If regression results based on a 45% threshold are relied on, the respective healthcare
regression specification (Table 2: H3) yields estimates suited to test the parameter
inequality restriction for equation (2.3) (sub-section 2.2). Based on the median
value of the cross-district population in 2003 (Pi) and the average healthcare coverage
rates in the initial period of 2000-01 of (i) districts under or equal to the 45%
threshold and (ii) the whole district sample, and assuming that the ratio of these
rates approximately corresponds to the ratio of the respective latent mean access
indices (μ∗/μ), the result would be compatible with restriction conditions (2.4),
i.e., with reverse signs: −αN(Pi)(= −α) = 0.0009(306.08) = 0.275 > δ(μ∗/μ)(=
(vw − vb)μ∗) = 0.17(0.31/0.37) = 0.142 > 0. However, the grid search on eligibility
dummies, also based on the alternative cut-off distances in spatial weight matrices,
suggests thresholds of 40% for healthcare (for which the parameter associated
with the numbers effect is statistically insignificant), and 55-60% for primary schools
(Table 2: H2 and S2-S3). The former percentage figure is close to the cross-district
average access rate for healthcare, which was nearly 38% in 2002-03, while the latter
tends to overstate the respective figure for primary education (51.5% in 2004-05).