FAMILY BACKGROUND, PARENTAL
INVOLVEMENT, AND ACADEMIC
ACHIEVEMENT IN CANADIAN SCHOOLS
James McIntosh
Economics Department
Concordia University
1455 De Maisonneuve Blvd. W.
Montreal Quebec, H3G 1M8, Canada
and
Danish National Institute of Social Research
Herluf Trolles Gade 11
DK-1052 Copenhagen K, Denmark
January 18, 2008
ABSTRACT
This study analyzes school grade performance in 2002 of a representative sample of
Canadian students aged 5 to 18. Family background variables, parental characteristics
and attributes as well as how parents view the importance of education and what they
actually do in terms of helping and guiding their children are all important factors in the
child’s success in the primary and secondary school system. The most important contributing factors were how important the parent thought grade performance and getting
further education were as objectives for their children. These two variables were more
important than parental educational qualifications or whether the child came from a low
income or dysfunctional home. These are optimistic findings. Children from disadvantaged families are not condemned to be at the bottom of the grade distribution. In fact,
children with poorly educated fathers can actually do better than average if their parents
have positive attitudes on the importance of school grades and further education. Girls
differ from boys in that they are less responsive to family attitude variables and the their
grades while higher than those for boys are more dependent on unobservables.
∗
E-mail Address: jamesm@vax2.concordia.ca
Telephone: 514 848 2424 3910
Journal of Economic Literature Classification Numbers: I20 J62
Keywords: School grades, test scores, beta probability model, parental involvement,
Canada.
1
1
Introduction
An individual’s success in post-secondary education and consequently in the labour market is determined primarily on how well he or she does in primary and secondary school.
It is, therefor, very important to have a clear understanding of what determines school
performance. In particular, it is important to identify the factors which can be influenced by educational or social policy. Although there has been some research on the
determinants of child and adolescent school performance it far from complete and there
are many unresolved issues. In fact, in Canada, there is very little research on this topic.
Two issues are considered in detail here. The first concerns the typology of causal
effects. Many studies which attempt to explain school grades do not classify causes by
type. This is done here by dividing causal factors into parent characteristics on one hand
and parent attitudes and actions on the other and assessing their relative contributions to
the explanation of grade performance. This distinction is important. While it is difficult
to alter parental characteristics like educational attainments parental attitudes and what
they actually do for their children in terms of helping them can change or be changed.
The second issue involves gender. Girls do better than boys at school. This is a universal
phenomenon and why it occurs is subject to much speculation as to whether its causes
are cultural, biological or economic or a combination of all three. But, the precise role
that family background plays is not clear and that issue will be examined carefully here.
The main results obtained in this research project using a representative sample of
Canadian students aged 5 to 18 indicate that it is what parents do for and with their
children together with their attitudes about the importance of doing well in school and
getting further education rather than their characteristics like educational qualifications
that account for most of the explained variation in school grades. Attitudes and practices
are amenable to change so this provides scope for schools to get better performance out
of their students by getting parents to promote the importance of doing well at school
and giving their children more support in their studies. Children who come from low
income households, having divorced or separated parents or parents who are on welfare
will actually do slightly better than average if they come from homes which have positive
attitudes and strongly support their children. Boys and girls respond differently to their
parents attitudes on the importance of doing well in school and getting further schooling.
Girls have higher predicted mean grades, are less influenced by their family environments,
and have a smaller proportion of problem respondents in a typology which emerges when
mixture distributions are used to deal with unobservable heterogeneity.
The paper is organized in the following way. The next section contains a review of
the literature on academic performance. Section 3 develops a theoretical model which is
tested on a data set described in section 4. Section 5 outlines the statistical procedures
2
used in the analysis. The results are outlined in section 6. Section 7 ends the paper with
a summary and discussion of these results.
2
A Brief Review of the Literature
There is a very large literature which deals with the determination of educational attainments. Social scientists have also been interested in academic performance. The two are
related, of course, because how well the individual does in primary and secondary school
largely determines the individual’s final post-secondary educational destination. In fact,
from a theoretical point of view attainments and performance are outcomes of the same
household process in which parents try to influence the activities which relate to their
children’s schooling performance, make investments of time and money in their children,
serve as their role models, and set objectives and priorities for them to follow.
The early theoretical contribution of Becker and Tomes (1979) provides a partial representation of this process by focusing on the role of parental investments by the current
generation in the determination of the success of the next generation. The intergenerational transfers in this model arise from altruistic parental objectives which are captured
by including the incomes or utility of their offspring in their own utility function. While
this type of model, or recent generalizations of it by Han and Mulligan (2001) for example, provide some insight into why there can be some correlation between the incomes
of parents and their children, two important features of the household which determine
how these transfers occur are missing.
First, What children actually contribute to their own success plays no role in these
models. This is a serious limitation since how hard children work at school or how willing
they are to learn new material are crucial in determining how well they do or how far they
go in the educational system. Their attitudes and motivation are crucial here. Once child
inputs are considered there are the associated problems of intergenerational differences
of opinion on what is required; parents want more effort and the children want to do
less. Weinberg (2001) makes some progress in dealing with these issues by modeling the
relations between parents and their children as an agency problem. The idea here is that
parents act as principals and provide incentives to their children, their agents, to act in
ways which are in their own long term interests as well as being coincident with their
parents altruistic objectives.
Unfortunately, this theoretical perspective has had little or no influence on the empirical research which examines academic performance. The research here divides into two
quite distinct sub-areas: the analysis of test score performance and actual school grades.
The notion that there are intertemporal objectives to be pursued or the possibility that
3
there may be intergenerational conflicts within the family are ignored in both branches
of this literature.
