services, and no large investment requirements, benefit incidence theory predicts the
opposite case as more likely to occur.11
Based on a grid search of access rate thresholds, the ex post threshold revealed by
spatial regressions turns out to exceed the average cross-district access rate for primary
schools in Niger, thus suggesting looser selection criteria for public investment
in this sector. As a second issue focused on here, to avoid violating an SWF equityrelated
axiom, the number of uncompensated losers should be treated as a separate
social objective, distinct from efficiency and distribution. For public healthcare, the
numbers effect proxy has the expected positive sign. However, relative to this effect,
econometric estimates for both sectors are to some extent sensitive to shifts in the
eligibility dummy, use of population as a control variable, and spatial heterogeneity.
Results of global spatial regressions and regressions with spatially varying bandwidths
cannot be easily compared. Relative to primary education, spatial regressions
yield statistically significant parameters associated with agro-climatic dummies, thus
implying that in this case spatial heterogeneity can partly be accounted for by spatial
regimes. However, spatial weight matrices are based on two a priori cut-off
distances, which are assumed to represent possible spillover effects with relatively
shorter and longer ranges: if long-T panel data were available, a more accurate procedure
would be to directly estimate the spatial weight matrix ([5]). On the otherhand, highly collinear GWR local coefficients can be associated with model instability:
this is found relatively often in GWR applications ([38]), and may partly
concern some GWR results of this analysis (Table 3: ρ(βzi)). Similarly to limitations
of OLS in terms of degrees of freedom for estimation, with small sample
sizes an increased risk of spurious correlations between local coefficients can lead to
failure of GWR to more thoroughly detect spatial heterogeneity, relative to results
achievable with larger datasets ([16]). Rather than regarding them as rival modelling
approaches and notwithstanding limitations in data availability in developing
countries such as Niger, both spatial regression and GWR can help shed light on
factors influencing changes in the geographical allocation of public service delivery
in a low-income economy. To gain further insights, the analysis would also benefit
from spatially disaggregated time series information when it becomes available (so
as to cross-check results based on more refined spatial scales), and from applications
to other developing countries.