Suppose we wish to estimate a model of household expenditures on alcohol ( \(A L C\), in dollars per month) as a function of household income (INCOME, \(\$ 100\) 's per month), and some other demographic variables.

a. Let RELIGIOUS \(=0,1,2,3\), or 4 if the household considers itself not religious, a little religious, moderately religious, very religious, or extremely religious, respectively. Is RELIGIOUS a quantitative or qualitative variable? Explain your choice.

b. Consider the model

What is the expected household expenditure on alcohol for a household that considers itself not religious? What is the expected household expenditure for a household that considers itself a little religious? What is the expected household expenditure for a household that considers itself moderately religious?

c. If we test the hypothesis \(\beta_{3}=0\) in model (b), what behavioral assumption are we testing? What is the expected household expenditure on alcohol if the hypothesis is true?

d. Let \(L I T T L E=1\) if the household considers itself a little religious, and zero otherwise. Similarly define the indicator variables MODERATELY, VERY, and EXTREMELY. Consider the model

What is the expected household expenditure for a household that considers itself not religious? What is the expected household expenditure for a household that considers itself a little religious? What is the expected household expenditure for a household that considers itself moderately religious? Very religious? Extremely religious?

e. If we impose the restrictions \(\gamma_{3}=2 \gamma_{2}, \gamma_{4}=3 \gamma_{2}, \gamma_{5}=4 \gamma_{2}\) on the model in part (d), how does the restricted model compare to the model in (b)?

Transcribed Image Text:

ALC = B + BINCOME + B RELIGIOUS + e