Use the data in SMOKE.RAW for this exercise.
(i) The variable cigs is the number of cigarettes smoked per day. How many people in the sample do not smoke at all? What fraction of people claim to smoke 20 cigarettes a day? Why do you think there is a pileup of people at 20 cigarettes?
(ii) Given your answers to part (i), does cigs seem a good candidate for having a conditional Poisson distribution?
(iii) Estimate a Poisson regression model for cigs, including log(cigpric), log(income), white, educ, age, and age2 as explanatory variables. What are the estimated price and income elasticities?
(iv) Using the maximum likelihood standard errors, are the price and income variables statistically significant at the 5% level?
(v) Obtain the estimate of σ2 described after equation (17.35). What is ? How should you adjust the standard errors from part (iv)?
(vi) Using the adjusted standard errors from part (v), are the price and income elasticities now statistically different from zero? Explain.
(vii) Are the education and age variables significant using the more robust standard errors? How do you interpret the coefficient on educ?
(viii) Obtain the fitted values, t from the Poisson regression model. Find the minimum and maximum values and discuss how well the exponential model predicts heavy cigarette smoking.
(ix) Using the fitted values from part (viii), obtain the squared correlation coefficient between y. and yt.
(x) Estimate a linear model for cigs by OLS, using the explanatory variables (and same functional forms) as in part (iii). Does the linear model or exponential model provide a better fit? Is either squared very large?