There may be some distinctions between test scores and grades but these appear to
be small. Test score responses are a one-off event and may reflect short term fluctuations
in individual performance. There may also be incentive problems present; students at
young ages may not appreciate the importance of doing well on an intelligence test
whereas they may be more inclined to take their school work seriously, especially in
households where parents put a high value on this. If there are other major distinctions
these are not obvious so the theoretical insights that the researchers who analyze test
scores have found should also be applicable to the analysis of school grades.1
While complete capital theoretic models of family decision making have not been
employed by researchers in this area some results on how academic performance is produced are available. Todd and Wolpin (2003, 2004) examine test scores in a production
framework first suggested by Ben Porath (1967), although what they say applies equally
to school grades. The timing of inputs plays a crucial role in their model because they
recognize that in addition to unobservable innate ability achievements are determined
by a capital accumulation process which involves the whole history of investments that
parents and schools make in the child. They also note that the estimation of such models
is particularly difficult even when there is more than one age at which achievement information was obtained. When there is achievement data available at different ages but no
information on parental investments prior to the last achievement, geometric distributed
lag models can be used to estimate the effects of the unobserved contributions which are
captured by the inclusion of the lagged achievement variable. These are referred to in the
literature as ‘value added models’. However, this procedure is less satisfactory than it
first appears because of the moving average error that is induced by replacing the lagged
parental inputs with the lagged value of the achievement and the untreated correlation
between it and the unobservable ability variable. Using the US National Longitudinal
Survey of Youth data they actually reject these models in favour of models based on
the observed lagged values of parental inputs and which control for unobservable child
effects so this criticism has empirical support as well.
Attention now turns to a review of the research that has been carried out on achievements. There are a large number of studies which examine test score behaviour. A
summary of the results here can be found in McIntosh and Munk (2006) and interested
readers may refer to that paper. School grades are, for the most part, analyzed by sociologists and educational psychologists, although economists have taken some interest
in the subject. This is surprising given economists interest in test score analysis and
1
One of the Canadian studies reviewed below, Connolly et al (1998), analyzes both and gets similar
results.
4
the importance of early scholastic performance as an indicator of later educational and
labour market success.
There are a large number of papers that analyze school grades, many of which were
written some time ago. Consequently, my review will focus on papers that are representative of the literature rather than being comprehensive. I start with the Canadian
literature. Two papers, Connolly et al (1998) and Adams and Ryan (2000), use the National Longitudinal Survey of Children and Youth which interviewed 5186 children aged
6-9 in 1994 and reinterviewed them again in 1996 providing two complete information
cycles. Both papers report significant effects of family background variables, parent support, teacher support, and the child’s attitude towards school using an achievement score
based on teacher ratings of the child’s class room performance. Adams and Ryan using
recursive path analysis examine the role of family dysfunction, ineffective parenting, and
the child’s academic focus on achievement as mediating variables. Unfortunately, neither
paper exploits the panel aspects of the survey. Value added models could be estimated
here in a random or fixed effects framework which deals with the endogeneity of the
lagged achievement variable and the application of a systems estimator like GMM would
probably lessen the damage caused by the moving average error present in distributed
lag models. Missing variables reduce the sample size by more than two thirds in each
paper so there may be serious selection problems. Neither paper offers any explanation
as to why this happens.
Turning now to some results based on American data, two papers that use the same
type of qualitative grade score outcome that is used in this research are discussed first.
In these two papers, Fehrmann et al (2001) and Tavani and Losh (2003), grades are
characterized by an integer outcome variable reflecting an ordered set of categories which
have both interval and letter grade representations. The highest grade is A/A+ and
corresponds to numerical grades between 90 and 100. There are seven other categories the
lowest being D for grades below 60 but the intermediate grades differ by five percentage
points so that the intervals are not the same for every grade.
The first study uses data from the US High School and Beyond Longitudinal Survey. The sample consists of 28051 students who were in their last year of high school
in 1980. In addition to the outcome variable there is information on ethnicity, gender, ability as measured by test scores, the socio-economic background of the parents,
parental involvement, homework and time spent watching TV. Their results are obtained
by running an ordinary least squares regression of their integer valued outcome variable
on the regressors mentioned above. They find that ability is the most important variable in explaining grades but parental involvement as well as homework, socio-economic
background, gender, and ethnicity also contribute.
The second paper uses a somewhat smaller survey (4012) of first year university stu5
dents sampled in 1995 whose grades employ this outcome measure and finds that variables
like motivation and expectations in addition to parental educational attainments. It is
not at all surprising that highly motivated students do well at school. Expectations are
probably based on the student’s opinion of how well he or she can do or how much effort
is planned so both of these so this should also be a good indicator. However, the real
value of the study is that it shows that parental attainments have a significant effect on
a population which has much higher than average ability having been admitted to university. Family background is, therefor, something that never disappears from the list of
performance determinants. Like the previous study, however, the explanatory variables
are all integer scales so the previous caveat applies.
Another outcome measure is the Grade Point Average, GPA. An early study, Dornbusch et al (1987), which focuses on the type of parenting style analyzes GPA data from
a sample of 7836 San Francisco high school students collected in 1985. For whites they
find that in addition to gender (girls do better) age, parental background, and family disruption children from households which are authoritarian or permissive do much worse
in school. What parents do and the way they do it seems to explain as much of the
variation in grades as who the parents actually are in terms of their characteristics. The
authors also report significant differences between the major American ethnic groups,
Asians, Blacks and Hispanics.
A more recent study, Pong et al (2005), uses a large sample of 17996 adolescents in
grades 7 to 12 from the US National Longitudinal Study of Adolescent Health. The data
was collected in 1994-1995. Like the Dornbusch et al (1987) study they focus on both
immigrant behaviour and parenting styles but these are defined in terms of the degree
which parents and their children cooperate in making decisions which relate to school.
They find that households in which both parties collaborate in decision making are the
most successful. They also find that along with the usual socio-economic and family
background variables parents trust in and expectations for their children are important.
