Use the data in 401KSUBS.RAW for this exercise.
(i) Compute the average, standard deviation, minimum, and maximum values of nettfa in the sample.
(ii) Test the hypothesis that average nettfa does not differ by 401(k) eligibility status; use a two-sided alternative. What is the dollar amount of the estimated difference?
(iii) From part (ii) of Computer Exercise C7.9, it is clear that e401k is not exogenous in a simple regression model; at a minimum, it changes by income and age. Estimate a multiple linear regression model for nettfa that includes income, age, and e401k as explanatory variables. The income and age variables should appear as quadratics. Now, what is the estimated dollar effect of 401 (k) eligibility?
(iv) To the model estimated in part (iii), add the interactions e40Ik ( (age - 41) and e401k ( (age 1 - 41)2. The average age in the sample is about 41, so that in the new model, the coefficient on e401k is the estimated effect of 401(k) eligibility at the average age. Which interaction term is significant?
(v) Comparing the estimates from parts (iii) and (iv), do the estimated effects of 401 (k) eligibility at age 41 differ much? Explain.
(vi) Now, drop the interaction terms from the model, but define five family size dummy variables: fsize1, fsizel2, fsize3, fsize4, and fsize5. The variable fsize5 is unity for families with five or more members. Include the family size dummies in the model estimated from part (iii); be sure to choose a base group. Are the family dummies significant at the 1% level?
(vii) Now, do a Chow test for the model
nettfa = (0 + (1jnc + (2 inc2 + (3 age + (4 age2 + (5e401k + u
across the five family size categories, allowing for intercept differences. The restricted sum of squared residuals, SSRr, is obtained from part (vi) because that regression assumes all slopes are the same. The unrestricted sum of squared residuals is SSRur = SSR1, + SSR2 + ... + SSR5, where SSR, is the sum of squared residuals for the equation estimated using only family size f. You should convince yourself that there are 30 parameters in the unrestricted model (5 intercepts plus 25 slopes) and 10 parameters in the restricted model (5 intercepts plus 5 slopes). Therefore, the number of restrictions being tested is q = 20, and the df for the unrestricted model is 9,275 - 30 = 9,245?