1 Introduction
More and more children do not grow up in traditional nuclear families. Instead, they grow up in single-parent households or in families with a step-parent. Hence, it is important to improve our understanding of the impact of "shocks" in family structure due to parental relationship dissolution on children. To give an example of the severity of this problem, we can look at a western country like Denmark. In 1980, almost 83% of all Danish children in the ages 0 to 17 lived with both of their biological parents, but this number steadily decreased to 73% in 2005 as shown in Figure 1. That is, more than 25% of all Danish children did not live with both of their biological parents in 2005. In many other western countries the divorced population is increasing as well, and for these countries we expect to see a similar picture as that depicted in Figure 1 for Denmark.
The topic of family structure changes has been studied extensively in the psychology and sociology literature and recently also in the economics literature. International studies mainly suggest a negative relationship between non-nuclear family structures and child outcomes. There are two potential explanations for this. First, families that split up may possess characteristics that are di¤erent (and worse) than what is seen in nuclear families, i.e. non-nuclear families are a selected group of families.1 Another explanation is that there may be negative causal e¤ects of separation.2 To analyze the e¤ect of a change in family structure on child outcomes properly, detailed data are required. Many international studies only have access to datasets where family structure is observed once during a child.s life and this "value" is then extrapolated to the entire childhood.3 This approach leads to imprecise results and is known as the "window problem" (Wolfe et al. (1996)). Danish register data makes it possible to avoid the window problem and to make quantitative economic analyses which can shed light on the selection and causation explanations. However, until now, register data from Denmark has not been exploited systematically to analyse family structure and its relation to child outcomes.
Thus, this study is an empirical study of the relation between family structure changes and several di¤erent child outcomes using an administrative register dataset consisting of the entire population of Danish children born from January to May 1985. These children are followed on a yearly basis until 2005, i.e. until they are 20 years old. The study is partially descriptive, but it also attempts to identify causal e¤ects of family structure changes. A di¤erences-in-di¤erences analysis is used for the latter purpose for the health outcomes.
Though descriptive in its nature, this study contains multiple contribu-
tions to the Danish and international literature. One contribution is to use
detailed data for the quantitative economic analyses to avoid the window
problem and obtain more precisely identi.ed results. Some other studies
are also using panel data, but they do not have a population sample of chil-
dren available for their analyses. Using a population sample implies a lot of
observations and thus more precision in the empirical analysis. Another con-
tribution is to illuminate new aspects of family structure by investigating a
variety of short- and long-term child outcomes. In particular, I focus on the
relation between family structure and child outcomes such as health (hos-
pitalizations), behavior (crime), and education (high school enrolment and
high school GPA). A third contribution is to propose new questions to this
area such as the importance of the timing of family dissolution, the short-
and long-term impact of multiple family structure changes, and the time
spent in a single-parent household. This study can be used as a reference
point for further studies.
To preview the results, in the descriptive analysis I .nd a negative rela-
tion between all three types of child outcomes and family structure changes.
The results further indicate that the number of family structure changes
might be more important for child outcomes than the years spent in a single-
parent household. The di¤erences-in-di¤erences analysis continues to show
a negative e¤ect on health from a family structure change, thus indicating a
negative causal e¤ect on children of experiencing a family structure change.
The remainder of the paper proceeds as follows. In Section 2, a literature
review is presented and in Section 3 the estimation strategy is explained.
Section 4 gives an introduction to the datasets used in the analysis, and
the empirical results are presented in Section 5 along with a sensitivity
analysis. Finally, the results are summarized and a brief discussion of policy
implications is presented in Section 6.
2 Literature Review
Human capital (HC) theory provides an explanation of family structure.s
(causal) e¤ect on child outcomes (Becker (1991) and Becker (1993)). The
intuition is that households are time- and money-constrained. With fewer
adults in the household there is less time and money to invest in children and
this may reduce child outcomes through decreased parent-child interaction
and fewer goods. Becker.s theories of the family suggest that two adults can
pool their resources and specialize in tasks within and outside the household,
thereby increasing total market and household production.
