Advocates for educational reform frequently call for policies to increase competition between schools because it is argued that market forces naturally lead to greater efficiencies, including improved student learning, when schools face competition. Researchers examining this issue are confronted with difficulties in defining reasonable measures of competition within local educational markets. We approach the problem through the application of Geographical Information System (GIS) tools to the development of a school competition index (SCI) for the state of Mississippi. The SCI captures the degree of competition each public school in the state faces from peer private schools spatially located within their local market area. We find that higher degrees of competition from private schools significantly increase public primary and high school efficiency, as measured by the proficiency rates on high-stakes examinations. It is anticipated that the current results will inform policymakers regarding the viability of competition-based reforms.
That is from an article by Misra, Grimes, Rogers, forthcoming in Economics of Education Review (December 2012).
Unfortunately I did not find the full paper online, but more competition can also have high impact on efficiency of public universities. In some countries there is only one public university [it does not compete against other public universities and therefore it has little incentives to improve efficiency]. Of course there is a lot to gain by reducing entry barriers to new private universities. Although this might not be necessary in the near future [or even now!] with many excellent classes available online for free [a nice way in which proactive students can circumvent the efficiency problem in higher education in developing countries].
[A specter is hunting the developing world, it is the specter of higher education for free . . . ].