22 CHAPTER 2
are likely to be different between schools. As a result, for quasi-privatized and budget-constrained public schools, LERs could have wide variations in cross-section as well as time series. The appendix presents a simple model that formalizes this idea.
Empirical Specification, Identification, and Estimation In the empirical analysis, I estimate a response function of educators to learn- ers taking into account school budget condition:
Hit = [I(y* > φit)β* + I(y* < φit)γit(p)]Lit + µi + εit, (2.1)
where β* ≥ γit(p), p denotes population group, and µi is the fixed effect that reflects unobserved school- and community-specific components. I(y* > φit) means that the school is not budget constrained, while I(y* < φit) means that it is budget constrained. In the latter case, adjustment of educators is lower
than the optimal. The derivation of γit(p) is given in the appendix. Here local condition f is also represented by population group p. Since, in the analysis
using the SRN, the information on subsidies and school fees is not available, I assume the patterns according to which these two variables are determined
differ across population groups. I estimate γit(p) as a reduced-form parameter in the estimation of (2.1).
In equation (2.1), as in many cross-sectional studies, it is likely that the
number of learners is correlated with the unobserved fixed component µi, which will bias the OLS estimate of the slope. For example, in communities experiencing rapid urbanization, where teachers can easily commute from urban centers and learners can migrate to them, the numbers of learners and educators will increase simultaneously. In this case, OLS estimates are biased upwardly. Assuming that parameters do not change over the four years, after conditioning on cross-group differences, we difference them between two periods:
∆Hi∈p = Σγi(p)∆Li∈p + ∆εi, (2.2) p
where ∆ is the differencing operator. The shocks are assumed to be ex post in each period.
The parameter of interest represents the degree of liquidity constraint. As we will see in the section “Distribution Comparison,” the empirical distribu- tions of LER motivate the analysis of determinants for the observed LER gaps across population groups. However, naive comparisons of LER distributions
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