The last paper in this review, O’Brien and Jones (1999), is an English study. It is
included for two reasons. First it gives some balance to the literature review by including
some non-American research. Secondly, the data used is very similar to the Canadian
data used in this study. The sample is quite small, 620, and was collected from 6 schools
in two predominantly working class London boroughs in 1995 and had an average age
of 14.33 years. The outcome variable was performance on the General Certificate of
Secondary Education (GCSE) as represented by a three category achievement responses:
higher, intermediate, and lower. In spite of the small size of the sample and the curious
use of a logit model which ignores the fact that the responses are ordered the authors
find some interesting results some of which are replicated here. They find that the child’s
expectations about continuing past GCSE’s are important. This result is difficult to
interpret, however, since it is as much an outcome variable as the school grade itself.
6
Being praised often by the mother, living in a home which is owned rather than rented,
and not having a boyfriend or girlfriend helped child to do well. Somewhat surprisingly,
gender, parent occupations, family structure, and variables which represent parenting
style were not significant.
To summarize the literature represented by these seven papers, family background
variables as well as variables which describe the parents style and degree of involvement
in their children’s school activities and the amount of support they provide either in
terms of rewarding them or helping them with their school work all matter. The relative
contributions of the each type of regressor depended on the individual paper.
3
A Theoretical Model of School Grades
School performance depends on a variety of factors. In addition to the obvious observation
that it depends on the individual’s innate ability, the amount of time and effort invested
by the parents in activities that help the child to develop are also crucial. Of course, the
characteristics of the parents also matter because the quality of the investments made in
children depend on them. Innate ability also depends on parental characteristics to the
extent that it is inherited. Furthermore, it is obvious that the motivation and the time
that the child is willing to devote to academic school activities are variables that also
need to be considered.
The literature on the analysis of test scores suggested that a production function
approach might be appropriate. School grades are a measure of performance and thus
reflect the characteristics and endowments of the child as well as the variable inputs
provided by both the parents and the child. Let y(t) be the aggregate grade score of the
child in period t. Then
y(t) = f [k(t), ep (t), ec (t), z(t), a]
(1)
where k(t) is a vector the child’s stocks of human capital at t, ep (t) and ec (t) are vectors
of parent and child inputs, respectively, and z(t) is a random shock which is observed by
all parties before any t-period decisions are made. a is innate ability and is constant over
time and is not affected by years of schooling or any investments that were made in the
child.
The grade score production technology differs from that considered by Todd and
Wolpin (2004) in two respects. It ignores the age specific aspects of parental contributions
to the child’s human capital formation process. This is possibly a limitation of the model
but it turns out to be a necessary simplification given the data that is available to estimate
the model. On the other hand, it explicitly recognizes the role that the child’s own inputs
play in determining how well he or she does in school.
7
Decision making within the household is complicated by the fact that the parent’s
view on how much time and effort the child should be putting into his or her academic activities does not always coincide with the child’s view. One way of modeling
these intergenerational conflicts is to assume that the decision making process within the
household has a non-cooperative structure. Added realism is achieved by modelling it as
a game where the parents are the first mover and make decisions in Stackleberg fashion
taking account of anticipated child responses. This reflects the idea that parents want
their children to behave in a certain way. They do this by spending time with them,
showing them what to do, giving them encouragement, sometimes imposing sanctions on
them, all in the hope that the child will come up with desired response. This process is
formalized by the following functional equation which describes the child’s objectives.
Vc [k(t), Y (t), ep (t), z(t)] =
Max{vc [y(t), ep (t), ec (t), z(t)] +
ec (t)
Et δVc [k(t + 1), Y (t + 1), ep (t + 1), z(t + 1)]}
(2)
where Y (t) = {y(s) : s < t} is the individual’s grade score history prior to t, δ is the
discount factor, and Et is the conditional expectation operator. vc is a concave per-period
von-Neuman utility indicator. It depends positively on the grade score, on the parent
inputs, on the shock, but negatively on the child’s own inputs since these are provided at
the expense of the child’s leisure activities. The model can be completed by specifying
the parent’s objectives as well as the equations which describe the evolution of the child’s
human capital stocks.
However, it is unnecessary to do this since all formal models in which the child
responds to the parental input variables will have the property that
ec (t) = ec [k(t), Y (t), ep (t), z(t)]
(3)
This means that a reduced form of equation (1) can be estimated without having any
information on the child’s own inputs in the production process. The parents also have
to solve an intertemporal optimization problem and it is assumed that this involves a
criterion function in which the welfare of the child is represented. This means that the
child’s stocks of human capital will reflect these decisions and since they were made by
the parents they will reflect the parent’s characteristics as well as depending on variables
which the parents observed at the time the decisions were made. Not all of these are
available to the researcher but parental characteristics are readily available in many
surveys and they can be used to capture effects that would normally be attributed to the
child’s stocks of human capital. Finally, the input vector of parental investments, ep (t),
can be taken to be exogenous since this what the child responds to when deciding what
level of effort is to be provided.
This model is quite different from the principal-agent model proposed by Weinberg
(2001). Mechanism design problems, of which agency is a special case, arise because
8
one party does not have the same information as the other and can not observe the
actions of the other. While it is common for parents not to always know what their
children are doing and even if they did and there were no information asymmetries there
would still be incentive problems in getting children to carry out what was wanted of
them. Mechanism design models usually require a participation or individual rationality
constraint. This does not make much sense in the present context, a point which Weinberg
himself recognized. His alternative to the participation constraint was to include both the
child’s utility and the value of the child’s action in the parents utility function. His model
also has a parental budget constraint. He shows that this does not bind at high levels of
parental income so that high income parents will not be able to control their children.
There is not enough structure in the model developed here to get any theoretical results
on this issue. However, the effects of parental income on performance can be examined
and the question of whether income effects decline as parental income increases will be
discussed in section 5.