However, HC theory cannot explain why children growing up in non-
nuclear families seem to have lower outcomes even with a step-parent present
(Gennetian (2005)). Possible explanations include asymmetric informa-
tion and monitoring (Weiss and Willis (1985)) or di¤erent bargaining power
among biological and step-parents (Lundberg and Pollak (1996)). The latter
explanations imply that biological mothers may act to ensure that a child liv-
ing with a stepfather is no worse o¤ than biological children of both adults in
the household. If the stepfather allocates less resources to a stepchild, but
the mother thereafter redistributes resources to make all children equally
well o¤, in total these children will be worse o¤ than children living in a
nuclear family. This holds despite there being two adults in the household.
Recent theoretical studies on child development and child outcomes sug-
gest that skills beget skills and capabilities today foster future capabilities
through self-productivity and dynamic complementarity. That is, higher
stocks of skills in one period create higher stocks of skills in the next period,
and stocks of skills acquired in one period make investments in future pe-
riods more productive (Cunha and Heckman (2007) and Heckman (2008)).
Thus, early investments in children are often most fruitful and even more so
if they are followed up by later investments, but this depends on the exact
technology of skill formation. Cunha and Heckman (2007) demonstrate that
some periods may be more e¤ective in producing certain skills (sensitive pe-
riods), or it may be the case that only one period is e¤ective in producing
a certain skill (critical period). With this theory in mind, the timing of
family structure changes might be extremely important for child outcomes.
An early family structure change might a¤ect children more negatively than
if they experience a family structure change in their teens. I return to this
question in the hypotheses and the empirical analysis, in particular by look-
ing directly at family structure changes in di¤erent age brackets. Finally,
the sociological and psychological literatures have also developed theories
of the relation between family structure and children.s outcomes. One ex-
ample is loss of parental control theories which focus on trauma or shocks
experienced during childhood, e.g. changing family structure. I will refer to
this theory as the stress theory. Ginther and Pollak (2004) summarize the
latter and related theories in more detail.
In general, the empirical literature cannot agree on whether selection
or causation (or maybe both) explain how children.s outcomes are related
to family structure. The selection theory claims that families that split
up may possess characteristics that are di¤erent (and worse) than what is
seen in nuclear families, i.e. non-nuclear families are a selected group of
families. Children from non-nuclear families will thus have worse outcomes
than children from nuclear families both before and after a family structure
change. Studies pointing in this direction are Björklund and Sundström
(2006), Björklund et al. (2007), and Piketty (2003). On the other hand,
Ermisch and Francesconi (2001) and Steele et al. (2009) argue among others
for causal e¤ects of separation, i.e. negative e¤ects on child outcomes caused
by a change in family structure. The potential causal e¤ect of separation
may be visible even before the separation formally occurs, especially if the
parents argue or .ght a lot before the actual separation (Amato (2000)).
Furthermore, a practical issue pointed out in Manski et al. (1992) em-
phasizes that assumptions about the actual process generating family struc-
ture and child outcomes are important for the estimation strategy. Strong
assumptions lead to more precisely estimated e¤ects, but at the cost of
maybe being less realistic. Thus, we need to consider this when choosing
the estimation strategy.
The main problem in empirical analyses of family structure is speci.-
cation of a counterfactual to divorce and separations (Ginther and Pollak
(2004)). "No divorce" is not a reasonable counterfactual since parents can-
not be forced to live together. This problem of identifying the e¤ect of
divorce or separation can be solved by using an instrument, e.g. a quasi-
experiment such as a reform in the rules of divorce. It has been done in the
studies by Gruber (2004) and Francesconi et al. (2005), but unfortunately
it is di¢ cult to .nd suitable reforms and thus good instruments. Further-
more, using divorce laws as an exogenous cause of divorce does not solve the
problem that changes in divorce regimes may directly a¤ect the nature of
intrafamily bargaining, and this may lead to di¤erent implications for the
children (Stevenson and Wolfers (2006)). Alternatively, one can consider the
death of one parent as an exogenous shock to family structure as in Corak
(2001) and Francesconi et al. (2005). The problem with using this .exoge-
nous.shock is, that it might not be completely exogenous if, for example,
the parent.s death is the result of several years of sickness. Then it might
be perfectly expected and the e¤ect on the child of losing a parent might be
reduced due to .preparation.for the event. If the parent.s death is due to
e.g. a tra¢ c accident, the loss is truly an exogenous and unexpected event.
