Consider the following model that relates the percentage of a household's budget spent on alcohol, \(W A L C\), to total expenditure TOTEXP, age of the household head \(A G E\), and the number of children in the household \(N K\).

Some output from estimating this model using 1200 observations from London is provided in Table 5.7. The covariance matrix relates to the coefficients \(b_{3}, b_{4}\), and \(b_{5}\).

a. Find a point estimate and a \(95 \%\) interval estimate for the change in the mean budget percentage share for alcohol when a household has an extra child.

b. Find a point estimate and a \(95 \%\) interval estimate for the marginal effect of \(A G E\) on the mean budget percentage share for alcohol when (i) \(A G E=25\), (ii) \(A G E=50\), and (iii) \(A G E=75\).

c. Find a point estimate and a \(95 \%\) interval estimate for the age at which the mean budget percentage share for alcohol is at a minimum.

d. Summarize what you have discovered from the point and interval estimates in (a), (b), and (c).

e. Let \(\mathbf{X}\) represent all the observations on all the explanatory variables. If \((e \mid \mathbf{X})\) is normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation?

f. If \((e \mid \mathbf{X})\) is not normally distributed, which of the above interval estimates are valid in finite samples? Which ones rely on a large sample approximation?

Transcribed Image Text:

WALC=,+B In(TOTEXP) + B3NK+BAGE + BAGE + e