Is History Destiny? Resources, Transitions and Child Education Attainments in Canada - December 2002

5. Multivariate Analysis of the Long Term Impact of Household Resources on Attainments

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The descriptive data presented in the previous chapter provide some prima facie evidence of the persistence of advantage or disadvantage in attainments over time. In this chapter, we consider a multivariate analysis of the long-term impact of household resources on attainments. Our starting point is an investigation of the associations between child, pmk and household characteristics in 1994 with attainments in 1998. There are two attractions to this approach. First, because we are not using contemporaneous data, these results are less subject to endogeneity bias than studies examining the determinants of current attainments as a function of current characteristics. (For example, children with low attainments may require additional parental care, reducing the time available to earn income. In such circumstances, causality runs from attainments to incomes.) Second, suppose that only current, not past, household circumstances determine attainments. If this is the case, we would expect, for example, to find no relationship between past incomes and current PPVT, math or reading scores. In other words, examining the links between past characteristics and current outcomes is one way of testing more formally the notion of "history as destiny." In chapter 7, we complement this analysis by including, as an additional characteristics, the child's prior attainments.

Specifically, we estimate the following relationship:

Where Y_ij is the attainment of child i, living in household j, , are parameters to be estimated, X_ij is a vector of child, pmk and household characteristics and u_ij is a white noise disturbance term.

Given the importance placed on differentiating the impacts of household resources by age, we estimate this model separately for our four cohorts. Our dependent variables are indicators of attainments in 1998: the PPVT score for children aged 4-6; and the math and reading scores for children aged 8-9, 11 or 13 and aged 15. We divide our regressors into three broad categories, child, pmk and household characteristics. Child characteristics are age, sex, and and indicator variables denoting quarter of birth, children with activity limitations, number of siblings and birth order. Pmk characteristics are age, sex, education, ethnicity and an indicator variable for suffers a chronic health condition. Household characteristics are province of residence, whether the household is in a rural location, household income per adult equivalent (using OECD equivalence scales) and household income squared.¹⁰ Mean values for these variables for each cohort of children are found in Table 1.

Table 1
Descriptive Statistics

	Children 4-6	Children 8-9	Children 11, 13	Children 15
Dependent variables
PPVT score	98.6
Math score		401.3	518.5	631.7
Reading score		223.9	268.6	289.2
Regressors
Child age (cycle 1)	1.02	4.6	8.0	11.0
Female	48.7%	48.9%	49.2%	51.1%
Born in 2nd quarter	28.3%	24.1%	27.6%	28.0%
Born in 3rd quarter	24.4%	26.3%	26.9%	25.3%
Born in 4th quarter	21.4%	26.0%	18.6%	22.2%
Limited in Activity	2.2%	4.0%	3.8%	5.2%
Siblings in the household	0.98	1.38	1.56	1.44
Child is the eldest child in household	44.8%	42.2%	42.5%	38.7%
Age of the PMK	30.1	33.4	36.5	38.7
PMK is female	97.2%	96.7%	96.0%	96.1%
Lone parent household	14.5%	17.2%	13.7%	15.8%
PMK has less than a high school education	14.8%	14.8%	16.4%	18.8%
PMK has a diploma/certificate	21.8%	21.1%	19.4%	21.6%
PMK has a university degree	17.9%	15.0%	14.9%	15.7%
PMK has a chronic condition	38.5%	40.4%	45.7%	46.5%
PMK is black	1.1%	1.3%	2.1%	1.4%
PMK is North American Indian	4.5%	4.2%	4.0%	4.2%
PMK is Chinese	1.6%	0.8%	1.2%	0.7%
PMK is other race	18.0%	16.5%	16.6%	11.3%
Newfoundland	1.6%	1.9%	2.0%	2.4%
Prince Edward Island	0.4%	0.5%	0.6%	0.6%
Nova Scotia	3.0%	3.1%	2.8%	3.4%
New Brunswick	2.1%	2.4%	2.6%	2.3%
Quebec	23.7%	22.3%	21.6%	22.5%
Manitoba	4.0%	4.1%	3.6%	3.5%
Saskatchewan	3.6%	3.8%	4.1%	4.0%
Alberta	10.9%	10.8%	11.0%	10.6%
British Columbia	12.0%	12.8%	13.4%	10.7%
Rural	16.6%	19.5%	19.3%	21.9%
Adult equivalent income	19449	18214	19392	20223
Adult equivalent income squared	562,779,038	485,111,031	545,515,422	573,313,282
Change variables
Child developed a long term condition	4.0%	5.5%	6.4%	8.9%
Child no longer has a long term condition	2.7%	4.4%	4.3%	7.1%
Child has more siblings in house	36.7%	14.7%	7.2%	5.3%
Child has less siblings in house	4.4%	7.2%	8.9%	16.1%
Child is now in a step family	6.0%	6.4%	5.4%	4.3%
Child is no longer in a step family	4.3%	5.7%	4.1%	4.1%
Child changed schools/daycare	55.4%	30.3%	26.6%	21.9%
Child moved	46.5%	38.2%	31.1%	28.6%
PMK divorced	9.4%	7.0%	4.4%	5.4%
PMK married	6.6%	7.0%	4.5%	4.7%
PMK gained education credentials	6.6%	7.8%	7.7%	7.0%
Household poor in 1994 / 1998	16.4%	15.0%	12.7%	9.4%
Household poor in 1994/ not poor in 1998	11.8%	15.7%	12.6%	8.7%
Household not poor in 1994 and poor in 1998	8.2%	7.4%	5.6%	8.7%