However, loosing a parent permanently due to parental death may not be
comparable to loosing a parent due to divorce. In the latter case the parent
is still alive and may still participate actively in the child.s daily life.
In this current study (as in most of the existing studies in the litera-
ture), the problem of not having a reasonable counterfactual is ignored and
the results of the empirical analysis in Section 5 thus have to be interpreted
with some caution. For reasons of comparison, I will carry out simple cross-
section estimation strategies, but also do a di¤erences-in-di¤erences (D-i-D)
analysis as done by Sanz-de Galdeano and Vuri (2007) to get closer to the
causal e¤ects. The D-i-D analysis makes it possible to control for common-
alities during the time periods for both children that do experience family
structure changes and those that do not. Moreover, .xed characteristics of
the same child is also di¤erenced away in this panel D-i-D. Thus, this leads
to results far beyond the simple cross-section analysis and thereby gives
some indication of the causal e¤ects of family structure changes.
3 Empirical Model
In the empirical analysis I attempt to test the stress theory, i.e. whether
children are traumatized in the short and the long run by shocks in fam-
ily structure during childhood. I investigate how the timing and sum of
family structure shocks a¤ect children to get information on negative im-
pacts (stress) accompanying a change in family structure. Furthermore, by
comparing the importance of years in a single-parent household to the im-
portance of the number of family structure changes experienced during the
entire childhood, I give some evidence on the validity of Beckers human cap-
ital theory. The main hypotheses analysed in the empirical study are the
following:
Hypothesis 1 A family structure change is a (negative) shock for the child
and thus has negative implications for the child.s outcomes both in
the short and long run.
Hypothesis 2 The number (and timing) of family structure changes a¤ect
child outcomes by stressing the child.
Estimates are based on a linear version of the education production func-
tion model (Todd and Wolpin (2003)). Assume that achievement for child
i, Ti, can be expressed as a linear function of the explanatory variables
Tija = _0 + _1Dija+_2Fij (a) + j + _ija; (1)
where Tija is the outcome for child i from family j at age a (education,
behavior (criminal activity), or health); Dija is a family structure change
(measured as year-to-year changes); F is a vector with child and family
background information (child.s birthweight and gender, ethnicity, number
of siblings at age 10, age at .rst separation, parental work experience, annual
wage income, and level of education); j is a family .xed e¤ect, e.g. norms
and values in the family; and, .nally, _ija is an error term.
Child outcomes depend on the child.s unobservable endowed ability which
I proxy by birthweight. This is a common way of dealing with unobserved
endowed ability in the literature (e.g. Behrman et al. (1994)). To get
consistent estimates, I include information on both contemporaneous and
historical inputs. Relevant background information such as labor market
information for the "social" parents (the parents living in the household) is
included in the analysis, as well as information on the child, siblings, child.s
age at the time of the .rst shock, etc.
As outcome measures I use education, measured as high school enrolment
and high school grade point average. Further, behavioral measures such as criminal activity are used, and .nally health outcomes (hospitalized in a
year, number of sickdays) are investigated. By studying this wide variety
of outcomes, di¤erent aspects of the e¤ect of family structure changes are
illuminated.
I also apply a di¤erences-in-di¤erences model for the health outcomes in
which I assume there are only two time periods, 1 and 2. Family structure
changes are now expressed as
D(i; t) =
8<
:
1 if divorce or separation in period t
0 if no divorce or separation in period t
Changing the notation slightly, we get the following expression for child
achievement as a function of family structure changes:
T (i; t) = _0 (t) + _1D(i; t)+ (i) + v (i; t) ; (2)
where _0 (t) is a time-speci.c component; _1 is the impact of parental di-
vorce or separation; v (i; t) is a serially uncorrelated transitory component;
and (i) is an individual-speci.c component representing unobserved pre-
disruption characteristics, e.g. stress associated with an unhappy family life.
D(i; t) is probably correlated with (i), i.e. we cannot identify the e¤ect of
parental divorce or family dissolution from OLS estimates of this equation.
