The question for empirical researchers is: how do we know? Higher wages and income clearly increase demand for nutrition, and so do higher education (endogeneity bias). And it is also possible that a third variable simultaneously affect nutrition and income (omitted variable bias). Schultz (2003) pointed out these issues.
But many studies have tried to overcome those problems, using experimental, quasi-experimental or instrumental variables. Behrman (1993), also Thomas and Frankenberg (2002) documented those studies. One of the most widely cited experimental study is The Work and Iron Status Evaluation by Thomas et al. (2006).
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