONS m i x t u re Economistsat Cambridge Univem*ty and University College,

Peer group effects matter so policy ~ndonrespect ive~~ - must limit 'cream-skimming

hy do some children do well at education. Perhaps nursery vouchers can be school? There are two obvious seen as an effort in this direction. However W possibilities. Firstly good parents. finding that well resourced schools had im-

Good parents provide good genes initially, portant effects on attainment would have far- and then provide help and encouragement reaching consequences: increased school ex- (overtly and by example) to their children. penditures could solve the problem of the Secondly well resourced schools. Small class poor and the underclass in one or two genera- sizes, experienced teachers and effective equipment seem likely to help children to do well. A third, less ob- vious possibility is the child's peer group. The im- portance of the peer group was first emphasised in the US by the 1996 Coleman Re- port (as discussed in Mur- ray 's a r t i c l e ) . I t is hypothesised that the pres- ence in the class or the

I' if above average children are drawn in the main fiom parents

of above average education and wealth, then mixing is contra y to the interests of the most articulate and

influential elements of the community"

school of fellow students who are more able, better behaved or more ambitious will im- prove the performance of a given student, both by providing a better learning environ- ment and by acting on incentives.

The weight of each of these factors has im- portant implications for social policy regard- ing schools. One cannot do much about the genes of parents, although one can encourage all parents to be more supportive of their chil- dren and to take a more pro-active role in their

tions. The policy implica- tions of a strong connection between peer groups and at- tainment are rather more subtle. The crucial question becomes: how should we mix our children in schools?

Our reading of the empiri- cal evidence, discussed be- low, is that the twin influ- ences of parents and peers far outweigh such school-based factors as class size and ex-

penditure. The rest of the article then draws out the policy implications of this conclusion.

The educational production function Most economic studies of children's attain- ment in school are based on the theoretical concept of the educational production func- tion. The child's attainment is viewed as an output, derived from a number of inputs. For our purposes, we divide these inputs into three classes:

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Parental inputs One would include here the parental genetic endowment, parental time devoted to the child, and the quality of that time. These variables are typically assumed to correlate with parental education and social class.

Conventional school Inputs This category comprises the most obvious policy variables: teacher quality (usually as- sumed to correlate with experience), class size, and available resources (often repre- sented by expenditure per pupil). One could include here as well variables describing in detail school type (curricula, discipline etc.) but this is seldom done in economic studies.

Peer group inputs Here we include variables to describe the quality of the child's peer group, typically represented by the average social class of the school's enrolment or, in some cases, by measures of average intelligence.

The production function approach then says that attainment is a result of these three types of factor. One should think of the rela- tionship between attainment and the inputs as being like that in a production process where certain physical inputs lead to certain physical outputs.

The production function in practice Such an approach to thinking about educa- tional attainment is important for policy

SOLVING 7TfE Vh4Z77'€D VARlABLE PHOBLEh4

Sometimes with survey data the statistical fecknitjlre of instnrrnental variabks i s aoail- able. This TCqUireS nomination offurther variables, notgenuinely in tJw production function, but c m i a t c d with the obseruuble inpats md uncorrelated with tht unobsm- able inputs. This i s obviously a tall order. In our work we have argued that region of birth of a child can be treated as an instru- mental variable.

analysis because it enables consideration of the effect of changing one variable holding the others fixed.

Consider trying to quanhfy the effect of reducing class size. A simple correlation be- tween survey data on attainment and class size will not be enough because it does not distinguish between the effect of class size and the effect of other correlated inputs. For example, expensive private schools might have small class sizes as well as a high-quality peer group. It could be the latter that is really important and not the former. The implica- tion of this is that, even if one is only interested in the effects of one or two inputs, one cannot escape a full-blown analysis that includes all inputs. The only exception is in cases where factors left out are completely uncorrelated with the variables of interest.

In practice, of course, however many in- puts one tries to include, variables are al- ways omitted, and in some cases there are good reasons to suspect they are correlated with variables of interest. A particularly awkward problem arises when there is un- recorded variation in parental ambition. Ambitious parents will tend to contribute high values of both observed (for example, time spent with their children) and unob- served inputs (for example, general ethos at home) and the effects of two will be con- flated. Much of the empirical work in this area suffers greatly from these econometric problems, and all surveys suffer from them to some degree.