Di¤erencing Equation (2) with respect to t and adding covariates implies:
T (i; 2) T (i; 1) = _0 + _1D(i; 2)+_2X (i) + (v (i; 2) v (i; 1)) ; (3)
where _0 = _0 (2) _0 (1), _2 = _2 (2) _2 (1) and X (i) is a vector of
observed characteristics assumed uncorrelated with v (i; t).
The model in Equation (3) is identi.ed if the conditional restriction is
ful.lled
P (D(i; 2) = 1 j X (i) ; v (i; t)) = P (D(i; 2) = 1 j X (i))
for t = 1; 2;
i.e. there is identi.cation if changes in the outcome variable over time would
have been exactly the same in both treatment and control groups in the
absence of divorce or separation (parallel trend assumption) at least when
including the covariates.
The D-i-D approach follows Sanz-de Galdeano and Vuri (2007). The
control group consists of those children that do not experience any family
structure change during childhood, and the treatment group is the children
that have experienced a family structure change from period 1 to period 2.
The dataset has to be set up in a certain way for this to work. First, in period
1, none of the children must have experienced a family structure change, i.e.
children who do not have (typically) their father in the household during the
.rst time period of their life have to be deleted from the sample. Children
most often stay with their mother in the year after a family structure change,
but few, especially older children, choose to stay with their father the year
after a family structure change. Figure 2 shows the distribution for Denmark
in 2008. For families that break up, about 14.5% of the children live with
the father the following year, whereas more than 80% of the children live
with their mother. Some of the oldest children choose not to live with either
parent the following year.
Secondly, the D-i-D strategy is only possible for the health outcomes us-
ing my datasource since D-i-D requires outcome measures that are observed
over time along with the changes in family structure. The educational out-
comes are not observed until the child is quite old, and thus the e¤ect of
Figure 2: Family type for children who lived with both mother and father the
previous year, but not in the current year, Denmark 2008. Source: Statistics
Denmark
early family structure changes cannot be analysed on the educational out-
comes. Observations on criminal activity start when the child is 15 years old
and thus also quite late. Health outcomes are available from the child is 6
years old and therefore health outcomes are preferred for the D-i-D analysis.
Due to the richness of the data, having yearly observations, it is possible to
de.ne the two time periods in the D-i-D analysis in di¤erent ways. I use
ages 0 to 11 as period 1 and ages 12 to 20 as period 2 in the main speci.ca-
tion. To test the robustness of the results and the importance of the timing
of family structure changes, I also repeat the analysis using ages 0 to 7 as
period 1 and 8 to 20 as period 2.
When empirically analyzing the e¤ect of family structure on child out-
comes, there are some challenges related to .nding the best speci.cation of
the empirical model. The problem arises because family structure is clearly
not random and thus simple OLS or probit parameter estimates may be
biased. OLS is nevertheless used in most of the existing literature and will
therefore also be used here for comparison. In addition to OLS and probit
estimation of Equation 1, I use D-i-D analysis to di¤erence away unobserved
individual-speci.c components. These might be components that can be re-
lated directly to family dissolution decisions and thus would bias a simple
cross-section analysis. In other words, the D-i-D analysis allows for the
possibility that parental divorce or separation is correlated with unobserved
family characteristics that may in.uence child outcomes. A family or sib-
lings .xed e¤ects analysis is employed in several studies in the literature,
but the advantage of D-i-D compared to a family .xed e¤ects analysis is
that also children without siblings are analyzed in the D-i-D framework.
Analyzing only families with siblings and only in cases where the siblings
have experienced di¤erent family structures reduces the external validity of
the study as pointed out by Mo¢ tt (2005). Thus, a D-i-D analysis is easier
to generalize to larger groups of the population.
4 Data
Estimations are based on an administrative register dataset consisting of
the entire population of Danish children born from January to May 1985.4
About 50,000 children were born per year in Denmark in the mid-1980.s.
Due to seasonality in childbirths, I have about 36,000 unique children in
the dataset. The data source contains yearly, rich information on family
background along with other information on children, parents, and siblings.
