Relationship between body mass index (BMI), health and family size


The relationship between the body mass index (BMI), household size and wealth is a neglected area in economics, and a contributing factor in nineteenth-century household fertility decisions was the net benefit that households received from larger families.

During the nineteenth century, a household’s net benefit of having a child was the expected agricultural productivity increase associated with having a larger internal labour force, less the present value of expected future outlays plus parental time used in child rearing.

Larger household sizes also reduced the uncertainty associated with short-term wage-labour. Household fertility decisions and child rearing were, in turn, related to household size and childhood health.

Therefore, during the US economic development, the net benefit agricultural households received from larger family sizes were a larger internal labour force and reduced labour market uncertainty, which were related to family member health and BMIs (Carson, 2011).

A population’s average BMI reflects the current net difference between calories consumed, disease climate and work environment.2 As the ratio of weight to height, BMIs are the ratio of net current to cumulative nutrition; therefore, BMI variation depends on when privation occurs. For example, individuals who receive inadequate nutrition during their youth reach shorter terminal statures, and their adult weights are distributed over smaller physical dimensions, therefore, higher BMIs. Alternatively, individuals who receive adequate nutrition are taller, and their adult weights are distributed over larger physical dimensions with lower BMIs. BMIs are also linked to modern health outcomes (Koch, 2011Must & Strauss, 1999Waaler, 1984); however, across subpopulations, the strength of this association remains debatable (Flegal et al., 2009, p. 240; Henderson, 2005, p. 340). For BMIs less than 19, there is an inverse relationship between BMI and mortality risk and a positive relationship for BMIs over 27 (Fogel, 1994Koch, 2011Waaler, 1984). Costa (1993) applies Waaler’s results to a historical population and finds that the modern height, weight and mortality relationship applies historically, and Jee et al. (2006, pp. 780, 784–785) find that the relationship applies across racial groups. Costa (2004, pp. 8–10) demonstrated that there were considerable differences between nineteenth-century Black and White BMIs, and Blacks had greater BMIs than Whites (Flegal et al., 2009Flegal et al., 2010Walker & Kawachi, 2011, p. 259). As the ratio of weight to height, BMI represents the lagged or mismatched effect of the timing of privation and may not be as good a measure for current net nutrition as weight after controlling for height (Carson, 2015b, 2017). Nonetheless, BMI has been shown to be a robust measure for mortality risk (Koch, 2011Waaler, 1984). Subsequently, BMI is an established measure for mortality risk, whereas weight after controlling for height is an alternative measure for current net nutrition.

It is against this backdrop and using robust statistics that this study considers three paths of inquiry into the relationship between nineteenth-century BMIs, family size and wealth.

First, how were BMIs related to family size, and were additional family members positively related to BMIs of existing household members?

Across the distribution, BMIs increased with family size, and larger families had greater BMI values. Second, reflecting how resources are related between generations, what was the relationship between BMI and height?

Given wealth and urbanisation, there was an inverse relationship between BMI and height during the US economic development. Third, how did BMIs vary across their distribution with respect to average wealth and inequality? Consistent with other studies, BMI values were higher in regions that had greater average wealth and lower inequality.

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