The only studies which do not face such a problem are randomised experiments, such as the STAR project in Tennessee. This study has obtained apparently definitive results on the effects of class size by randomly assigning children to classes of different sizes and fol- lowing their progress over a number of years. For obvious reasons, such experiments are relatively rare. There are ways of getting round the problem of omitted variables in survey work (see Box) but they are by no means certain to work.

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Balancing the inputs - recent thinking The modem era of attainment studies began with the Coleman Report (1966) which em- phasised the importance of parental socio- economic variables and peer group variables as opposed to conventional school inputs. Its finding that parental characteristics, espe- cially education, have strong independent ef- fects on attainment has not been seriously challenged. Haveman and Wolfe (1995) sum- marise a great deal of the research into this claim.

It was at one time received wisdom in the economics of education that conventional school inputs had only minor effects on at- tainment. Likewise, Hanushek (1986) pro- vides an extensive survey and concludes “there appears to be no strong or systematic relationship between school expenditures and student performance”.

However, this view was challenged by Card and Krueger (1992) who found a s i g h - cant correlation between the rates of return to schooling in different US states and state- wide educational quality as measured bycon- ventional inputs. Altonji and Dunn (1995) re- cently supported this finding but Betts (1995) defends the traditional view that conven- tional school inputs are relatively unimpor- tant. Research carried out by OFSTED last year on the relation between class size and attainment showed some evidence of benefits from smaller class sizes (Ofsted, 1995). How- ever, the benefits occur only for fairly dra- matic reductions in class size, and accrue in the main only to beginners and so reducing class sizes still does not appear to be a cost-ef- fective way of increasing attainment.

Coleman’s findings on peer-group effects have also been controversial with some claim- ing there is little evidence of separate peer- group effects (such as Averch (1972) and Hanushek (1971) and others confirming Cole- man’s findings (Summers and Wolfe (1977); Henderson et al. (1978)). Peer-group effects have also been found to be important in teen-

age pregnancy and school dropout behaviour (Evans et al, 1992).

The UK is fortunate in having the National Child Development Study, a comprehensive longitudinal survey that has followed a group of children as they grew up. The original group comprised every child born in one week in March 1958 and a large amount of information on the child, its parents and schooling has been collected at intervals. Us- ing this data, we have recently estimated an educational production function for attain- ment in Maths and English at age 11 (Robert- son and Symons, 1996a). Overall our evidence supports the emphasis on parents and peers in educational attainment: we found strong evidence of peer group effects as well as ef- fects from parental social class and educa- tional level; at the same time there appears to be very little evidence of effects from the con- ventional school inputs. Our measures of at- tainment at age 11 are sigruticantly related to earnings at age 33. As an example we com- pared a male with father in the top socioeco- nomic group, whose father and mother stayed on at school beyond minimum leaving age, and who attends a school in which half of his fellow pupils have parents in the top group, to a male with father in the bottom socio-economic group, whose parents left shoo1 at the minimum age and with no class mates with fathers in the top group. We pre- dict he will score about 20 per cent higher in Maths and English at 11, which is then trans- lated into an increase of about 30 per cent in wages by 33.

Peer groups and social policy If parents and peers are the major influence on achievement, we suggest that attention should focus more on admissions policy than on increasing the resources of schools. We wish to establish a simple framework in which such policy can be systematically ana- lysed. Assume children arrive at school with a particular endowment of quality. The in- crease in quality produced by the school ex-

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perience depends on the average quality of the child's peer group. Assume social welfare is represented by the sum of attainment on leaving school of all children. At once a ques- tion emerges: is it better to mix children in schools, or should we educate them in schools segregated by quality?

The answer to this question depends on how the peer group variable enters the pro- duction function. Roughly speaking, if in- creasing the average 'quality' of students in a class increases individual attainments of pu- pils in that class less, the higher average qual- ity already is, (where the effect of average quality exhibits decreasing returns) one should mix children in schools. If the reverse is true (and it exhibits increasing returns) one should segregate schools into ability groups.

