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"The impact of household characteristics on child survival and height, conditional on age, is examined using household survey data from Brazil. Parental education is found to have a very strong positive effect on both outcomes and this is robust to the inclusion of household income and also parental heights, which partly proxy for unobserved family background characteristics. We find that income effects are significant and positive for child survival but insignificant for for child height although the latter depends on identification assumptions. Parental height has a large positive impact on child height and on survival rates even after controlling for all other observable characteristics."
Thomas et al. (Mon,) studied this question.