In preliminary work, we experimented extensively with this specification. We used different functional representations for incomes, for ages and for education attainments. (For example, we expressed education in terms of years of schooling and different categorical groupings of levels of education attained by the pmk. We used log of incomes and categorical descriptions of the level of household income, including dummy flags for poverty status rather than a continuous income measure.) We experimented with the inclusion of other child, pmk and household variables suggested in the literature, including hours worked outside the home per parent present and home ownership. Following the discussion outlined in chapter 2, we tried average incomes over all three cycles of the NLSCY. We also explored the impact of including neighbourhood characteristics such as: neighbourhood unemployment rate, percentage of adults in the neighbourhood who had not completed high school, proportion of lone mother families in the neighbourhood. Given that we are focussing on educational attainments, we investigated the importance of information from the teacher questionnaires such as teacher characteristics (e.g., level of education, gender, years of experience) and classroom characteristics (e.g., class size; mixed grade class). Using any of these alternative specifications has no meaningful impact on the results reported below and, in general, these variables were not themselves particularly important (and hence in the interests of parsimony, we do not include them in our base specification).

The estimation method for the results reported in Table 2 is weighted least squares, with the weights being those supplied by Statistics Canada to make these data representative given attrition in the NLSCY since 1994. As discussed in Appendix A, these weights eliminate all meaningful attrition bias. In addition, we use the Huber (1967) — White (1980) correction to the regression standard errors to ensure that the results are robust to heteroscedasticity. Lastly, in preliminary work, we experimented with categorical representations of the dependent variable (e.g., dividing scores into 5 rank ordered groups) and estimating for example ordered probits in place of a continuous dependent variable. Again, such an approach does not produce results that are qualitatively different from those reported here.

Table 2
Select Determinants of Child Attainments by Cohort, Weighted Least Squares Estimates