We find evidence of decreasing returns in our empirical work, as do Henderson et al. who note also that it follows that "a uniform mixing of students by achievement will be opti- mal". The point is clear enough: if two schools have different average qualities and high and low quality children from the better and worse schools respectively are swapped between them the high quality children will suffer, but that will be

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Moreover, if above average children are drawn in the main from parents of above average education and wealth, then mixing is contrary to the interests of the most articu- late and influential elements of the commu- nity. Busing has been very controversial in the US and inner-city comprehensive schools are deeply unpopular among the middle classes in the UK, who look increasingly to educate their children privately.

Different systems for the allocation of chil- dren to schools imply different amounts of mixing of children in schools. In principle, comprehensive schools select all children in some catchment area but the geographical distribution of the population limits the amount of mixing that canbe achieved by this means (hence busing). Moreover the middle classes seem perfectly willing to move house to place their children in good schools.

Parts of the state school system seem to be

" while mixing is the welfare maximum, the choices of parents in

pursuit of the best for their children leans ineluctably towards

segregaton, the weljare minimum''

more than offset by gains for the lowquality children. In general higher quality children will suffer frommixing in schools while lower quality children will benefit more. It was surely these considerations, perhaps not ex- pressed exactly in these terms, that were be- hind the shift to comprehensive schools in the UK and part of the motivation of the busing movement in the US.

Mix and match If mixing is a social goal, it remains unclear how best to achieve it. Roughly as many lose from mixing as gain, so it is difficult to organ- ise a clear democratic majority in its favour.

evolving to what we have called free-matching (Rober- ston and Symonds 1996b), wherein parents apply to any school they please and schools select freely among applicants. If peer groups are all that matter, the best schools are, by definition, those with the best average quality of existing enrolment.

These schools will be vastly oversubscribed and can select' the cream of the incoming group, thus cementing their place in the hier- archy. The natural outcome of this system in the long run is perfect segregation, wherein the best school invariably receives the best tranche of the incoming cohort, the second- best school the second best tranche, and so on. However, perfect segregation represents, in fact, a welfare minimum.

When a school system functions like this, the more information parents have about schools, the worse the welfare outcome. If parents knew nothing about schools and the allocation of children were by chance, then

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optimal perfect mixing would result. Perfect knowledge facilitates perfect segregation. This may explain some of the instinctive op- position of sections of the teaching profession to the publication of ‘league tables’ showing the relative performance of schools in public examinations.

Providing incentives We have reached the pessimistic conclusion that, while mixing is the welfare maximum, the choices of parents in pursuit of the best for their children leads ineluctably towards segregation, the welfare minimum.

There is however a radical solution: the laissez-faire. The key point is that in principle one should be able to formulate prices that deal with the peer group effect (Rothschild and White, 1995). I supply services to my peer group; they supply services to me. In prina- ple, nothing stops these services attracting competitive prices.

If a school charged a fee per child that cor- responded to the benefit a child receives from their peer group minus the benefit they sup- ply to their peer group, these prices would lead to the welfare optimum of perfect mix- ing. Charging these fees means that children of less than average quality pay fees, while above average children receive payments for attending schools. (Vandenberghe, elsewhere in this issue, recommends a similar incentive scheme for parents to promote desegrega- tion.) Schools wish to attract some high qual- ity children to raise the quality of the peer group, thus enabling them to extract fees from

lower quality children (as Eton has known for 500 years).

One problem with this scheme is immedi- ately apparent: the parents of the lowest qual- ity children would be required to pay poten- tially high fees to place their children in schools. Since, in practice, these children would be largely drawn from the poorest so- cial groups, one would be trying to extract large compulsory fees from those least able to pay. Means-tested vouchers may provide some sort of approximation to the optimum. Parents could be given a sum of money to be spent on schooling, inversely related to their wealth. This is not a new idea. Consider John Stuart Mill in On Liberty:

Ifthegovernment would make up its mind to require for each child a good education, it might save itselfthe trouble of providing one. It might leave to parents to obtain the education when and how they pleased, and content itself w i th helping to pay the school fees of the poorer classes of children, and defraying the entire schooling ex- penses of those who have no one else to pay for them.

Apart from certification and public exams, the school system would then be allowed to be determined by market forces. The details of such a system and how one could begin to move towards it have yet to be thought through. Nothing like this exists anywhere in the world. But the evidence on peer groups is clear. If we are to get the most from our education system, we must find a way of desegregating our schools 0