This rich datasource implies more reliable estimates of the e¤ect of family
structure changes on child outcomes than what is seen in most existing
studies. Family structure changes are observed until the child reaches the
age of 18. After this point in time, the child is registered as an adult whether
or not the child still lives with his/her parents.
In the Danish tax and income registers created by Statistics Denmark,
the children and their parents are followed on a yearly basis from the year
of birth to 2005 if they have not left the country or died. Parental .gures
are identi.ed each year based on the household characteristics of that year.
If the child lives with both biological parents, parental information concerns
the biological parents. If, on the other hand, the child lives with one biolog-
ical parent and one step-parent, then the parental information collected is
for these individuals. I will distinguish between biological and non-biological
parents by referring to either .biological.or .social parents..
At this point it is useful to de.ne precisely what is meant by a family
structure change. Throughout this study, family structure changes will be
de.ned as follows unless explictly noted:
De.nition 1 A family structure change is any change in the compo-
sition of biological or social parents that the child experiences. It does not
have to be a legally binding change, such as divorce or remarriage.
Thus, any observed change in the number or identity of the (biological or
social) parents in the household from one year to the next is considered a
family structure change. This can be a reduction in the number of .parents.,
but also an increase in the number of .parents..
The registers provide information on the parents. and children.s mar-
ital status, residence, education, income, labor market activities, health,
criminal activity, etc. This includes information on the number of hospital-
izations and days in hospital, whether the individual has been convicted of a
crime, the children.s highest completed level of education, whether they are
currently enrolled in education, and their grade point average if they have
completed high school. While most Danes complete high school at age 20,
some Danish children take an optional 10th grade before enrolling in high
school and they may therefore still be enrolled in high school at the age of
20. It is also very popular among the Danish youth to take a sabbatical year
between high school and college. Thus, higher educational goals may not be
clear in 2005 when the children are 20 years old. When investigating educa-
tional outcomes, I therefore focus on high school enrolment and high school
completion, which in short will be referred to as high school enrolment.
Furthermore, information on criminal activity and health is available
in the data, which enables analyses of both short and long-term outcomes,
cognitive and non-cognitive. I measure children.s health in two ways; an
indicator for being hospitalized during the year in question and the number
of days in the hospital. In some cases I aggregate this information into an
indicator for ever being hospitalized as this provides less noisy information.
Health information is available from 1991 on. Thus, health outcomes can be
investigated on a yearly basis beginning when the child is 6 years old. For
criminal activity I use a dummy for being convicted in the year in question,
but in some cases I also aggregate the information into an indicator for ever
being convicted. The age of criminal responsibility is 15 in Denmark so I
cannot investigate this behavioral outcome before the child is 15 years old.
Educational, health, and behavioral outcomes are important outcomes both
for the children themselves and more generally for society. These variables
are therefore the focus of this study.
In Denmark, GPAs from high school range from 0 to 13 with 8 as the middle grade. 6 is equivalent to passing the exam. However, by looking at the number of observations it is clear that we only have a measure of GPA for those who actually have completed high school by age 20. Thus, it seems reasonable to use high
school enrolment as the main outcome variable for education instead of the
GPA from high school. It is also clear from the table that only 8% of the
children are hospitalized during 2005, whereas 47% of the children have ever
been hospitalized. When hospitalized, they spend 3.6 days in hospital on
average. The most common reason for being hospitalized is problems during
a pregnancy (for girls). 7% of the children are convicted of a crime during
2005, but 19% have ever been convicted. However, the gender distribution
is very uneven as only about 2% of girls get a conviction in 2005.
After a separation, most of the children live with their mother. The
children that live with their father are usually in the group of 11- to 16- year-
olds, i.e. the oldest children. On average, children growing up in non-nuclear
families experience their .rst family structure change at age 6. Finally,
fathers have a higher annual wage income than mothers, and fathers.work
experience is also higher. Most of the children have one sibling by the age
of 10 and the gender composition of the sample is almost 50/50.