	Children 4-6 PPVT	Children 8, 9 Math score	Children 8, 9 Reading score	Children 11, 13 Math score	Children 11, 13 Reading score	Children 15 Math score	Children 15 Reading score
Child characteristics
Has activity limitation	-10.87 (3.67)**	15.58 (0.73)	5.00 (0.23)	-1.61 (0.08)	-9.93 (1.35)	-42.65 (2.06)**	-16.59 (1.48)
Is eldest	2.18 (2.28)**	9.12 (1.55)	3.59 (0.90)	21.04 (2.79)**	9.89 (2.96)**	9.28 (0.79)	3.60 (0.64)
Number of siblings	-1.44 (2.98)**	5.38 (1.55)	2.95 (1.19)	8.81 (2.24)**	5.65 (3.25)**	-4.29 (0.56)**	0.82 (0.24)
PMK characteristics
Lone parent	1.13 (0.91)	-10.39 (1.31)	2.87 (0.63)	-6.52 (0.56)	0.71 (0.18)	-12.99 (0.67)	-3.69 (0.56)
Age	0.40 (4.07)**	0.27 (0.51)	0.09 (0.25)	1.41 (1.67)*	0.58 (1.85)*	2.09 (1.71)*	1.14 (2.39)**
Did not complete high school	-3.86 (3.07)**	-16.00 (1.89)*	-24.18 (4.08)**	-14.12 (1.42)	-7.94 (1.67)*	6.04 (0.37)	0.99 (0.12)
Obtained post-high school diploma	1.40 (1.59)	-1.52 (0.25)	2.18 (0.58)	-4.22 (0.53)	-0.76 (0.24)**	14.77 (1.01)	1.73 (0.26)
Obtained university degree	3.66 (2.95)**	30.59 (3.57)**	11.32 (1.60)	23.48 (2.04)**	8.40 (2.02)**	63.64 (3.52)**	8.08 (1.44)
Household characteristics
Income (x 1000)	0.23 (3.87)**	-0.0003 (0.01)	0.52 (1.96)**	1.08 (1.06)	0.37 (1.00)	2.95 (1.99)**	1.02 (1.70)*
Income squared (x 100000)	-0.0009 (1.81)*	-0.0002 (0.56)	-0.00025 (1.07)	-0.00069 (0.44)	-0.00011 (0.22)	-0.0039 (2.10)**	-0.0016 (2.02)**
R2	0.17	0.31	0.17	0.29	0.16	0.25	0.19
Sample size	3084	981	982	872	873	446	445
Mean, dependent variable	98.6	401.3	223.9	518.5	268.6	631.7	289.2
Notes: 1. Absolute value of t statistics in parentheses. 2. Standard errors calculated using Huber (1967) — White (1980) method. 3. * significant at the 10% level, ** significant at the 5% level. 4. Variables included but not reported are child age, sex, quarter of birth, PMK suffers chronic illness, PMK lone parent status, PMK race, province of residence, lives in rural area. 5. Weights are from Statistics Canada (200x) to account for attrition and sample representativeness.

Selected results are reported in Table 2 by cohort. There are several striking features. First, the characteristics listed here have the most well-measured impact on attainments when we restrict attention to the youngest cohort, children who, as of 1998, were aged 4-6 (and thus were 0-2 when the first cycle was fielded). This is consistent with the claim made in our literature review that, generally, household resources and characteristics become progressively less important as children become older. Second, observable child characteristics have some impact on these attainments. Having an activity limitation at the time of first observation is associated with a large reduction in PPVT scores 4 years later, and also has an adverse effect on math and reading scores for children in the oldest cohort. Being the eldest child has a small, positive impact on attainments, but one that is not always well-measured. There is no consistent pattern to the coefficients on the number of siblings. Other child characteristics such as age, sex and quarter of birth never have a statistically significant impact on the attainments examined here.

Education levels of the pmk have a consistent impact on attainments. Relative to the omitted category, pmks who have a high school diploma, children with pmks with less than high school education consistently have poorer attainments; children with careers with university degrees consistently have better attainments. Furthermore, these effects are large in magnitude. Consider a hypothetical example of two children, aged 5 in 1998 (i.e. at the time of the third cycle of the NLSCY) who are identical in all characteristics used in these regressions save the education of their career. The pmk of one child did not complete high school; the pmk of the second child has a university degree. The difference in PPVT scores of these two children is 7.5 points or 7.6%.¹¹ A similar calculation for older children produces percentage differences in attainments ranging from 3 to 16 per cent. Note too that these results are obtained after controlling for career marital status, age, and household income levels. Children with older pmks also tend to obtain higher scores although the effect is not always well measured. Across all attainments, and holding all other characteristics constant, a child with a pmk aged 20 would have scores 4-7% lower than a child with a pmk aged 35. By contrast, being a lone parent has no statistically significant impact on these attainments when controlling for these other child, career, and household characteristics. This finding is consistent with Dooley et.al., 1998a or Curtis and Phipps (2001), for example who find that cognitive outcomes for children living in lone-mother households are not necessarily worse than those for children living in two-parent families, other factors equal.

Incomes appear to have some effect on the outcomes considered here, though the pattern is uneven across children of different ages. Also, the coefficients are difficult to interpret directly because the magnitudes of the dependent variables vary by age and measure. One way of overcoming this is to re-express this relationship as an elasticity. With the exception of the math score for children 8 and 9 years old, this is remarkably small and constant for the youngest three cohorts, ranging in value from 0.03 to 0.05. However, it is three to four times larger for the small sample of children aged 15, that is the oldest cohort. For these young adolescents, the elasticity is 0.15 for the math score and 0.12 for the reading score. The latter implies that a 10 per cent increase in equivalent household incomes is associated with a 1.2 per cent increase in the reading score.

