SCHOOL QUALITY, CLUSTERING, AND GOVERNMENT SUBSIDY 51 and
∆Yjk = γ0 + γ1 ln pjkt + γ2 ln gjkt + γ3∆Ljk + γ4 ln pjkt∆Ljk + γ5 ln gjkt∆Ljk + z′jkζ + ∆ξj,
(3.3)
where ∆ is the difference operator, Yjk is the number of educators, Ljk is the number of learners, yjk is the LER, and gjkt is the per-learner subsidy from the government. Here zjk includes indicators of former departments. In both specifications, we take the first difference between two periods to eliminate school- and location-specific unobserved fixed effects.
The LER is used as a measure of school quality. However, we also admit that this measure can only partially capture overall school quality, which is determined by such other measures as teaching facilities (classroom condi- tions) and quality of school administration. I constructed the LER from two school censuses in 1996 and 2000, which focus on school facilities.12 Since the government subsidy allocation had in principle not changed before 2000, we assume that the subsidy reported for 2000 was basically applied to the period before 2000.
To supplement the limited number of subsidized educators, community members can collect school fees and employ educators privately. I therefore also test whether a change in the number of learners induces a change in the number of educators who are privately employed in the community. If the government allocates subsidy more to disadvantaged schools (that is, a smaller number of educators relative to the number of learners), poten-
tial bias in γ2 would be upward since differenced ξjt are positively correlated with per-learner subsidy gjkt. On the other hand, if government subsidy allo- cation increases inequality in the number of educators, we expect a down-
ward bias in the estimate. However, since fixed unobservables are already differenced out, the systematic component of endogenous subsidy allocation has no impact on our estimates.
Finally, the determination of per-learner subsidy is also of interest in the empirical analysis. Though one possible way to eliminate the bias mentioned
earlier is to use instruments for gjkt, we lack identifying instruments in the available data. Therefore I simply examine the effects of school fees, the initial LER, former departments, and school type and location fixed effects.
12 Since measurement errors are reported on number of learners in the Annual School Surveys, we decided to use the 1996 and 2000 SRNs. These have a simplified questionnaire structure focusing on school facility information. Therefore, they are likely to have smaller measurement errors.
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