Private Education in India: A Novel Test of Cream Skimming

I. INTRODUCTION Students in private schools routinely outperform those in public schools both in the United States and around the world. (1) But do private schools make students better or do they simply attract better students? Most studies find that private schools do attract better students. The question then becomes whether this "cream skimming" effect fully or only partially explains private school performance. It is a difficult question because researchers do not observe all elements of student quality and, due to peer effects, individual student quality enters into aggregate school performance in complicated ways (Altonji, Huang, and Taber 2010). The question is also difficult because in most places in the world there are many more children in public school than in private school. As a result, the private schools have a very large population of students to select from and it is easy to imagine that in one way or another the private schools select the cream of the students from the public schools. In this article, I take advantage of the remarkable fact that in many districts in India a majority of students are in private schools. 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. In contrast, if the private effect is caused by higher-quality private schools then the private effect will be constant even as the share of private schooling increases. Perhaps, private schools cream skim from the public schools even as the cream in the public schools diminishes. In this case we might still see a private effect even as private schools increase their share of the school population, but we would also see decreasing private and public scores as the private share of schooling increases. Most generally, cream skimming says that the private school effect is a compositional illusion created by the way children are allocated to schools. Thus, if cream skimming is the explanation for higher performing private schools, then as the share of private schooling increases there should be no effect on mean test scores taken over the entire population of children. II. A MODEL OF CREAM SKIMMING Let student quality in the total population be uniformly distributed on 110,11; so, mean quality in the population is 1/2. Cream skimming can take a wide variety of forms; assume that compared to the public schools the private schools increase their draw from the zth percentile by a factor of 13. In this case, the probability distribution function (PDF) of the private distribution is given by: (a)/(a + [bata] - [bata]z), x [less than or equal to] z (a + [bata])/(a + [bata] - [bata]z), x > z where a is a parameter for the total draw from the public distribution, that is, the private share. Using this PDF and the corollary PDF for the public schools, the mean score in the private schools is given by (a + q - q[z.sup.2])/2(a + q - qz) and the public mean by (-1 + a + q - q[z.sup.2]/2(-1 + a + q - qz). Figure 1, for example, shows the private and the public PDFs with z = .2, [bata] = .1, and a = .04. With these parameters, the private share of schooling is 12%, the mean score in private schools is .567, and the mean score in public schools is .491. Figure 2 shows the public, private, and population means as the private share increases. When the private share is low, public school scores must be close to the population average, but the private effect can be large as private schools can select from the cream of a very large pool of public school students. …