Another way of exploring the magnitude of the impact of these characteristics, as measured in 1994, on outcomes measured in 1998, is via calculating the size of the change they induce relative to some base value. To do so, we first calculate the predicted attainment score for a child in a defined "base category". Here, this is a Caucasian boy, born in the first quarter of the year, living in urban Ontario, whose pmk is female, of average age, has completed high school and whose family have the same income as the average family in this sample. We then vary select characteristics and see how this affects the attainment in question.

Results are reported in Table 3 and in Figures 11 and 12. Table 3 reports the impact on attainments, expressed as a percentage change, of varying child, pmk and household characteristics. The striking feature is that, individually, few changes have an impact of any meaningful magnitude on these attainments. The exception to this is changes in the education level of the pmk which tends to have a larger impact. However, looking at these characteristics individually may obscure the fact that in practice, sets of characteristics 'cluster' together. For example, women who have children at a very young age, tend to have less education and live in poorer households. Conversely, older mothers have more education and, all other factors held constant, tend to live in better off households. This observation suggests that considering the cumulative impact of these changes may be more instructive. Figures 11 and 12 provide us with this information. Figure 11 shows the percent change in attainments by cohort relative to the base category for children living in poor households (those at the 25^th percentile of adult equivalent incomes) whose pmk has less than a high school education and who is 10 years younger than the mean age for that cohort. The cumulative impacts of these characteristics producing a larger effect, ranging from a fall in attainments of 4 to 12 percent. Figure 12 shows the percent change in attainments by cohort relative to the base category for children living in better-off households (those at the 75^th percentile of adult equivalent incomes) whose pmk has a university education and who is 10 years older than the mean age for that cohort. The cumulative impacts of these characteristics producing a larger effect, ranging from an increase in attainments of 6 to 16 percent. There are also large differences when we compare across these two cases. A 'disadvantaged' child — one with a young mother who has not completed high school living in a household at the 25^th percentile of income in 1994 — obtains scores on the mathematics and reading tests in 1998 that are 13 to 22 per cent lower than an 'advantaged' child — one with an older mother possessing a university degree living in a household at the 75^th percentile of income in 1994.

Table 3
Simulating the Impact of Changes in Household Resources on Child Attainments

	Age 4-6	Age 8-9		Age 11, 13		Age 15
	PPVT	Math	Reading	Math	Reading	Math	Reading
Base	98.1	400.5	225.7	502.6	261.4	560.08	279.4
Change child
Has activity limitation	-11.1%	3.9%	2.2%	-0.3%	-3.8%	-7.6%	-5.9%
Eldest	2.2	2.3	1.6	4.2	3.8	1.7	1.3
Number of siblings	-1.5	1.3	1.3	1.8	2.2	-0.8	0.3
Change PMK
No high school	-3.9	-4.0	-10.7	-2.8	-3.0	1.1	0.4
University	3.7	7.6	5.0	4.7	3.2	11.4	2.9
Ten years younger than mean	-4.1	-0.7	-0.4	-2.8	-2.2	-3.7	-4.1
Ten years older than mean	4.1	0.7	0.4	2.8	2.2	3.7	4.1
Change household
Income to 25th percentile	-1.4	0.1	-1.2	-1.1	-0.8	-1.7	-1.0
Income to 75th percentile	1.8	-0.2	1.4	1.4	1.1	1.8	0.9
Notes: 1. Percentages are changes in attainment given change in child, PMK or household characteristic relative to base case. 2. Figures in bold refer to changes based on parameters that are statistically significant at the 10 or 5 per cent level. 3. For the base case, we set all the dummy variables in the base case specification to zero and any continuous variables at the mean for that age group.

To conclude, in this chapter we have considered the impact of 'history' as represented by pmk and household characteristics as of cycle 1 (1994) on attainments in cycle 3 (1998). Using multivariate regressions, we find that the impact of these characteristics varies by age of the child. Generally, the education of the pmk tends to have a larger, better measured impact than most other characteristics. Incomes tend to have a statistically significant impact, but one that is relatively small in magnitude, although there is some suggestion in these data that this effect is larger for older children. Larger effects are observed once we recognize that certain characteristics tend to cluster together. We find that children with young, poorly educated pmks living in relatively poor households have attainments 4 to 12 percent below those of the base case; by contrast children with older, better educated pmks have attainments 6 to 16 percent above the base.

• ¹⁰The inclusion of the dummy variables denoting province of residence captures provincial specific effects including curriculum design and resources devoted to education.
• ¹¹The figure of 7.5 points is obtained by adding up the absolute value of the coefficients on "did not complete high school" and "obtained university degree".