Homework Assignment #4

1. Use the data in WAGE2.RAW for this exercise.
   1. Estimate the model log (wage) = B ₀ + B ₁ educ + B ₂ exper + B ₃ tenure + B ₄ married + B ₅ black + B ₆ south + B ₇ urban + u and report the results in the usual form. Holding other factors fixed, what is the approximate difference in monthly salary between blacks and nonblacks? Is this difference statistically significant?
   2. Add the variables exper ² and tenure ² to the equation and show that they are jointly insignificant at even the 20% level.
   3. Extend the original model to allow the return to education to depend on race and test whether the return to education does depend on race.
   4. Again, start with the original model, but now allow wages to differ across four groups of people: married and black, married and non-black, single and black, and single and non-black. What is the estimated wage differential between married blacks and married non-blacks?
2. (Computer exercise). There has been much interest in whether the presence of 401(k) pension plans, available to many U.S. workers, increase net savings. The data set 401KSUBS contains information on net financial assets ( nettfa) , family income ( inc ), age of the worker (age) , a dummy for eligibility in a 401(k) plan ( e401k) , and several other variables.
   1. Estimate a multiple linear regression model for nettfa that includes family income, age, and e401k as explanatory variables. The family income and age variables should appear as quadratics (i.e., include both age and age ² ). What is the estimated dollar effect of 401(k) eligibility on net financial asset?
   2. Define 5 family size dummy variables using fsize : fsize1, fsize2, fsize3, fsize4, and fsize5 . The variable fsize5 is a dummy that takes on the value of 1 if a family has 5 or more members and 0 otherwise. Fsize4 takes on the value of 1 if a family has 4 members and 0 otherwise. Likewise for the other 3 family size dummies. Include the family size dummies in the model estimated from part (i); be sure to choose a reference group. Are the family dummies jointly significant at the 5% level?
      
      
   3. (Bonus question) Consider the regression model from part (i). Suppose I am interested to know whether the effect s of income, age, and eligibility depend on having a big family (i.e., fsize5=1 ). Do a Chow test for the model from (i) between the two groups, fsize5=0 and fsize5=1 , but allowing for intercept differences for fsize5 . In other words, your null hypothesis should be that the coefficients on the interaction terms between fsize5 and the 5 independent variables from part (i) are jointly zero.
3. Suppose you collect data from a survey on wages, education, experience and gender. In addition, you ask for information about marijuana usage. The original question is: "On how many separate occasions last month did you smoke marijuana?"
   1. Write an equation that would allow you to estimate the effects of marijuana usage on wage, while controlling for other factors. You should be able to make statements such as, "Smoking marijuana five more times per month is estimated to change wage by x%"
   2. Write a model that would allow you to test whether drug usage has different effects on wages for men and women. How would you test that there are no differences in the effects of drug usage for men and women?
   3. Suppose you think it is better to measure marijuana usage by putting people into one of four categories: nonuser, light user (1 to 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 effects of marijuana usage on wage.
   4. Using the model in part iii. Explain in detail how to test the null hypothesis that marijuana usage has no effect on wage. Be very specific and include a careful listing of degrees of freedom.
   5. What are some potential problems with drawing causal inference using the survey data that you collected?

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