There is a summary of the research in the New York Times:

In those families, if the first child was a girl, it was more likely that a second child would be a boy, according to recent studies of census data. If the first two children were girls, it was even more likely that a third child would be male.

Demographers say the statistical deviation among Asian-American families is significant, and they believe it reflects not only a preference for male children, but a growing tendency for these families to embrace sex-selection techniques, like in vitro fertilization and sperm sorting, or abortion.

Here is the source article.  There is one small problem with the conclusion:

To reduce the probability that there was an eldest child not in the household, we also restricted our sample to families where the oldest child was 12 years or younger.

Here is the problem.  Let’s suppose that Asian-American parents have a preference for boys but do not engage in any manipulation, except that they keep trying until they get one boy.  Consider two families.  Both families have kids spaced 3 years apart.  The first family has a girl and then a boy and stops.  The second family has 4 girls before the first boy is born.  The first family is included in the sample, the second is not.  More generally, families whose first two children are girls are less likely to be included in the sample than the boy-girl families.  This statistical selection makes it look as if the parents are actively engaged in selection.

The 12 year cap may exclude very few families and so this selection effect may be too small to generate the statistics they are reporting, but it’s hard to know for sure.  The sample sizes are not large.   Here is a graph showing large and overlapping confidence intervals.

It is worth acknowledging that even my alternative story relies on Asian-American parents having a stronger preference for boys than the American population as a whole.  However, it doesn’t require the assumption that they engage in pre-natal sex selection.

Update: The ever-vigilant Marit Hinnosaar (are you noticing a pattern here?) has pointed out to me that I mis-interpreted their sample selection criterion.  As she puts it:

The situation you discribed would create a problem if their sampling method was: include in the sample each household iff the age difference of the children is no more than 12 years. But that is not what they did. With the sampling method they used, they included households, where the oldest child in the household was born not earlier than in 1988 (they used 2000 census data and excluded households that had a child older than 12). This does not lead to the biased sample that you described, since for the researchers these two households that you described are equivalent in terms of whether to include in the sample.