We use simple linear regression to further investigate the relationship between changes in school attendance, the F'ONCODES index, and FONCODES expenditures. Table 6.1 shows results for four regressions. The change in the district-level school attendance rate is the dependent variable in all of the specifications. The independent variables are the FONCODES index only (row 1), per capita FONCODES expenditures on education only (row 2), both the index and expenditures (row 3), and per capita expenditures instrumented with the index (row 4). An identifying assumption of the instrumental variables specification is that initial conditions, as measured by the modified FONCODES index, affect _changes_ in school attendance only through their effect on the amount of funding received by a district.

The results in Table 6.1 suggest that changes in school attendance are consistently related to the FONCODES index: when only the index is included in the regression, a one-standard deviation increase in the index is associated with a non-trivial increase in the attendance rate of 0.043 points. Changes in school attendance are also related to differences in per capita FONCODES expenditures: when only per capita expenditures are included in the regression, a one-standard deviation increase in expenditures is associated with an increase of 0.043 in the attendance rate.l1 When both the index and expenditures are included in the regression, the effect of school expenditure decreases substantially. This is perhaps not surprising, since the FONCODES index is the main determninant of FONCODES expenditures. Finally, when per capita expenditure is instrumented with the index, the effect of education expenditures is significant and very large indeed: a one-standard deviation in expenditure is associated with an increase in the school attendance rate of 0.141 points.

attendance rates in the later years. Moreover, if attrition is negatively correlated with income, so that children in poorer areas are more likely to drop out during the school year than their counterparts in rich: r areas, our estimates could _underestimate_ the effect of FONCODES expenditures on attendance. The LSMS surveys provide some evidence that attrition does affect measures of district-level school attendani ce rates. The 1994 LSMS was conducted between June and August, and the 1997 LSMS was conducted between September and November. In the 1994 LSMS, there is a drop in attendance rates of primary-ag -d children of two percentage points, from 96.6% to 94.6%, between June and July. This decline is concentrated among children in districts with a higher value of the FONCODES index. For example, for children in districts with a value of the FONCODES index greater than 14 (roughly the median), the attendance rate declined from 96% to 92%. However, there is no systematic change in attendance rates across months after July in either the 1994 or 1997 LSMS. Since the 1993 census was conducted in June, a portion of the high rate of attendance in 1993 shown in Figure 6.1 may reflect the higher attendance durittg the earlier part of the school year. Furthennore, given that attrition after June is more likely for poorer children, the results may undlerstate the gains made by children in poor districts relative to those in rich districts between 1993 and 1996. As a double-check on our results, we repeated the analysis of Figures (. I and 6.2 using the 1994 and 1997 LSMS surveys, including and excluding observations from June. Although the results are somewhat noisier, since there are fewer districts, we found that the results based or the LSMS surveys are similar to those using the census and INEI, and that excluding June has almost no effect on the relationship between the gain in attendance and the FONCODES index.

**18** The standard deviations of the FONCODES index and per capita expenditures are 7.6 points and 9.7 soles, respectively.

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