In Table 2 the distribution of family structure changes for the sample
is shown. The highest number of (observed) family structure changes for
a child is 135, but it is not common to experience such a high number of
family structure changes. Even when collecting 8 and more family structure
changes into one single category, only 1% of the sample is present here. The
most common number of family structure changes is 0, i.e. the child grows
Table 2: Total family structure changes during childhood by 2005.
up in a nuclear family. 27% of the children have experienced 1 or 2 family
structure changes during childhood, implying that they have experienced
the parents separate and potentially also experienced a step-parent moving
into the household afterwards. In some cases, the children with 2 family
structure changes experience one parent moving out of the household and
then the same parent returns some years later. A descriptive analysis (avail-
able from the author upon request) shows that these families are di¤erent
than .normal.nuclear families. Thus, even though it is the same biological
parent who is moving back into the household, this is counted as 2 family
structure changes.6
Focusing on descriptive evidence, Figures 3 to 5 show three di¤erent
outcomes plotted against the child.s age and separately by the .nal number
of family structure changes the child experiences during childhood. The
pattern from the .gures is clear: the more family structure changes, the
worse the children.s outcomes. This can of course be a selection e¤ect as the
families with most family structure changes might be di¤erent than a typical
nuclear family. This will be investigated later. But .rst it can be seen in
Figure 3: No high school enrolment by the age of the child and the .nal
number of family structure changes during childhood. 1985-cohort.
Figure 4: Convictions by the age of the child and the .nal number of family
structure changes during childhood. 1985-cohort.
Figure 5: Hospitalizations by the age of the child and the .nal number of
family structure changes during childhood. 1985-cohort.
Figure 3 that more than 60% of children with three or more family structure
changes do not enrol in high school compared to about 40% of the children
in nuclear families. For convictions the picture is just as clear as shown in
Figure 4. At the age of 20, more than 12% of the children experiencing three
or more family structure changes have been convicted whereas less than 6%
of the children in nuclear families have been convicted. When splitting the
sample by gender, the numbers are even more disturbing. More than 20% of
the boys with three or more family structure changes have been convicted in
the year they turn 20 whereas less than 10% of the boys in nuclear families
have been convicted. A similar di¤erence is observed for girls, but at much
lower levels. For hospitalizations the picture is slightly more blurred. There
is not much di¤erence in the probability of hospitalization between those
experiencing one or two family structure changes, but there is still quite a
big di¤erence between children from nuclear families and children from the
families with most family structure changes. This also holds for boys and
girls separately, but with girls having more hospitalizations at the higher
ages and vice versa for the youngest ages. The .gures for boys and girls
separately are available from the author upon request.7
5 Estimation Results
In the empirical analysis I .rst look at cross-section estimations as is com-
mon in the literature. When investigating hospitalizations, convictions, and
no high school enrolment using a probit estimation procedure, I generally
.nd highly signi.cantly estimated marginal e¤ects as shown in Table 3. All
the estimates point to a negative relation between single-parent households
(or family structure changes) and children.s outcomes. Furthermore, using
OLS, the relation between GPA and years in a single-parent household and
the total number of family structure changes during childhood is analyzed.
Again I .nd highly signi.cantly estimated coe¢ cients as shown in Table 3
and all estimates point to a negative relation between single-parent house-
holds (or family structure changes) and children.s GPA after high school.
These results con.rm what is generally found in other empirical studies
using data from both the US and Sweden, for example Björklund et al.
(2007). Relatively few children live in single-father households compared to
single-mother households and the marginal e¤ects for this group are thus
less precisely estimated.
Interpreting the coe¢ cients in Table 3 as causal e¤ects, the most interesting observation is the relatively larger e¤ect family structure changes have
as compared to the e¤ect of years in a single-parent household. For all out-
comes, the .e¤ect.of a(nother) family structure change is about four times
higher than the .e¤ect.of living a(nother) year in a single-parent household
during the childhood. As expected, the .e¤ect. of experiencing a family
structure change (0/1) is higher than the .e¤ect. of the number of family
structure changes, as the .rst variable captures the .total e¤ect.of experi-
encing family structure changes. Thus, these results suggest that instability
of households has a greater impact on children.s outcomes than potentially
a lower household income and fewer adults in the household to take care of
the children. In other words, this .nding provides some evidence against
the mechanism suggested by Becker (Becker (1991) and Becker (1993)).
