in GS with the reverse pattern for those who switched from PS to GS. They also showed that people who lived closer to PS were more likely to attend PS and in turn, reported higher scores. As long as those who lived closer to PS were no different in terms of their ability compared to those who lived farther away, the estimates were causal, in that they estimated the local average treatment effect or LATE parameter in an instrumental variables framework.<sup>15</sup> After much commentary, the rights group remained unconvinced. Simple comparisons were obviously biased due to selection; studies that controlled for parental and child characteristics were biased due to selection on unobserved characteristics; studies that looked at child switching were biased due to selection on time-varying unobserved characteristics, and, like always, the exclusion criterion in the instrumental variables framework was suspect. What if parents whose children had higher ability bought houses closer to PS? Or, what if PS located in areas where children were higher ability?<sup>16</sup> By now, the lack of certainty was starting to gnaw at people. Would their ever be a resolution to this question? It was at this point that a study arrived with an experimental design.<sup>17</sup> In this study, a team went to villages and gave money to people who were currently going to GS to go to PS instead. The people who would get this money would be _randomly_ selected from the population of those who were currently patronizing GS. This would create two identical groups—in observed and unobserved characteristics—one of whom would receive the money and another who would not. As long as those who received money were more likely to go to PS, researchers could compare the quality of learning across people who received the money and those who did not. After appropriately adjusting for the fact that not all who received the money would go to a PS, one could causally estimate the impact of PS attendance on test-scores.<sup>18</sup> After completing data collection, researchers were surprised to discover that Math and Science testscores were identical in GS and PS. Puzzled, they decided to investigate further. What they found was that, although, PS did focus on Math and Science, PS overwhelmingly gave consumers what they wanted. In some cases, this coincided with the definition of “better” as improvements in Math and Science scores. In other cases, it did not—PS also taught the vernacular language and other services that the GS did not—and in these things, the PS were uniformly higher quality.

<u>Study Type 3: The third type of study that emerged from this effort was those concerned with the costs</u> of schooling. These studies showed first, that government teachers earned a lot more than private

> 15 There are a large number of studies in the first two categories, ranging from Jimenez and Tan (1991)  who looked at 5 countries to Bold and others (2011) from Tanzania. Other examples include Andrabi and others (2008b), Wadhwa (2009), Tooley and others (2011), Aslam (2009) and French and Kingdon 2010). Studies based on child-switching require longitudinal data and are rarer; two examples are Singh (forthcoming) who uses data from the Young-Lives data in the Indian state of Andhra Pradesh and finds larger changes in test-scores from private attendance in rural, but not urban areas and Andrabi and others (2011) who find large improvements in Pakistan for children tested in language and Mathematics. Andrabi and others (2014) present an example of an instrumental variables approach, using the distance to the private school conditional on the distance of the family from the center of the village as a source of exogenous variation.

> 16 These critiques are based on referee reports for the papers above 

> 17 See Muralidharan and Sundararaman 2014b.

> 18 There was one more twist: because there was also a concern that taking people away from GS to PS would reduce the quality of GS, in another set of villages no one received the money, but people still applied for it. This twist ultimately turned out not to be important, so we leave it out of our description.

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