Influence of Place of Birth on Adult Mortality: The Case of Spain

We use a unique data set from Spain and we estimate life expectancy at age 50 for males and females by place of residence and place of birth. We show that, consistent with expectations regarding the influence of early conditions on adult health and mortality, the effects of place of birth on adult mortality are very strong, irrespective of place of residence. Furthermore, we find that mortality levels observed in a place are strongly influenced by the composition of migrants by place of birth. This is reflected in a new measure of heritability of early childhood conditions that attains a value in the range 0.42–0.43, implying that as much as 43 percent of the variance in Spain’s life expectancy at age 50 is explained by place of birth. Finally, we find evidence of the healthy migrant effect, that is, positive health selection of migrants, at a regional level. Supplementary Information The online version contains supplementary material available at 10.1007/s10680-023-09679-y.


Adjustment of probabilities of dying
Because the population and mortality data we employ are not linked, the quantities  , (, , ) and  , (𝑥, 𝑠, 𝑡) are not in a one to one correspondence due to yearly migration flows.That is, death and out-migration or in-migration are concurrent (competing) events and, to compute an unbiased conditional probability of dying for a given one-year interval, we must introduce some adjustments.The probability of joint occurrence of both events is the product of ′ and  , is defined as: Using these expressions we can compute the corrected age and sex specific conditional probabilities of dying, ′ , (, , ), from 2003 to 2019 and for all combinations of regions of birth and residence.This gives 135,762 computed death probabilities.We then estimate the cohort populations at each time t,  , ′ , as follows: When  =  0 (year 2003), we set: The number of deaths in the period under examination is: We then pool these conditional corrected probabilities of dying ′ , (, , ) in order to get the  , (, ) and compute the rest of the life table functions by sex, region of birth and region of residence.This procedure is detailed in the main text.

Alternative strategies to construct a pooled life table for the period under observation
The following is a description of alternative strategies to compute a single estimator of e50 for each cell of the 11x11 place of birth and residence matrix.

i. Standard actuarial method
In each cell we compute mortality rates for age groups [50 +k,51+k) to [81+k, 82+k] and for the k th year (0 ≤  ≤ 17) after the onset of observation (year 2003).Each of these rates is computed using the ratios  , (, , )/ , * (x,s,t) where  , * (x,s,t) is the average exposure, namely, the arithmetic average of  , (, , ) and  , ( + 1, , +1).We estimate 17 sets of mortality rates, one per year under observation, and convert them into conditional probabilities of dying using standard actuarial procedures (assuming uniformly distributed deaths, cohort homogeneity, etc…).These conditional probabilities are then used to build (left censored at age 50+k) life tables for each year k.Finally, we combine these life tables using weights that for each group [50+k,51+k) in the year 2003+k is equal to the fractional contribution represented by the population of the cohort that attained age 50+k in the year 2003+k.The result is a single sequence of (weighted) conditional probabilities that can then be chained together to construct a single life table representing the mortality experience after age 50 for the entire period for each cell of the place of birth x place of residence matrix.

ii. Poisson model: option to identify cohort or period effects
We model deaths counts for each age interval in each period,  , (, , ), as a Poisson random variable with offset  , ′ (x,s,t).The includes dummies for age or, alternatively, a function of age that reproduces the curvature of the mortality rates with age (a Gompertz, a Weibull, alternative).The model may/may not include dummies for the period to which the counts refer to or the cohort (defined at the outset of observation, in 2003) that contributes to the death counts and exposure (offset).Once the model parameters are estimated one can compute predicted values for the rates and, from them, life tables from age 50 for each year under observation.Finally, one can pool these using weights proportionally to the contribution to the exposure counts for year under observation.

iii. Gompertz model
Each cohort aged 50 ≤  ≤ 68 at the outset contributes to mortality rates mx+k , k=0, 1,…16.Cohorts aged  ≥ 69 at the outset contribute to mortality rates my, my+1,…m85+ There will be one observation for mortality rate m50, two for mortality rate m51, three for mortality rate m52 and so on up until m69 for which we will have 16 observations.By the same token, there will be two observations for mortality rate m70, three for mortality rate m71 etc…until 16 mortality rates for m85+.We can then estimate the following Gompertz model : where  is the year to which the rate corresponds to (or a dummy for year or some other metric for year).We then predict mx(t) using the mean value of t for all x from 50 to 82, transform the predicted rates into probabilities, and build a single life

Figure S2 :
Figure S2: MRRs from the quasi-Poisson model defined by eq.S10 by region of birth

Table S1 :
Geographic units, life expectancy, GDP per capita (in euros) and table.where (, min ( 82,  + 16)) is the observed probability of surviving from x to the maximum age we can observe for a cohort and (,  + min (82,  + 16))  is the same probability in a standard mortality pattern.Z is a vector of covariates that may include period or cohort identification.Once the parameters of the model are estimated, a unique life table can be computed.Note that methods (iii) and (iv) can generate estimates of period OR cohort effects that could be used explicitly if so desired.The approach we use in this paper ignores period/cohort changes and, as is done in methods (i) and (ii), we compute a pooled life table in terms of mortality by place of residence but is the worst performer for mortality by place of birth.This type or correspondences are likely due to health selection effects (healthy immigrant entering Madrid and healthy outmigrants exiting Canarias).