4
The Data
The data comes from the 2002 Statistics Canada Survey of Approaches to Educational
Planning, (SAEP).2 The dependent variable is the answer to the survey question
‘Based on your knowledge of your child’s school work and report cards how
did he/she do overall in school?’
The parent answering the questionnaire could select the following six answers: 90%100% (mainly A+ ), 80%-89% (mainly A/A−) , ........., Below 50% ( mainly E, F, or R).
The distributions of the answers to these responses for both genders are shown in the first
six rows of Table 1A. The rest of this table and Table 1B contain summary statistics for
variables which describe the characteristics of the household in which the child resided
at the time of the interview. Most of these relate to the child’s parents and are dummy
variables which take the value one if the condition of the category is satisfied. Most of
the variables mean what they appear to mean. The dummy variables in Table 1B convey
parental attitudes or the frequencies of certain practices involving the management their
child’s school activities.
The sample is representative of the country as a whole. The were 10788 randomly dialled telephone interviews. 2524 had children under the age of five and hence, reported no
school performance for their child. There were 966 missing child grades for the age group
2
See Shipley et al (2003) for addional information about the survey.
9
5-8 so that almost all of the missing observations are for young children. It, therefore,
seems reasonable to treat the reduction in the sample size as being caused by exogenous
factors which means that the there will be no selection biases in the parameter estimates.
The final sample size is 6793 with 3422 boys and 3371 girls. Statistics Canada weights
are used in the computation of the sample means to make the sample representative of
the country as a whole as well as in the estimation procedure.
5
Statistical Model
The grade score data is qualitative and is the parents response to the survey question
‘overall, how did your child do in school?’ Starting with the highest category, the possible
answers are the intervals [0.90,1.00], [0.80,0.89], etc. Since this is the data that is collected
it is desirable to use a statistical procedure which uses the data exactly as it was obtained
from the respondents.
Three different statistical models were used to analyze the grade data. Two ordered
probability models with known threshold points, one using the Beta distribution and the
other using the doubly truncated normal distribution, were used to analyze the interval
data . A doubly truncated normal regression model was also used to analyze grades when
they were represented by the mid-point of the interval. All three methods yielded very
similar results but the regression model appeared to provide the best fit for the data
and suffered from fewer computational problems in spite of the fact that the procedure
used grades which are measured with error. Because of the similarity of the results for
all three procedures only those for the regression model are reported. These appear in
Table 2 for each gender.
By a regression model it is meant that the grade, yi , for respondent i has a doubly
truncated normal distribution3
f (yi , µi , σ) =
1
φ((yi
σ
− µi )/σ))
yi ∈ [0, 1]
[Φ((1 − µi )/σ)) − Φ((−µi )/σ))]
(4)
where µi = Xi β and φ() and Φ() are the normal density and cumulative distribution
functions, respectively. Xi is the vector of covariates whose weighted means are displayed
in Tables 1A and 1B.
3
See Johnson and Kotz (1970: Ch. 13) for details.
10
For this distribution the expected grade for respondent i is
E(yi ) = µi + σ
[φ((−µi )/σ)) − φ((1 − µi )/σ))]
[Φ((1 − µi )/σ)) − Φ((−µi )/σ))]
(5)
The estimates of the (β, σ) parameters are obtained by maximizing a likelihood function
which depends on a finite number of mixtures of these truncated normal density functions.
These are displayed in Table 2 for each gender. In order to save space some of the
attitude and activity estimates are represented by the average of the estimated dummy
coefficients. The number in round brackets to the right of the variable name gives the
number parameters in the average.4
6
Empirical Results
For the models the values of McFadden’s Psuedo R2 reported in Table 4 are 0.221 and
0.158 for the boys and girls, respectively and while not particularly large they are acceptable for the cross section models that are estimated here. Many of the variables
are significant with the parental attitude to grades and further schooling being the most
important. Positive parental attitudes to good grades and the importance of further
education, having a parent with a university degree, and having been tutored had a positive effect on grades. On the other hand, having a Canadian parent, having homework
supervised, or the number of times the a parent contacted the respondent’s school all
had a negative impact on the respondent’s grade. Grades also decline with age for both
genders.
These negative results may appear counterintuitive but there are plausible explanations for them. Canada has very stringent entry requirements which ensures that
immigrants to Canada are of the highest quality. Immigrants are also likely, being immigrants, to be very ambitious for their children so it is not surprising that this has a
positive effect on grade performance. Given the recent difficulties that many European
countries have experienced with their immigrants it is reassuring that immigrants to
Canada pass through our educational system without any observable difficulties. Helping with home work and visiting the respondent’s school is probably an indicator that
the respondent is having school difficulties so the negative signs are quite reasonable.
4
For example, there are three dummies for the parent’s attitude towards more education for boys.
The question here is ‘How important is it that your child gets more education past high school?’ The
three dummies represent the answers: somewhat important, important, and very important, with the
residual category being not important al all. The three estimated coefficients are 0.083* (0.041), 0.126**
(0.040), and 0.152** (0.040) and the average is 0.120** (0.040) as indicated in Table 2.
11
The effects of having parents who have separated or divorced or coming from a
household which is on welfare are relatively small. The impact of household income is
also small and not significant. Thus it would appear that children from disrupted or
low-income households will not automatically do poorly in school because of that.
Unobservable effects were treated by estimating mixtures of the distributions described in equation (4). The models estimated here follow a procedure developed by
Heckman and Singer (1984) and use the distribution
g(yi , µi , σ A , σ B ) = pA f (yi , µi , σ A ) + pB f (yi , µi , σ B )
(6)
where pA + pB = 1 are the mixing probabilities. Initially, µi = Xi β was allowed to have
type specific intercept terms, β 0A and β 0B , however, this turned out to be unnecessary
because the variance terms, (σ A , σ B ), pick up the differences in E(yi ) across the two types.
Only two mixtures were used since models involving more that two mixtures would never
converge. The estimates of the probabilities and variance terms are shown in Table 4.