It is also interesting to note that the e¤ect of family structure changes on
children.s outcomes is linear for all outcomes, but high school GPA. When
including dummies for 1 family structure change, 2 changes, 3 changes, and 4
or more changes and comparing to children with no changes in the analyses,
it turns out that the marginal e¤ects are linear as shown in Figure 6. Includ-
Figure 6: Marginal e¤ects for ever hospitalized, ever convicted, no high
school enrolment, and high school GPA by the number of family structure
changes.
ing squared or cubic terms of the total number of family structure changes
in the di¤erent speci.cation also reveals the same picture; the coe¢ cients
for the squared and cubic terms are insigni.cant, whereas the coe¢ cient for
the linear term is highly statistically signi.cant. The marginal e¤ects for
high school GPA is not as clearly linear as for the other outcomes, but this
may be explained by the fact that the children with a high school GPA is
a smaller and positively selected sample. Thus, they are not representative
for the full sample and I will therefore not rely heavily on the potential
non-linear pattern shown by this outcome measure. Instead, I will continue
to include a variable for the total number of family structure changes in the
estimations as this measure seems to be linear for the main sample.
Now focusing only on years in a single-mother household as in most
of the literature and again investigating cognitive and non-cognitive child
outcomes in 2005 by OLS and probit, we see in Table 4 that for the di¤erent
Table 4: OLS and probit estimation results for the e¤ect of years in a single-
mother household at di¤erent ages on various child outcomes in 2005.
outcome variables the .e¤ects.di¤er by the age of the child. This con.rms
what has also been seen previously in the literature. The age groups are
de.ned based on the type of care the child receives besides parental care.
For example, children in the ages 0-2 are eligible for daycare, children in the
ages 3-5 usually attend preschool, and children aged 6 and older are in school.
For hospitalizations and convictions, living in a single-mother household in
the .rst three age groups seems to be important. The marginal e¤ects are
generally higher for the younger age groups. For GPA, the period 3-5 years
of age seems to be most important, whereas for high school enrolment all
age groups are important, but the marginal e¤ects are again higher for the
younger age groups. Thus, living in a single-mother household in the earliest
childhood seems to have the most detrimental e¤ect on most outcomes.
Families that split up may be a selected group. Thus, many studies
include covariates in their cross-sectional estimations to control for this se-
lection. If the signi.cance of the coe¢ cient for family structure change dis-
appears after including the covariates, this is interpreted as evidence for se-
lection being the explanation of negative e¤ects of family structure changes.
That is, if the coe¢ cient turns insigni.cant, there is no evidence of a causal
e¤ect of family structure changes on children.s outcomes. I have also in-
cluded covariates8 in all the estimations shown in Tables 3 and 4, but the
signi.cance of the coe¢ cient for family structure change does not disappear.
However, the size of the coe¢ cient decreases somewhat.9 Since there is no
evidence for selection being the main explanation for the negative relation
between child outcomes and family structure changes, I decided to show the
most raw numbers in the tables, i.e. without the covariates included.
Another way of investigating the selection and causation explanations
is to carry out a di¤erences-in-di¤erences (D-i-D) analysis of the health
outcomes. The parameter of interest is the coe¢ cient to the interaction
between treatment (experiencing parental divorce or separation) and the
age dummy (aged 12 or older). The comparison age group consists of those
between the ages of 6 and 11.10 Any statistically signi.cant coe¢ cients on
this interaction term are interpreted as a causal e¤ect of family structure
changes. The D-i-D analysis is possible solely for the health outcomes, since
this is the type of outcome for which there is information for most years
(from the child is aged 6 and on). The two outcomes that are depicted in
Table 5 are .rst a variable counting the total number of years a child has
been hospitalized in each period and, secondly, the total number of days
spent in hospital by period. Results are shown both with and without a list
of covariates that includes the child.s birthweight, gender, ethnicity, number
of siblings at age 10, parental work experience, parental annual wage income,
and parents.level of education.
The parameter of interest shows a statistically signi.cant positive e¤ect
Table 5: Di¤erences-in-di¤erences estimates of the e¤ect of experiencing a
Family structure change at age 12 or older on children’s health outcomes.
