In India, the results are more ambiguous. The cross-sectional results for the distance to the nearest primary school are insignificantly different from zero, as are the fixed-effects estimates. District fixed-effects yields a marginal effect estimate that lies between the crosssectional year-specific ones. The marginal effect of the distance to the nearest secondary school is insignificantly different from zero in the cross-sectional and state fixed-effects estimates, but becomes larger in absolute value and statistically significant in the district fixed effects estimates. In Niger, region fixed-effects yield estimates that are between the cross-sectional yearspecific ones. It is possible that this could just mean that regional fixed-effects are not sufficient to take account of the relevant local attributes and therefore the results just give an “average” of the cross-sectional results.

These exploratory results from three countries do not suggest that cross-sectional estimates systematically understate the impact of distance on enrollment—which would bias the results toward the small impacts described above. Of course the exploration has limitations: in only two cases can the fixed-effects be estimated at a level that one might reasonably expect school placement decisions to be made at (districts in India, districts and clusters in Bangladesh). They rest on the assumption that attributes that are geographically fixed would drive any selective placement. Moreover, they are limited to only three countries where the requisite data are available and the problem of compensatory selective placement could differ across governments, for example, if more effective governments might be better at locating schools where enrollments would have been lowest in their absence.

To some, the inability to systematically control for potential endogeneity of the distance to school in DHS data might raise the question of whether it is worthwhile carrying out this multi-country analysis at all. The fact that the fixed effects in Bangladesh and India revealed no substantive bias is one finding supportive of going ahead. In addition, there are advantages to going ahead with implementing the same empirical specification across a number of data sets from a variety of circumstances. First, the approach avoids the issue of publication bias where non-significant findings are ignored. Second, it puts the variability of the estimated effects in focus—the elasticity of the distance to primary school ranges from -0.3 percent to 0 (or even positive in the case of Senegal) and a selective review of the literature emphasizing the largest findings could potentially overstate the “typical” response substantially. The results can certainly be interpreted as a summary of the conditional associations between enrollment and distance found in these data sets. Making the next step to interpret these as estimates of the causal effects is clearly less obvious, but the evidence suggests that it is not unreasonable.

_Non-linearity in the relationship_ The estimates so far have specified enrollment as a simple linear function of distance but the impact of distance on enrollment might vary.<sup>6</sup> Two alternative specifications of distance are explored: (1) a non-linear specification that estimates a probit model with distances included up

> 6 Except to the extent that the probit model itself introduces an element of non-linearity.

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