Question

4. Suppose you are trying to perform a comparison of the relationship between getting a college degree and your wage at age 45. You perform a regression which includes many demographic and personal variables, plus having a college degree. However, one variable you do not have is intelligence.

(a) What are the likely consequences of leaving out this variable on the returns to a college degree? Explain, relating your answer to the idea of selection bias.

(b) Suppose you have two variables you could include in the models: the individual’s high school grades, and the size of the individual’s bedroom. Which variable would be most likely to serve as a useful control? Explain.

(c) Suppose you could include both, rather than just one. Would you? Explain.

Answer 1

(a) An individual's college degree is largely based on his intelligence. If the variable intelligence is left out, then the returns to his college degree will be hugely affected. This would involve selection bias. Selection bias is the bias introduced by the selection of individuals, groups or data for analysis in such a way that proper randomization is not achieved, thereby ensuring that the sample obtained is not representative of the population intended to be analyzed.

(b) An individual's bedroom size may depend on his income. But there are exceptions where people with satisfactory wage, decides to save the money for future and may not have a large sized bedroom. There are even people who, inspite of being rich, prefers to live in their ancestral house.

On the other hand, an individual's high school grades is in direct relationship with his college degree. Below a certain marks, the college degree may be not even applicable. So this variable is of huge importance.for the variable college degree.

Hence the variable measuring individual's high school grades is most likely to serve as a more useful control than that measuring the size of the individual's bedroom.

(c) If there is a chance to include both, both of them must be included. As size of the bedroom is moderately related to his wage and inclusion of any variable having any connection with the mentioned variables helps in the betterment and accuracy of the regression analysis.