Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 22

Use the subset of 401KSUBS.RAW with fsize = 1; this restricts the analysis to single person households; see also Computer Exercise C4.8.
(i) What is the youngest age of people in this sample How many people are at that age
(ii) In the model
nettfa = 0 + 1 inc + 2 age + 3 age 2 + u, what is the literal interpretation of 2 By itself, is it of much interest
(iii) Estimate the model from part (ii) and report the results in standard form. Are you concerned that the coefficient on age is negative Explain.
(iv) Because the youngest people in the sample are 25, it makes sense to think that, for a given level of income, the lowest average amount of net total financial assets is at age 25. Recall that the partial effect of age on nettfa is 2 + 2 3 age, so the partial effect at age 25 is 2 + 2 3 (25) = 2 + 50 3 ; call this 2. Find and obtain the
two-sided p-value for testing H 0 : 2 = 0. You should conclude that is small and very statistically insignificant.
v) Because the evidence against H 0 : 2 = 0 is very weak, set it to zero and estimate the model nettfa = 0 + 1 inc + 3 (age - 25) 2 + u. In terms of goodness-of-fit, does this model fit better than that in part (ii)
(vi) For the estimated equation in part (v), set inc = 30 (roughly, the average value) and graph the relationship between nettfa and age, but only for age 25. Describe what you see.
(vii) Check to see whether including a quadratic in inc is necessary.