The standard errors are computed from the inverse of the weighted information matrix.
Robust standard errors were also computed but they were almost identical to the standard
errors in Table 2 so the measurement errors induced by the use of the interval midpoint
appear to have no impact on the results. How these parameters should be interpreted
will be discussed in the next section.
7
Discussion and Conclusions
Like most of the studies referred to in the literature review, the grade performance of
a random sample of Canadian secondary school students was shown to depend on a
set of variables which reflected the environment of the child when the performance was
measured. There are three types of variable. First there are baseline variables: age,
language whether the parents were Canadian, and geographical location. Secondly there
are parental characteristics like the father’s and mother’s level of educational attainment
and variables which characterize the economic and social circumstances of the child’s
environment like whether the child’s parents were welfare recipients, or were separated
or divorced. Income for the household was also available and is a measure of both parental
characteristics involving their occupations and employment records as well as the level of
material advantage for the child. In Table 3 these will be referred to as Group I variables.
Finally, there are variables which reveal parental attitudes and the type of involvement
in activities designed to help their child do better at school. These will be referred to as
Group II variables.
12
Group I and II variables are different from each other in a number of important
respects. First, Group I variables describe who the parents are in terms of their defining
social and economic characteristics. At the time their children are attending school most
parents will have completed their formal educations and embarked on a work career.
As a result short run education policies will have virtually no effect on variables in this
category. Some of what children get from their parents is genetically determined and it
is Group I variables, especially the educational attainments of the father and mother,
that are most likely to capture the genetic relations between the two generations. With
the exception of the two parental attitude to education variables, Group II variables
describe what parents actually do for their children in terms of specific support activities
to help the child do better at school or those which provide emotional support or reward
successful outcomes as well as their attitudes. Unlike Group I variables, these attitudes
and practices could be changed in the short run in response to programmes which made
parents more aware of the importance of education or getting more involved with their
child’s schooling.
The computations in Table 3 are designed to determine the relative importance of
these two groups of variables. The first row in Table 3 gives the value of the ln-likelihood
of a model using the baseline variables mentioned above. Since Group I and Group II
variables are likely to be correlated with Group II being dependent on Group I variables,
Group I variables are the first variables to be added to the baseline variables. The values
of the ln-likelihood function in the second and third rows of the table show the effects
of adding first the Group I variables and then both the Group I and Group II variables,
respectively. The effects of unobservable heterogeneity that arise from mixing are shown
in the fourth row.
As the percentage increases in the third and fourth columns of the table indicate
that for boys it is the Group II variables that are doing most of the work. Only 24.0%
of the increase in the ln-likelihood function from its baseline value is due to the Group
I variables so the activities and attitudes of the parents are much more important in
explaining the grade performance of their children than the variables that describe their
attributes and account for 60.7% of the explained increase in the ln-likelihood function.
Unobservables explain the remaining 15.3%.
For girls the results are quite different. Group I variables account for 29.8% of the
explained increase in the ln-likelihood function. Group II variables explain only 21.2%
and the other half of the increase is due to mixing.
A number of consequences follow from this result. First, since Group I variables do
not contribute very much to the explanation, it suggests that inherited genetic factors
are not particularly important in determining how well children do in school. While the
parent’s educational qualifications are an indication of their intellectual ability, having
13
well educated parents can be advantageous for a large number of reasons which are
not related to the parents genetic makeup. Since parents can also serve as good role
models or promote behaviour like being conscientious, ambitious, and methodical; all of
which are likely to contribute to making the child more successful at school, only part of
the variation explained by the parent’s characteristics could be due to inherited genetic
endowments. However, the small role for genetics conflicts with the results of Plug and
Vijverberg (2003: 633) who found much larger genetic effects.5
Secondly, the fact that the most important factors contributing to grade success
appear to be associated with what parents do for and with their children suggests that
education policy should also focus on the parents as well as the children. Educating
parents may turn out to be an effective way to get better results from the children in
contrast to some of the more traditional policies that have been suggested to get better
results by improving teacher quality or reducing class sizes. It is clear from the large
and significant coefficients associated with the parent attitude to education variables
that getting parents to be more aware of the advantages of doing well in school and
the benefits that this brings to their children could be an effective policy for raising
average grades. For example, the model for boys shows that a change in attitudes to the
importance of school grades from not important to very important would raises school
grades by 12.2 percentage points for boys!6
There are no independent measures of the respondent’s ability like an assessment by
the teacher or a test score in the SAEP data. School grades obviously depend on ability
so there is an estimation problem if nothing is done to counter the effects of leaving out
a variable which is likely to be correlated with some of the covariates. Heckman and
Singer (1984) devised a procedure which dealt with an unobservable variable like ability
by assuming that there were a finite number of ability types. The probability distribution
of each type had a mean function which could depend on a set of common covariates but
with a type specific intercept term. These intercept terms represented the different levels
of ability for the types and can be estimated along with the type probabilities using a
finite mixture distribution. When there are only two mixtures, equations like (6) describe
the distribution.
It should be noted that in this framework what is meant by ability here is not
something which depends on any attribute of the parent like a genetic endowment, for
example. If respondents get any genetic benefit from their parents this is captured by
5
Instead of parental educational attainments they used parental IQ tests to measure the child’s
inherited ability and claimed that “about 55-60 percent of parental IQ relevant for schooling is genetically
transmitted”. That may account for the differences between the two outcomes although one should be
cautious about accepting results involving adoptees.
6
The mean grade for boys whose father does not think that education is important at all is 68.8%
whereas it is 81.0% for boys whose father thinks that education is very important.
14
the coefficients associated with the parental characteristics and these do not vary across
type. This could be seen as a limitation of the model employed here but an attempt
to estimate a latent class model7 where slope coefficients are also allowed to vary across
types so that unobserved ability can depend on parental characteristics as in McIntosh
and Munk (2007) failed to converge even for two mixtures. Thus the models used here
appear to be as general as possible given the data.
