Question 1
Type the following command in Stata to load the SMOKE dataset:
a) You are interested in examining whether living in a state with restaurant smoking bans is associated with reduced smoking. Using a regression, test the hypothesis that mean cigarettes smoked per day (cigs) is the same for those living in states with (restaurn=1) and without (restaurn=0) restaurant smoking restrictions. What do you conclude?
b) You worry that those living in states with restaurant smoking restrictions may have higher incomes - since rich states tend to adopt such policies more quickly than poor states. Repeat the test you conducted in part (a), but now test that the means are equalconditional on the respondent's annual income (income). What do you conclude?
c) Suppose individuals with high income can afford to eat out more often, and are thus impacted to a greater extent by the restaurant smoking restrictions. If this is the case, then the effect of income on cigarettes smoked may differ in states with and without smoking restrictions. Modify your regression from part (b) to allow for this possibility. Run this new regression in Stata and interpret each coefficient.
d) Using the model you set up in part (c), formally test whether the effect of income on number of cigarettes smoked differs in states with and without smoking restrictions. What do you conclude?
e) Using the model you set up in part (c), test whether the relationship between income and smoking differs in states with and without restaurant smoking restrictions (in lecture we called this a Chow Test). What do you conclude?
f) You decide to add education to the regression. Rather than controlling linearly for education (educ), however, you decide to define dummy variables for less than high school (educ<12), high school graduates (12≤educ<16), and college grads (educ>=16). Why might it be unwise to add all three of these dummy variables to your regression model?
g) Define the high school & college graduate dummies in Stata and add them to your regression model. (For simplicity, add them to the model you ran in part (b), before you allowed the impact of income on cigarettes smoked to vary in states with and without smoking restrictions.) Interpret your estimate of the intercept parameter.
h) Run the model from part (g) again, but this time use a log-linear specification, with the dependent variable being the natural log of the number of cigarettes smoked per day. Interpret your estimate of the coefficient on the restaurndummy.
i) The regression you ran in part (h) had only 310 observations, while the model you ran in part (g) had 807 observations. Why is this? Does this have any impact on your interpretation of the coefficient on the restaurndummy in part (h)?
Question 2
Note that math4 is the percentage of students performing at a satisfactory level on a 4th grade math exam, lunch is the percentage of students eligible for free or reduced lunch, enroll is school enrollment, and expppis expenditures per pupil:
a) Estimate the model:
math4 = _0 + _1lunch + _2 ln(enroll) + _3 ln(exppp) + u
by OLS and obtain the usual standard errors and robust standard errors. How do they compare?
b) Implement a Breusch-Pagan Test to test whether the error in this regression model is homoskedastic. What is the value of the F-statistic? What do you conclude?
c) Use the residuals (ûi) from the model you estimated in part (a) and run a regression ofln(ûi2) on lunch, ln(enroll), and ln(exppp). Call the predicted value from this regressiongi, and let hi=exp(gi). Use these hito obtain WLS estimates of the model in part (a). Are there big differences between these estimates and the OLS estimates? Which estimates are more precise?