A necessary condition to identify the impact of pollution is that variation in infants’ pollution exposure is uncorrelated with other characteristics of the infant or the infant’s families that may affect infant health.
It would be a problem, for example, if first children were more likely to be low birth weight and mothers systematically moved to cleaner environments between the first and second births because their incomes increased.
In order to check that the variation in pollution is uncorrelated with mobility, we performed the following exercise.
We first estimated the actual “within family” variation in each pollutant.
We then estimated what the within family variation would have been if each mother had stayed in the location in which she was first observed.
The within family variances were virtually identical: the actual and simulated within standard deviations for ozone are 0.939 and 0.947, respectively,for CO are 0.301 and 0.271, respectively, and for PM10 are 0.410 and 0.407, respectively, for ozone.
This suggests that mothers do not appear to be systematically moving to cleaner or dirtier areas between births.