Unlike the Heckman-Singer procedure there are potentially two parameters (β 0j , σ j )
which could be used to represent type j instead of just one. As mentioned in section 4
the differences in the intercept terms across the two types were negligible which raises
the question as to how the variances should be interpreted. It is clear from equation
(5) that the larger the value of σ j the bigger the difference between E(yi |σ = σ j ) and
µi . For type A boys Table 4 reveals that σ A = 0.253. For this type the difference,
µi − E(yi |σ = σ A ), is 0.088. Truncation is important here and Pr{yi ≥ µi |σ = σ A } is
significantly less than 0.5 However, for type B µi − E(yi |σ = σ B ) = 0.004 and truncation
plays almost no role at all in determining E(yi |σ = σ B ). So the variance parameters
take over from the intercept terms in characterizing type specific ability with the higher
variance being associated with the lower ability type.
One of the more interesting features of the data is very large difference in the grade
performance between the two genders. The simple fact is that the girls are much better
at school than the boys. The data in Table 1 shows that while 17.0% of the girls are in
the top grade category only 12.6% of the boys are. For the next highest category there
is still a difference but it is not as great. Similar gender differentials have been found
using reading achievement test data from the Canadian component the Programme for
International Student Assessment tests (PISA) for the year 2000. See HRSDC (2004:
9). The experience of many other countries is similar so this result is neither new nor
surprising.
What is surprising is the absence of explanations of this phenomenon. Unfortunately,
the results based on the SAEP survey data used in this study are more informative
about what does not explain these gender differences than what does. The first point to
note that is that the major component of each mean is the intercept term which makes
up 68.2% and 81.7% of the means for boys and girls, respectively. Secondly, with the
exception of the variable which represents parents attitudes to school grades, there are
no significant differences in the parameter estimates associated with attitude, activity or
family background variables. Girls are less responsive to the school grade variable than
boys but the difference, although significant, is small. The biggest difference is in the
intercept terms, 0.130** (0.059), which suggests that the reason why girls do better than
boys is minimally related to the way that they respond to their family backgrounds but
7
Deb and Trivedi (1997) describe latent class models for count data.
15
depends on factors located outside the home. The typologies are different as well. A
much higher proportion of boys 0.083 are low achievers, type A, than the proportion,
0.022, for girls.
The failure of boys to keep up with the girls in terms of school performance is
symptomatic of a broader set of problems that are related to the age at which boys
mature and the way boys learn to deal with the changes that have occurred in child and
adolescent society. Many of these are discussed in Sax (2007).
One of the predictions of the Weinberg (2001) model was that high income households
would not be able to influence their children’s school performance. Although the model
here is not informative on this point the question is, nonetheless, interesting. The mean
function is significantly concave in household income. As an alternative to using the
natural logarithm of household income a quadratic version was also estimated. Neither
of the terms were significant and the natural logarithm formulation fitted the data slightly
better so it was the preferred formulation. But this was not significant so there is no
support for the Weinberg hypothesis. Blau (1999) also found, using NLSY data, that the
effect of income was extremely small so that household income does not determine the
amount of leverage that parents have over their children.
The survey does not contain any information on the quality of the school as perceived
by the parent. This is unfortunate. However, parent characteristics like educational attainment are likely to be correlated with the quality of the school which the respondent
attends since it is uncommon for well educated or affluent parents to live in neighbourhoods with poor schools or send their children to low quality schools. Consequently,
there are some variables in the survey which capture school quality effects.
As is the case in many countries Canadian grade performance of young children
and adolescents depends significantly on the environment where they resided. Family
background variables, parental characteristics and attributes as well as how parents view
the importance of education and what they actually do in terms of helping and guiding
their children are all important factors in the child’s success in the primary and secondary
school system. Unlike most of the research done on the school performance of children
this study focused on the relative importance of various types of contributing factors. The
main result was that the most important contributing factors were the degree to which
parents supported their children as well as their outlook in terms of how important they
thought grade performance and getting further education were as objectives for their
children. These variables were more important than parental educational qualifications
or whether the child came from a low income or dysfunctional home.8
8
I am not the first researcher to find results like this. Feinstien and Symons (1999: 308) in their
study on English test score write “Of the family inputs, only parental interest has a consistently strong
impact. In contrast to what is usually found, social class, family size, and parental education are not
16
These are optimistic findings. Children from disadvantaged families are not condemned to be at the bottom of the grade distribution. In fact, children with poorly
educated fathers can actually do better than average if their parents have positive school
grade and education attitudes and praise their children when they do well. The good
news continues with the result that children from immigrant families, that is with fathers or mothers not born in Canada, do slightly better than average so the integration
problems that many European countries have experienced are not present in Canada,
at least as far as their participation in the educational system is concerned. Finally, as
was noted earlier in this section, educating parents about the benefits of getting good
grades or going further in the educational system could lead to significant improvements
in average grade performance. But there are limits here since between 65% and 70% of
Canadian parents already believe that these objectives are very important.
References
[1] Adams, Gerald R. and Bruce A Ryan (2000) “A Longitudinal Analysis of Family
Relationships and Children’s School Achievement in One- and Two-Parent Families”
Paper # W-01-1-8E, Applied Research Branch, Strategic Policy, Human Resources
Development Canada.
[2] Blau David M (1999) “The Effect of Income on Child Development” Review of
Economics and Statistics 81 261-76.
[3] Becker, Gary S. and Nigel Tomes (1979). An Equilibrium Theory of the Distribution
of Income and Intergenerational Mobility. Journal of Political Economy. 87, S143162.
[4] Ben Porath, Y (1967). “The Production of Human Capital and the Life Cycle of
Earnings” Journal of Political Economy 75: 352-365.
