Consider household expenditures per person on apparel. Use the data file cex 5 for this exercise.

a. What percentage of the households spent nothing on apparel in the previous quarter?

b. Estimate a linear regression with \(A P P A R\) as dependent variable and use as explanatory variables INCOME, SMSA (Standard Metropolitan Statistical Area \(=1\) if household lives in an urban area, and \(=0\) otherwise), ADVANCED, COLLEGE, and OLDER ( \(=1\) if someone in the household is 65 years of age or older). Discuss the signs and significance of the estimated coefficients. Interpret the coefficient of INCOME. Interpret the coefficient of ADVANCED.

c. Repeat the estimation in (b) using only observations for which APPAR \(>0\). What are your answers to the questions in (b) now?

d. Create the variable \(S H O P=1\) if \(A P P A R>0\), and \(S H O P=0\) otherwise. Estimate a probit model with dependent variable \(S H O P\) as a function of the variables in (b). What factors significantly affect the decision to buy clothing?

e. Estimate a Tobit model with dependent variable APPAR. Compare the coefficient estimates signs and significance to those in b and (c). Calculate the marginal effect of income on the expected amount spent on APPAREL for a household living in an urban area, with income \(\$ 65,000\), containing someone with an advanced degree and no one 65 or older in the household. Repeat the calculation for a household with \(\$ 125,000\) income.