The estimates, that we have presented and discussed so far, are based on the raw, unweighted data. In the absence of details on the weights that were provided to us, this was a safe strategy to follow. Any measurement errors in the weights or possible non uniformity in their calculations between countries may contaminate the cross country comparisons.17 Nevertheless, the issue of sensitivity of the principal results to the use of weights is of interest. In this section, we report the results of estimation on the weighted data and compare them with the earlier evidence. As the following discussion shows, the principal qualitative conclusions are fairly insensitive to the use of weights.
Table 42 presents the key summary statistics for 5 of the 7 countries, based on the weighted data. As already noted, while we did not have the weights for Panama, those for Portugal are identical. A comparison of Tables 1 and 42 shows that the weights have very little impact on the summary statistics, especially in case of Belize and Philippines. This is confirmed by Table 43 which reports the difference between the weighted and the unweighted estimates. The differences are most noticeable in case of the school enrolment rate, especially in Cambodia and Namibia. For example, in Cambodia, the weighted figures underestimate, in relation to the unweighted figures, the percentage of children who are in school and do not work and overestimate the number of children who combine schooling with employment.
Table 44 presents the IV, OLS estimates of the current school attendance variable in Namibia based on the weighted data. These estimates are comparable to those based on the unweighted data presented in Table 13. The numerical magnitudes of the coefficient estimates, though very rarely the sign, do vary between the comparable estimates. Given the focus of interest of this study, we restrict our attention to the coefficient estimates of the work hours, (work hours)2 variables. In case of both the IV and the OLS estimates, the statistical significance of the estimated impact of child labour hours on current school attendance in Namibia increases with the use of weighted data in the estimation. Also, Table 44 confirms that long hours of child labour do have a detrimental effect on school attendance. Table 45
17
For example, while Panama does not seem to have published weights, all the weights were equal (namely 50) for Portugal.
presents the corresponding estimates, on weighted data, for Philippines. These are comparable with the unweighted data based estimates presented in Table 21. A comparison shows that, unlike in case of Nambia, the estimated impact of child labour hours on schooling is quite robust between the weighted and the unweighted data, with respect to both size and significance. Once again, the highly significant coefficient estimate of the work hours variable in Philippines shows that child labour has a negative impact on child schooling at the point of the child’s entry into the labour market.
The 3 SLS coefficient estimates of the SAGE equation, using the weighted data, for Belize, Cambodia and Sri Lanka are presented in Table 46. A comparison with the corresponding estimates, based on unweighted data, presented in Table 34 shows that, while the magnitudes change somewhat, the direction of impact of child labour on SAGE is robust between the weighted and the unweighted data. For example, Sri Lanka continues to differ from the others in the sense that the first few hours of child labour impact positively on SAGE though, eventually, the impact does become negative because of the negative sign of the (work hours)2 coefficient. Note, also, for Sri Lanka that the turning point, i.e. the weekly work hours beyond which child labour impacts negatively on SAGE, declines from 13.21 hours on the unweighted data to 9.15 hours on the weighted one.
The 3SLS estimates of SAGE presented in Tables 34 and 46 ignore the truncation of hours of child work at zero. Table 47 presents the corresponding 3SLS estimates of SAGE in the presence of Tobit estimation of the child labour hours equation. These estimates strengthen the findings of the negative impact of child labour on schooling. In case of Sri Lanka, the inverted U shaped relationship, witnessed earlier, between child schooling and child labour now gives way to a monotonically decreasing relationship. In other words, the limited support that the Sri Lankan evidence provided to ILO Convention No. 138, Art. 7(b) disappears on the use of Tobit estimation of child labour hours.
Before concluding, we wish to comment on the wide divergence that exists in many cases between the IV and the OLS estimates. We put this down to, primarily, two factors: (A) The IV estimates of the schooling equation take into account the potential
The larger the “endogeneity”18 presented in the tables, the greater will be the divergence between the IV and the OLS estimates. The reader can readily verify this
by examining the Hausman statistic
( )
χ for testing for statistical significance of the 12 difference between the OLS and IV estimates presented in the tables.(B) The weaker the correlation between child labour hours and its instruments, the greater will be the divergence between the IV and OLS estimates of the impact of child labour on child schooling. Given the cross sectional nature of the data sets that are used here, the wide difference between the OLS and the IV estimates, in some cases, reflects the absence of strong correlation. One needs to keep this in mind in interpreting both the OLS and the IV estimates with care.
18
See Stewart and Gill (1998) for a lucid discussion of the possible causes of such “endogeneity” and on their econometric implications that help to explain the difference between the OLS and the IV estimates.