[5] Connelly, Jennifer A., Virginia Hatchette, and Loren E. McMaster (1998) “School
Achievement of Canadian Boys and Girls in Early Adolescence: Links With Personal
Attitudes and Parental and Teacher Support for School.” Paper # W—98-14E,
Applied Research Branch, Strategic Policy, Human Resources Development Canada.
[6] Deb, Partha and Trivedi, Pravin K. (1997). Demand for Medical Case by the Elderly:
a Finite Mixture Approach. Journal of Applied Econometrics 12: 313-336.
[7] Dornbusch, Sanford M., Phillip L. Ritter, Herbert Leiberman, Donald F. Roberts,
and Michael J. Fraleigh (1987). “The Relation of Parenting Style to Adolescent
School Performance” Child Development, 57 1244-1257.
always significant and have relatively small effect in magnitude"
17
[8] Fehrmann, Paul G., Timothy Z. Keith, and Thomas M. Reimers (1987). “Home
Influence on School Learning: Direct and Indirect Effects of Parental Involvement
in High School Grades” Journal of Educational Research 80, 330-337.
[9] Feinstein, Leon and Symons, James (1999). “Attainment in secondary school”. Oxford Economic Papers 51: 300-321.
[10] Han, Song and Casey B, Mulligan (2001). “Human Capital, Heterogeneity and Estimated Degrees of Intergenerational Mobility” Economic Journal 111, 207-243.
[11] Heckman, James J. and Singer, B. (1984). ‘A Method for Minimizing the Impact of
Distributional Assumptions in Econometric Models for Duration Data”. Econometrica 52: 271-320.
[12] Johnson, Norman, L. and Samuel Kotz (1970). Continuous Univariate Distributions
1 Houghton Mifflin, Boston, USA.
[13] McIntosh, James and Munk, Martin D. (2006). “What Do Test score Really Measure?” Unpublished Manuscript.
[14] ––––- (2007). “Scholastic Ability vs. Family Background in Educational Success:
Evidence form Danish Sample Survey Data”. Journal of Population Economics. 20,
101-120.
[15] Murphy, K. M and R.H.Topel (1985) “Estimation and inference in two-step models”
Journal of Business Economic Statistics. 3 370 379.
[16] O’Brien, Margaret and Deborah Jones (1999). “Children, parental employment, and
educational attainment: an English case study” Cambridge Journal of Economics,
23, 599-621.
[17] Plug, Erik and Vijverberg, Vim (2003). “Schooling, Family Background, and Adoption: Is it Nature or Nurture?” Journal of Political Economy 111, 612-641.
[18] Pong, Suet-ling, Lingxin Hao, and Erica Gardiner. (2005). “The Roles of Parenting Styles and Social Capital in the School Performance of Immigrant Asian and
Hispanic Adolescents” Social Science Quarterly 86 928-950.
[19] Shipley, Lisa, Sylvie Oullette, and Fernando Cartwright (2003). “Planning and
preparation: First results from the Survey of Approaches to Educational Planning
(SAEP) 2002”. Education, skills, and learning research paper, Statistics Canada.
[20] Taviani, Christopher and Susan C. Losch (2003). “Motivation, Self-Confidence, And
Expectations As Predictors Of The Academic Performance Of Our High School
Students” Child Study Journal 33, 141-151.
18
[21] Todd, Petra E. and Wolpin, Kenneth I. (2003). “On the Specification and Estimation
of the Production Function for Cognitive Achievement” Economic Journal 113: F3F33.
[22] ––––— (2004) “The Production of Cognitive Achievement in Children: Home,
School, and Racial Test Score Gaps” PIER Working Paper #04-019.
[23] Weinberg, Bruce A. (2001) “An Incentive Model of the Effect of Parental income on
Children” Journal of Political Economy 109, 266-280.
19
TABLES
TABLE 1A
Sample Summary Statistics Part I
Weighted (Standard Deviation)
Respondent’s Characteristics
Boys
Girls
Average Grade Score %
0-49
50-59
60-69
70-79
80-89
90-100
0.013
0.035
0.173
0.365
0.288
0.126
(0.116)
(0.183)
(0.378)
(0.482)
(0.452)
(0.332)
0.006
0.014
0.098
0.350
0.362
0.170
(0.078)
(0.116)
(0.298)
(0.477)
(0.481)
(0.376)
Characteristics
Age
Number of Siblings
Household Income ($)
Canadian Father
Canadian Mother
Parents On Welfare
School Contact
Parents Separated or Divorced
English
12.617 (3.660)
0.858 (0.836)
65633 (46509)
0.845 (0.362)
0.859 (0.348)
0.065 (0.246)
5.134 (12.398)
0.265 (0.441)
0.723 (0.448)
12.648 (3.632)
0.844 (0.824)
63817 (46509)
0.844 (0.362)
0.853 (0.354)
0.064 (0.244)
3.539 (9.870)
0.270 (0.444)
0.740 (0.438)
0.114
0.169
0.052
0.293
0.131
(0.318)
(0.375)
(0.224)
(0.455)
(0.338)
0.104
0.156
0.053
0.292
0.137
(0.305)
(0.363)
(0.225)
(0.454)
(0.344)
0.141
0.198
0.075
0.362
0.179
(0.349)
(0.398)
(0.263)
(0.481)
(0.383)
0.145
0.196
0.076
0.362
0.170
(0.352)
(0.397)
(0.264)
(0.481)
(0.376)
0.215
0.187
0.275
0.241
0.082
(0.411)
(0.390)
(0.477)
