Question

Econetrics:
Suppose you are interested in estimating the relationship between wages and obesity. To do this you consider estimating the following regression model.

W=β1+β2Obesity+e ei~N(0,σ^2)

where W is a measure of an individual’s wage and Obesity is a measure of how obese the individual is.


a. What do economists mean when they talk about the causal effect of obesity on wages?
b. Explain why the OLS estimator of the above equation is unlikely to provide a consistent estimator of the casual effect of obesity on wages. What effect will the OLS estimator estimate?
c. The hormone FGF21 regulates how much sugar we eat. In a recent study in Denmark, scientists found that patients with a particular defective variant of the hormone FGF21 were 20% more likely to be higher consumers of sugar. How might an econometrician use this medical information to estimate the causal effect of obesity on wages. Be careful to outline both the advantages and potential pitfalls associated with your suggested approach.

**Typo Econometrics for heading

Answer 1

a.Economists mean that the amount of obesity in a person directly affects the wage that he/she is earning.

b. The above equation is unlikely to provide a consistent estimator of the causal effect of obesity on wages because of omitted variable bias. The above equation is a single variable regression, while wage may be affected due to other variables as well, which might be correlated with obesity.
The OLS estimator will estimate that the amount by which wages will increase if obesity in an individual increases by 1 unit.

c. The study shows that patients with defective variant of the FGF21 hormone are 20% more likely to be consumers of sugar,
Also, more consumption of sugar leads to obesity. Therefore, both the effects are correlated (and hence leaving out the defective hormone variable would lead to omitted variable bias).

We can include this information in our regression model using a dummy variable.

W = ₁ + ₂XObesity + ₃Hormone + e

where 'Hormone' is the dummy variable which takes the value 1 if the hormone is defective
and takes the value 0 if the hormone is not defective.

The advantage of this method is that we can overcome the omitted variable bias and achieve a consistent estimator, but it can also lead to a problem of multicollinearity, where the Hormone and Obesity variables can be correlated with each other.