As the private share of school enrollment increases simple cream skimming becomes less plausible as the explanation for a higher rate of achievement in private schools. If the private schools cream skim when they are at 10% of public school enrollment how much cream can be left in the public school pool when the private schools account for 60% of total enrollment? Thus, if this simple form of cream skimming is the explanation for the higher achievement rate in private schools, we would expect the “private effect,” the difference between private and public scores, to be smaller in regions with a high
share of private schooling.