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Suppose that you collect data from a survey on wages, education, experience and sex. In addition, you ask fo rinformation about marijuana usage. The exact question on your survey is “On how many separate occasions last month did you smoke marijuana?”
a. Write an equation that would allow you to estimate the relationship between marijuana usage and the wage, while controlling for other factors. You should be able to make statements such as “Smoking marijuana five more times per month changes the expected wage by x%.”
b. Write a model that would allow you to test whether drug usage has a different relationship with wages for men and women. How would you test the null hypothesis of no difference in the relationship between drug use and wages for men and women,conditional on the other variables?
c. Suppose you think it is better to measure marijuana usage by putting people into one of four categories: non-user, light user (1to 5 times per month), moderate user (6 to 10 times per month) and heavy user (more than 10 times per month). Now, write a model that allows you to estimate the relationship between marijuana usage,coded in this way, and the wage, conditional on the other variables.
d. Using the model in problem 2c, explain in detail how to test the null hypothesis that marijuana usage is unrelated to wages,conditional on the other variables. Be very specific and include a careful description of degrees of freedom.
e. Do you think that the estimates in 2a and 2c represent causal effects of marijuana usage on wages? Explain why or why not in three sentences or less.
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