On child outcomes. This can be interpreted as the causal effect of experiencing a family structure change after age 12. Thus, children who experience
that their parents divorce or separate when they are 12 years old (or older)
have worse health outcomes (more often hospitalized, more days in hospi-
tal) than children that do not experience a family structure change during
their childhood. The results do not change remarkably after including a
wide array of covariates which again indicates that selection is not the main
explanation for the e¤ect of family structure changes on children.s health.
That is, children.s lower outcomes in families that incur family structure
changes are not caused by remarkably worse characteristics of these families
compared to nuclear families. This is somewhat surprising and does not
support the .ndings in many of the studies in the literature. However, it
does support the .nding in Francesconi et al. (2005).
Table 6: Di¤erences-in-di¤erences estimates of the e¤ect of experiencing a
family structure change at age 8 or older on children.s health outcomes.
For testing the robustness of the results I have carried out a series of
sensitivity tests. First, I have excluded all children whose parents are immi-
grants, i.e. the children were born in Denmark in the relevant time period
to biological parents not born in Denmark. The reason for excluding these
children from the sample is that these families may have a di¤erent culture
in particular with respect to whether or not it is acceptable to divorce or
separate. However, excluding the children born by immigrants does not
change the main results.11
As shown in Table 6, I have also tried to change the de.nition of the age
brackets for the time periods. The descriptive evidence in Table 4 suggested,
that the timing of family structure changes might be important for most of
the outcomes, in particular for the health outcomes. Thus, I have now
de.ned time period 1 as children aged 6 to 7 and time period 2 as children
aged 8 to 20. By changing the time periods, I only exclude individuals that
experience parental divorce or separation before they turn 8. Moreover, I
can assess the e¤ect of much earlier family structure changes, i.e. when the
children have just started in school. By comparing Tables 5 and 6, we see
that the parameter of interest is still signi.cant and positive. The size of
the coe¢ cient is even bigger in Table 6 than in Table 5 implying that earlier
family structure changes might be more detrimental to child outcomes than
later family structure changes. It might also be the case that what we see in
the table is that the result of moving the age bracket 4 years down makes it
possible to experience even more family structure changes during childhood.
This might be causing the .stronger.e¤ect on child outcomes.
6 Conclusion
More and more children do not grow up in traditional nuclear families. In-
stead they grow up in single-parent households or in families with a step-
parent. Hence, this paper aims at improving our understanding of the im-
pact of "shocks" in family structure due to parental relationship dissolution
on children. Today, in some countries, more than 40% of all children do not
grow up in a household with both of their biological parents.
Using a Danish administrative register dataset, I .nd in the empirical
analysis that children who have experienced family structure changes during
childhood seem to have worse educational outcomes and a higher propensity
of being hospitalized and convicted of a crime. The children in the dataset
experience up to 13 family structure changes during childhood. More family
structure changes imply worse outcomes and might actually be more impor-
tant than the number of years a child has spent in a single-parent household.
Also the age at which the family structure change occurs seems to be im-
portant as separations at younger ages are more negatively related to the
outcomes. Finally, the D-i-D analyses show that there seems to be a causal
e¤ect of family structure changes on health outcomes. A causal e¤ect on
child outcomes is also found by Francesconi et al. (2005) using German data.
However, the results are in contrast to studies using Swedish and U.S. data,
which .nd only a selection e¤ect of family structure changes (for example
Björklund and Sundström (2006) and Björklund et al. (2007)).
Particularly for studies using Danish or Scandinavian data, this study
is thought to be a useful reference study for further research on the topic
of family structure changes. Many of the analyses in other studies in the
literature are replicated and extended in this study and I use both short-
and long-run outcomes as well as cognitive and non-cognitive outcomes.
This study, like most of the studies in the literature, ignores the problem of
having a reasonable counterfactual to separation or divorce. Thus, in future
research I expect to look more into families that are already separated to
avoid the problem of the .missing.counterfactual.
The lack of a clear counterfactual makes it di¢ cult to give policy recommendations. The study clearly shows that family structure changes cause negative e¤ects on children.s outcomes, but despite this .nding it is not necessarily a better option for the child that the parents do not separate. However, for ethical reasons, it is not possible to investigate this question further as we cannot force families to either split up or remain together.
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