The authors attribute the success to the Kindergarten teacher's "treatment effect". I wrote the following comment 6 months ago after reading a new paper by Caroline Minter Hoxby but it appears to apply to this research.
Interpreting the Causal Effects of a Randomized Experiment When Subjects Optimize Conditional on Treatment Status
Matthew E. Kahn
Introduction
You are a parent who has one 9 year old child. You must allocate your scarce time between working in the market and investing in your child’s human capital. Your child is currently on the waitlist for admission to an elite school. There is a 50% chance that your child will be accepted and a 50% chance that your child will be denied this slot. This outcome will be determined by a coin flip.
Unbeknownst to you, a Ph.D. researcher is salivating at the opportunity to use a large sample of children such as your kid to study whether attending an elite school raises test score outcomes. This researcher foresees an ideal experimental design. For the subset of kids whose parents wanted them to attend this school, there is a randomization to see who actually gets to go. This randomization means that the unobservables at the baseline are the same for the control and treatment group. The PHD is confident that a simple before/after comparison for the treatment group and the control group will yield a clean estimate of the causal ATE of attending an elite school.
Unbeknownst to the PHD, essential heterogeneity lurks. The researcher implicitly assumes that unobserved home production of child skill formation is not taking place. But, consider the case in which you, the parent, believe that investments you make at home in your child are complementary to attending the elite school. If your child is admitted to the school, you plan to increase your investments in your child because the private returns of doing so have increased. The PHD , who cannot observe the black box, of what goes on within each household in the treatment and control group, implicitly assumes that the unobservables (home production) do not change over time.
But, in this case the kid who was assigned to the elite school who has the parent who believes that parental input are a complemnt invests more in the kid. The econometrician ascribes the ex-post increase in the test score (the noisy measure of the kid’s human capital) to attending the elite school.
In this sequential case of complementarity, the econometrician over-states the true treatment effect. In a nutshell, the program evaluator has assumed away the possibility of household production augmenting the extra resources that have been invested in the child by the randomization. Of course, if school inputs are substitutes for parental inputs then random assignment to the elite school will crowd out parental investments. It will especially crowd out such investments for parents with the highest opportunity cost of time.
So, Leonhardt and Raj Chetty credit the teacher -- but I believe that this overstates the teacher's contribution. The good teacher is a commitment device and the parents match her efforts with investments of their own.