Question

The data set data_ksubs.csv contains information on net financial wealth (nettf a), age of the survey respondent (age), annual family income (inc), family size (fsize), and participation in certain pension plans for people in the United States. The wealth and income variables are both recorded in thousands of dollars. In particular, the variable e401k is equal to 1 is the person is eligible for 401k, a retirement savings plan sponsored by the employer, and 0 otherwise.

a. Create a scatter plot of nettf a against inc. Can you observe any visible correlation between nettf a and inc? Do you think that a regression of nettf a on inc may feature heteroskedasticity? Explain.

Answer 1

Suppose that the Least-Squares assumptions are satisfied and estimate the fol-

lowing regression model:

nettf ai = β0 + β1male + β2e401k + β3inci + β4agei + ui

, i = 1, . . . , n. (2)

Report the estimated values of the regression coefficients and discuss their signs

(if it is or it is not as expected), their (heteroskedasticity robust) standard errors,

and significance level. Also, report the R2

, the adjusted R2

(R ̄2

) and the value

of the F-statistics for the null hypothesis that all the slope coefficients are equal

to 0. Do you reject the null hypothesis?

(c) We now introduce some additional variables and some nonlinearities in the

model. We add the square of age (agesq), the square of income (incsq), a

dummy for the individual being married (marr), and the household size (fsize).

We thus estimate the following model.

nettf ai =β0 + β1male + β2e401k + β3inci + β4agei (3)

+β5incsqi + β6agesqi + β7marri + β8fsizei + ui

, i = 1, . . . , n.

Obtain the OLS estimators of the regression coefficients and their (heteroskedas-

ticity robust) standard errors. Compare the new estimators with those obtained

in (b). How have they changed? Compare the adjusted R2

in this model and in

model (2). Obtain the F-statistic to test for the null hypothesis that β5, β6, β7

and β8 are jointly equal to 0, and for the null that β5 and β6 are jointly equal

to zero.