Econometric model

Our goal is to assess the role of parental health measures in the health of children at very young ages. Given the variety of health measures in our sample, we group them and test the link and transmission between parental and child health.

Parental health measures are known to depend on family characteristics and investments in children’s health. A number of factors that influence parental health and health behav- ior will affect the health of the children. It is obvious that unobserved factors such as the unobserved parental health behavior, genetic components and time preferences may affect both parents’ and their children’s health. We attempt to account for the endogeneity of parental health by following two approaches. First, we consider how the effect of mater- nal health on the health of the children changes once we control for paternal health and paternal characteristics. Then, we try to obtain more direct evidence on the effect of the parental health on the child’s health by estimating fixed effects models.

We first estimate a model for the health of the child i at a certain age between birth and six years of age, only including the measures of maternal health and maternal characteristics: Equation 5.1 presents the link between the health of the mother and the health of the children:

Healthi = β1+ β2Healthmi+ Xmi0 γ + Y 0

iλ + ui. (5.1)

where Healthi is a measure of child i’s health in early childhood, which covers anthropo-

metric, self-reported and self-rated health. Healthmi denotes child i mother’s (m) health

(it also includes mother’s health behavior). Xmi is a vector of mother characteristics that

includes education, household income, family status, private health insurance, age, na- tionality and municipality size. Yi is a vector of children characteristics that includes sex,

siblings, parity and age. This specification yields an upper bound estimate of the extent to which health is passed from mother to child.

In order to reduce unobserved heterogeneity likely to affect Healthmi, we include measures

Equation 5.2 presents the link between the health of the parents and health of the children:

Healthi= β1+ β2Healthmi+ β3Healthf i+ Xm,f i0 γ + Y 0

iλ + ui. (5.2)

We estimate equations 5.1 and 5.2 for all age groups and all different health measures of the child, as well as for girls and boys, respectively.15

The health status of the parents and of the child may be correlated with unobserved fac- tors, even after including the father’s health and the father’s characteristics and even if we control for various child, parent and household characteristics in the OLS regression. One way to account for the endogeneity is to apply instrumental variable approaches. Usually, the instruments that find the strongest support result from natural experiment or from institutional changes affecting otherwise similar populations in a different ways. In our data, we do not observe such instruments. Another difficulty is that we have to deal with more than one potentially endogenous variable (health and health behavior of mothers and fathers). Thus in this analysis we are not able to apply instrumental variable approaches.

An alternative way to use the instrumental variables in tackling the problem of causal inference is to study the health status of children over time during the first six (three) years of a child’s life. We try to identify the intergenerational transmission coefficient of health by exploiting variation in health measures over time.

Equation 5.3 presents the transmission between health of the parents and health of the children:

Healthit= α + βHealthjit+ Xjit0 δ + Y 0

itγ + fi+ uit. (5.3)

In equation 5.3, we explicitly take into account an individual fixed effect fi. Healthit

denotes the health of the child i in t, Healthjit denotes the vector of health measures

of both mothers and fathers, Xjit is a vector which includes all family characteristics

and Yit includes all controls at the child’s level i. If fi is constant over time, the model

will recover an asymptotically unbiased estimate. Within this model, we analyse the

intergenerational transmission of the parent’s health on the child health, conditional on time-variant family background variables, captured in Xjit. The coefficient on parental

health β is our parameter of interest. The parameter can be used to test a variety of hypotheses. First, β provides information on whether the children of parents with poor health also experience poor health in early childhood. Second, the coefficient β can be interpreted as a health gradient. A high coefficient indicates a strong transmission of health characteristics from parents to children. Finally, the coefficient β can be decomposed into the impact of mother’s health and father’s health on the child’s health. We apply within- transformation to eliminate fi. The identifying assumption is that parental health across

children is uncorrelated with the unobserved determinants of the child’s health.

∆healthit= β∆healthjit+ ∆Xjitδ + ∆Yitγ + ∆uit. (5.4)

After eliminating fi, we assume that the conditional mean independence assumption holds

(equation 5.5). Conditional mean independence

E(∆uit|∆healthjit, ∆Xjit, ∆Yit) = 0 ∀t = 1, 2. (5.5)

implies:

E(∆uit|∆healthjit, ∆Xjit, ∆Yit) = 0 s ≤ t. (5.6)

This implies that the error terms are uncorrelated with ∆healthjit, ∆Xjit, ∆Yit within one

period (equation 5.5) and are uncorrelated between different periods (equation 5.6).

In the following, we first estimate cross-sectional models with anthropometric health mea- sures for children, mothers and fathers. Second, we distinguish between models with self- reported health measures and self-rated health measures for the children and self-rated health measures of the parents. All models include a measure of parental health behavior, namely whether or not a parent smokes. Finally, we estimate fixed effects models for different health measures.