The one school characteristic that is consistently and significantly correlated with learning achievement is teacher engagement in teaching in MP and UP and teacher presence in Karnataka. In all three states, most other school or teacher characteristics are not associated with test scores. In Karnataka 88 percent of teachers are present and of those present, almost 80 percent are actively engaged in teaching. Since most teachers who are present are teaching, this may explain why teacher attendance is significant in the score regressions and not teacher activity.

Based on the regression coefficients, we calculate that if about half the teachers were engaged in teaching in MP and UP i.e., teaching activity roughly doubled in magnitude, scores would be higher by 17-31 percent in math and language in the three grades. We would have expected an increase in teacher activity of this proportion to be associated with a bigger increase in score. One reason for a small effect is that teacher activity may not measure real teacher effort precisely. Another reason is that teachers may not be effective in classrooms in MP and UP. For example, if average teacher attendance and engagement in teaching in MP and UP were to be the same as in Karnataka and assuming all other factors influencing learning stayed constant, the average scores in grade 4 in MP and UP would still be below 40 percent, far from the average of 70-75 percent in Karnataka.

Although we have reported test score correlations (not causations) based on a cross section survey, our findings are consistent with international evidence on the impact of school and teacher characteristics on student test scores. A number of studies find no conclusive impact of class size on student performance (Hanushek, 1998; Lazear, 1999) consistent with our results from MP and KA. There is evidence however that the impact of policies on class size may depend on the level of education concerned and the absolute level of class sizes. Class size may matter when the average size is quite large, as in UP schools which have average class size of 70.

On the other hand, there is fairly robust evidence that of the school level variables which can be influenced by policy, factors to do with teachers and teaching are the most important influences on student learning. The broad consensus is that teacher quality is the single most important school variable influencing student learning (DarlingHammond, 2000; Rockoff, 2004; Rivkin, Hanushek and Kain, 2005). But what it is about teachers that matters is less well known. Researchers agree that many important aspects of teacher quality are not captured by the commonly used quality indicators such as education, experience, and subject matter knowledge. Two recent studies find that teacher attendance has a positive impact on test scores (Duflo, Hanna and Ryan 2007; Miller, Murnane and Willet, 2007). Broadly parallel to these findings, our results show that teacher effort is positively correlated with student performance, unlike other attributes of schools or teachers including education and experience that have no correlation.

# **4.2.3 How Much of the Variation in Test Scores Is between and within Schools?**

Regressing scores on school fixed effects gives the variation in scores attributable to variation in observed and unobserved characteristics across schools and villages. The 13