Question 1. Consider the multiple regression model:
Suppose that assumptions MLR.1-MLR4 hold, but not assumption MLR.5
(a) Are the standard t and F-statistics valid if the sample is suf?ciently large? If not, what would you do about it?
(b) Suppose that the sample is very small. What is the implication for the heteroscedastic robust standard errors? Suppose that someone said that you instead should use Feasable Generalized Least Squares to correct for heteroscedasticity in small samples.
What would be your response?
Question 2:
Data description:
Criminal and labor market histories of a sample of Californian men born in 1960 or 1961 with at least one arrest prior to 1986. 2,725 observations.
Variable description:
1. narr86 # times arrested, 1986
2. nfarr86 # felony arrests, 1986
3. nparr86 # property crme arr., 1986
4. pcnv proportion of prior convictions
5. avgsen avg sentence length, months
6. tottime time in prison since 18 (months)
7. ptime86 months in prison during 1986
8. qemp86 # quarters employed, 1986
9. inc86 legal income, 1986, $100s
10. durat recent unemp duration
11. black =1 if black
12. hispan =1 if Hispanic
13. born60 =1 if born in 1960
14. pcnvsq pcnvˆ2
15. pt86sq ptime86ˆ2
16. inc86sq inc86ˆ2
(a) Estimate a linear probability model that explains whether a man was arrested in 1986 by his prior criminal and employment record (pcnv, avgsen, tottime, ptime86, qemp86).
Use robust standard errors. Why do you need to correct for heteroscedasticity? Justify your answer.
(b) What is the interpretation of the intercept?
(c) Interpret the effect of time locked up in 1986 (ptime86) on the probability of arrest. Is this a big effect?
(d) Set all explanatory variables to zero, except for ptime86, and compute the predicted probability of arrest in 1986 for a man who was locked up in all 12 months in 1986. Does this prediction make sense?
(e) Test whether avgsen and tottime are jointly statistically signi?cant at the 5% level. Would your test be valid if you had not used robust standard errors in (a)?
(f) Calculate the predicted probabilities and verify that all the ?tted values are between 0 and 1. What is the smallest value you observe? And the largest?