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The perfect instrument: Your DNA

Do fat people earn lower wages?  Finding a correlation between weight and wages does not mean that a causal relationship exists.  For instance, assume that body type has no effect on wage. If more motivated people have higher wages and also exercise more, we may find a negative relationship between body weight and wages.  On the other hand, people with high wages may have more money to pay for food and thus may be larger. Literally, they may be “fat cat.”

To control for these spurious correlations, we need a good instrument.  The instrument would be correlated with body type but uncorrelated with unobserved factors which effect wages.  Norton and Han (2008) use an innovative instrument: individual genotypes which help determine body weight.  The authors also use siblings lagged BMI as an instrument as well.  The data set used is Add Health, which focuses on adolescent health.

Both genetic and environmental factors determine weight.  Thus we would expect the genotype to be highly correlated with the phenotype, weight.  It must be the case that the genotype used as instruments must only effect weight.  If the same genes that affected weight also influenced intelligence, then genotype would be a poor instrument.  

Using these novel instruments, the authors conclude that “an increase in BMI as a late teen has no statistically significant effect on either employment or wages for a person in their mid-twenties.”