(0.428)
(0.275)
0.212
0.180
0.283
0.241
0.079
(0.409)
(0.385)
(0.451)
(0.430)
(0.270)
Mother’s Education
Less Than High School
High school Diploma
Some Post-Secondary Education
Diploma in Post Secondary Education
University Degree
Father’s Education
Less Than High School
High school Diploma
Some Post-Secondary Education
Diploma in Post Secondary Education
University Degree
Region
Atlantic
Quebec
Ontario
Prairie Region
British Columbia
Sample Size
3422
20
3371
TABLE 1B
Sample Summary Statistics Part II
Weighted (Standard Deviation)
Parent Attitude or Activity
Boys
Girls
Importance of school grades
Not important at all
Somewhat important
Important
Very important
0.005 (0.072)
0.043 (0.203)
0.311 (0.463)
0.641(0.480)
0.004
0.044
0.298
0.654
(0.062)
(0.205)
(0.457)
(0.476)
Importance of more education past high school
Not important at all
Somewhat important
Important
Very important
0.047
0.047
0.215
0.691
(0.212)
(0.213)
(0.411)
(0.462)
0.036
0.038
0.211
0.716
(0.186)
(0.190)
(0.408)
(0.451)
Frequency of helping with homework
Never
Less than once a weeks
Once a week
A few times a week
Four or more times a week
0.138
0.089
0.132
0.244
0.397
(0.346)
(0.284)
(0.339)
(0.429)
(0.489)
0.853
0.064
3.539
0.154
0.270
(0.354)
(0.244)
(9.870)
(0.360)
(0.444)
Time spent interacting with child
0-5 hours per week
6-10 hours per week
11-20 hours per week
20 + hours per week
0.081
0.214
0.251
0.446
(0.272)
(0.410)
(0.434)
(0.497)
0.177
0.217
0.260
0.438
(0.267)
(0.412)
(0.439)
(0.496)
0.139
0.141
0.198
0.075
0.362
(0.346)
(0.349)
(0.398)
(0.263)
(0.481)
0.125
0.085
0.130
0.286
0.374
(0.330)
(0.279)
(0.336)
(0.452)
(0.484)
0.010
0.077
0.267
0.646
(0.099)
(0.266
(0.443)
(0.478)
0.007
0.055
0.241
0.697
(0.086)
(0.278)
(0.428)
(0.460)
Frequency of supervision of homework
Never
Sometimes
Often
Very often
Frequency of praising the child
Never
Sometimes
Often
Very often
School Contact and Tutoring
Frequency of school contact
Child tutored outside of school (yes)
5.134 (12.398)
0.135 (0.031
21
3.539 (9.870)
0.136 (0.343)
TABLE 2
Weighted Maximum Likelihood Parameter Estimates
(Standard Error).
Variable
Estimate
Age
Number of Siblings
ln(Household Income)
Canadian Father
Canadian Mother
Parents On Welfare
Parents Separated or Divorced
Boys
-0.004** (0.001)
0.006** (0.002)
0.006† (0.003)
-0.021** (0.006)
-0.008 (0.006)
-0.008 (0.008)
-0.006 (0.005)
Girls
-0.004** (0.001)
-0.005* (0.002)
-0.001 (0.003)
-0.009† (0.005)
-0.014** (0.005)
-0.014† (0.008)
-0.009* (0.004)
0.007 (0.005)
0.009 (0.008)
0.017** (0.005)
0.021** (0.007)
-0.004 (0.006)
0.011 (0.008)
0.004 (0.005)
0.034** (0.006)
-0.006 (0.006)
-0.006 (0.008)
0.008 (0.006)
0.040** (0.007)
0.012* (0.006)
0.005 (0.007)
†
0.009 (0.005)
0.032** (0.006)
0.063** (0.009)
0.120** (0.040)
0.015** (0.006)
0.017 (0.013)
-0.032** (0.006)
-0.008 (0.006)
0.042** (0.005)
-0.001** (0.000)
0.024** (0.010)
0.094** (0.030)
0.008 (0.006)
0.017 (0.013)
-0.025** (0.004)
-0.009 (0.006)
0.035** (0.004)
-0.001** (0.000)
Mother’s Education
High school Diploma
Some Post-Secondary Education
Diploma in Post Secondary Education
University Degree
Father’s Education
High school Diploma
Some Post-Secondary Education
Diploma in Post Secondary Education
University Degree
Averages of Parent Attitudes
Parent’s Attitude to School grades (3)N
Parent’s Attitude to More Education (3)
Time Spent with Child (3)
How Often Child Praised (4)
Homework supervised (3)
Help With Homework (4)
Child Tutored
Number of School Contacts
Notes:
†, ∗,and ** mean significant
at 10%, 5%, and 1%, respectively.
N indicates a significant gender difference.
22
TABLE 3
Relative Contributions To The Likelihood function:
Characteristics vs. Attitudes and Activities.
category
boys
girls
ln(L) %
%∆
ln(L) %
%∆
Baseline Variables
2733.153
0.0
0.0
3130.476
0.0
0.0
Baseline + Group I
2855.858
24.0
24.0
3257.974
29.8
29.8
Baseline + Group I + Group II
3167.435
84.7
60.7
3345.166
50.0
21.2
3245.732
100.0
15.3
3559.585
100.0
50.0
Baseline + Group I + Group II
+ Unobservables
Psuedo R
2
0.221
0.158
TABLE 4
Predicted means by Gender and Type
(Standard error)
Quantity
Boys
y
E(y)
Xβ
Xβ − β 0
βN
0
0.774
0.773
0.784
0.249
0.535** (0.045)
Probability
Type A
Type B
E{y|σ = σA } = 0.696
σA = 0.253** (0.024)
pA = 0.083** (0.018)
E{y|σ = σ B } = 0.780
σB = 0.088** (0.024)
pB = 0.917** (0.019)
Quantity
Girls
y
E(y)
Xβ
Xβ − β 0
βN
0
0.805
0.805
0.814
0.150
0.665** (0.038)
Probability
Type A
Type B
E{y|σ = σA } = 0.664
σA = 0.329** (0.066)
pA = 0.022** (0.003)
E{y|σ = σ B } = 0.808
σB = 0.087** (0.001)
pB = 0.978** (0.008)
23