The abstract of the paper is at http://www.nber.org/papers/w19542 , and the paper is at http://artsci.wustl.edu/~pantano/Birth_Order_School_Performance.pdf . One could ask if it is fair to younger children to not push them as hard, or if it is fair to the oldest to be prodded to set an example. All three of children often say that we aren't being fair, which is perhaps a sign of our impartiality smile. The description of how parents raise first-borns reminds me of the Tiger Mother.

http://www.nber.org/digest/mar14/w19542.html
BIRTH ORDER AND STUDENT PERFORMANCE

V. Joseph Hotz and Juan Pantano

...mothers with two children were almost 8 percent less likely to say that their second child was one of the best in his class.
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Does birth order correlate with student performance, and if so, why? In
Strategic Parenting, Birth Order and School Performance (NBER Working Paper No. 19542),
V. Joseph Hotz and Juan Pantano present both empirical and theoretical
evidence on these questions. They study all children born to the female
respondents in the 1979 National Longitudinal Survey of Youth in families of
two, three, or four children.

They find that birth order affects perceived academic performance for 10- to
14-year-olds. On average, mothers with two children were almost 8 percent less
likely to say that their second child was one of the best in his class.
Earlier-born children also had higher scores on the Peabody Individual
Achievement Test and the Peabody Picture Vocabulary Test at age ten. The effects
of birth order persisted for second children even when the sample was restricted
to "intact" families in which children's performance had not been affected by
divorce or other family disruptions.

The evidence suggests that earlier-born siblings are more likely to be "subject
to rules about TV watching and to face more intense parental monitoring
regarding homework" and that "mothers are more likely to report that they would
increase the supervision of one of their children in the event that child
brought home a worse than expected report card when the child in question was
one of her earlier-born children."

The authors draw on game-theoretic models that emphasize reputational concerns
in an attempt to explain the correlation between birth order and children's
school performance. They conjecture that earlier-born siblings will put forth
more effort in school and end up performing better because parents are more
likely to set higher standards for earlier-born children and to impose
consequences for poor performance. The study concludes that "parental reputation
dynamics may explain part of the observed birth order effects in school
performance."