The total rate of education by level (TETi) is given by:
TETi = PoPi/ PoPT = ∑ nPoPi x / nPoPx * nPoPx / PoPT = ∑ nTEi x * nCix where:
PoPi = the number of people with at least one completed grade in educational level i;
PoPT = the total population;
nPoPi x = the number of persons in the age group x to x+n with at least one completed year of educational level i;
nPoPx = the number of people in the age group x to x+n;
nTEix = the education rate by age group;
nCx = the age distribution of the population;
that is, the weighted mean of the rates of education, where the weights are given by the distribution of the population for each age group.
Between 1970 and 2000, the rates of educational attainment for the total population had moved sufficiently for both sexes, registering a reduction in the proportion of people with no formal education and a growth in all other levels (see Tables 4 and 5). However, the age structure of the population also moved, revealing more elderly, as can be observed in Figures 13 and 14. As discussed earlier, the improvement in educational attainment was more accented in the younger age groups.
Let us now analyze how much of the difference among the prevalence rates by level of education in the period can be attributed to the change in the age structure of the population, and how much to the change in education rates, in synthesis, to decompose the effect.
Table 4. Educational attainment by level and year, females.
No education Primary Secondary Tertiary
1970 39.44 54.35 5.14 1.06
1980 28.08 58.26 9.83 3.83
1990 19.84 58.16 15.65 6.35
2000 11.25 60.61 19.93 8.20
Table 5. Educational attainment by level and year, males.
No education Primary Secondary Tertiary
1970 34.83 58.41 4.27 2.49
Figure 13. Relative distribution of the female population by age group, 1970 and 2000.
0.00
Figure 14. Relative distribution of the male population by age group, 1970 and 2000.
The expression used to decompose the difference (∆) between the rates will be:12
∆ = TETi A
where the first term computes the contribution for the difference between rates A and B that can be attributed to the change in the distribution of the population by age group;
the second can be attributed to the change in the rates by education.
The results of the decomposition by sex can be seen in Tables 6 and 7.
Comparing the first line of the two tables, we can see that the improvement in the level of education for women in the given period was greater than for men. The effect of the change in the age structure on the difference in the rates by education depends on the level that is being analyzed. For people with no formal education, the older age structure tends to increase the TETi, because the rates are higher in the older ages, diminishing the difference between the rates of the two periods. In fact, if there were no change in the age distribution, the rates in 2000 would be lower in this educational level, and the difference between the rates would be bigger.
Table 6. Decomposition of the difference in the female prevalence rates between 1970 and 2000.
No education Primary Secondary Tertiary
Original difference -28.19 6.26 14.80 7.14
Contribution of the difference
between distribution 1 2.00 -1.55 -0.51 0.07
Contribution of the difference
between age specific rates 2 -30.19 7.81 15.31 7.07
Total contribution -28.19 6.26 14.80 7.14
Proportion of the difference
given by 1 -0.07 -0.25 -0.03 0.01
Proportion of the difference
given by 2 1.07 1.25 1.03 0.99
Table 7. Decomposition of the difference in the male prevalence rates between 1970 and 2000.
No education Primary Secondary Tertiary
Original difference -23.59 5.29 13.25 5.06
Contribution of the difference
between distribution 1 0.85 -0.84 -0.17 0.16
Contribution of the difference
between age specific rates 2 -24.44 6.13 13.41 4.90
Total contribution -23.59 5.29 13.25 5.06
Proportion of the difference
given by 1 -0.04 -0.16 -0.01 0.03
Proportion of the difference
given by 2 1.04 1.16 1.01 0.97
With relation to the primary and secondary levels, the two components of the difference have contrary signs, but in contrast to the previous level, the TETi grew in the given period. The results show that the aging of the population caused a decrease in the difference between the rates of the two periods or, said another way, the TETi 2000 would have been bigger if the age structure of the population had not changed. The effect of the change in the distribution of the population is bigger for the primary level than for the secondary, since the first population tends to be younger than the second.
For the tertiary level, the population at this level is older, and the two components act in the same direction, increasing the difference between the periods and the TETi of 2000.
Between levels, the effect of the change in the age structure is stronger at the primary level (-25 percent and -16 percent of the rates for females and males, respectively), since people complete this level at lower ages.
In Table 8 we can observe how the difference between education rates among women and men in 2000 can be explained by the variation in age structures. In 2000, the proportion of women who completed at least one year of secondary and tertiary education is greater than for men, and less for those who completed at least one year in primary. Thus, the difference between rates is positive for the higher levels and negative for the lower level. The older age structure of women who completed at least one series at the primary level (Figure 15) is responsible for 11 percent of the difference. However, as more women have recently begun to take advantage of the opportunity for secondary and tertiary education, the age structure in these levels has become younger (Figures 16 and 17). The difference in the age structure diminishes the difference between rates.
Even if men and women had the same age distribution in these levels, women would still have the bigger prevalence rates over men.
Table 8. Decomposition of the difference between male and female prevalence rates in 2000.
Primary Secondary Tertiary
Original difference -3.09 2.42 0.66
Contribution of the difference
between distribution 1 -0.35 -0.30 -0.01
Contribution of the difference
between age specific rates 2 -2.74 2.72 0.67
Total contribution -3.09 2.42 0.66
Proportion of the difference
given by 1 0.11 -0.13 -0.02
Proportion of the difference
given by 2 0.89 1.13 1.02
0.00
Figure 15. Proportion of men and women with primary degrees by age group, 2000 census.
Figure 16. Proportion of men and women with secondary degrees by age group, 2000 census.
0.00
Figure 17. Proportion of men and women with tertiary degrees by age group, 2000 census.
Conclusion
In this paper we examined the changes in the prevalence rates of education for people 15 years and older with no formal education and with at least one completed level of primary, secondary, and tertiary education, by age groups and sex, for the period 1970 to 2000. We observed that in this 30 year period, there was a noticeable decrease in the proportion of males and females with no formal education in all age groups. For the older age groups, an increase in formal education resulted in an increase in the percentage of people with a primary education. For the younger age groups, the increase in the ratio of people with secondary and tertiary education is more significant. As a consequence, the analysis of the curves of the prevalence rates in secondary and tertiary education, by age group and year, suggests a bigger school attendance period for the years 1990 and 2000.
The cohort analysis showed that although the participation of women in the higher degrees of education was lagging behind the men, there was an increase in the participation of the cohort aged 15-19 years in 1970 in the tertiary level. Added to a longer life expectancy for women, men and women in 2000 practically had the same proportion. For secondary education, the proportion of women in the two younger cohorts, 15-19 and 20-24 was already superior to men in 1970.
Moreover, preliminary analyses on mortality differentials and immigration by education demonstrated the importance of these variables in the study of the growth of prevalence rates for educational levels.
When comparing the differences between the rates of 1970 and 2000 for educational attainment, we find that the relative rates for women showed a bigger alteration than for men. We also found that part of this difference can be attributed to the change in the age structure of the Brazilian population. The older age structure in 2000 tended to diminish the difference among the rates for no formal education, primary and secondary, but the impact on the 2000 rates is not the same in the three levels. The rates for people with no formal education decreased in the given period and the difference is negative. We can say that had there been no change in the age distribution of the population, the rate in 2000 would be even less. For primary and secondary education, the difference is positive, and had the age structure been the same as in 1970, the rates of 2000 would be bigger. With relation to the tertiary level, the older age structure contributed to an increase in the rate for 2000.
The impact of the different age structures of men and women by education in 2000 showed that if men and women in the secondary and tertiary levels had the same distribution by age, then the rates for women in these levels would be higher.
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