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 \(K I D S=0,1,2, \ldots\) be the number children in the household. Is \(K I D S\) a qualitative or quantitative variable? Interpret the coefficient of KIDS in the model

What is the marginal impact of the second child? What is the marginal impact of the fourth child?

b. Let \(O N E K I D=1\) if there is one child, and zero otherwise. Let \(T W O K I D S=1\) if there are two children, and zero otherwise. Let \(M A N Y=1\) if there are three or more children, and zero otherwise. Consider the model

Compare the interpretation of this model to that in part (a). Is the impact of an additional child the same as in the model in (a)? What is the impact of the first child on expected household expenditure on alcohol? What is the impact of having a fourth child on the expected household expenditure on alcohol?

c. Is there a set of parameter restrictions, or constraints, that we can impose on equation (XR7.9.2) to make it equivalent to equation (XR7.9.1)?

Transcribed Image Text:

ALC B+BINCOME + SKIDS + e = (XR7.9.1)