Homework 6 (4 Points), due at the beginning of class on October
28, 2014
Please using the sibs data to answer the following questions.
• Q1 (1 point) Please report multiple regression below estimated by OLS
wage = β0 + β1 educ + β2 exper + β3 married + β4 black + u (1).
Interpret β1 and β4 . Please discuss fully why β̂1 you just got might be a biased estimate
for the true causal effect of educ on wage. Can you write down a SEM model for wage
y1 and educ y2 ?
• Q2 (1 point) Consider the variable brthord, which is the birth order (it is one for a
first-born child, two for a second-born child, and so on). How to include brthord in
the SEM? What are the assumptions you need to make if you want to use brthord as
the instrumental variable for educ? How to check those assumptions?
• Q3 (1 point) Report the 2SLS estimator of β1 for the new multiple regression
wage = β0 + β1 educ + β2 exper + β3 married + β4 black + β5 sibs + u (2)
where sibs is the number of siblings. What is the consequence if we estimate (2) still
using brthord as the IV but without sibs? Finally, report the first-stage regression with
sibs, and show me how to verify whether brthord is a weak IV.
• Q4 (1 point). Now use both brthord and sibs as IVs for educ, and report the 2SLS
estimate of (1). Is β1 overidentified? Please report and interpret the Test for Overidentification (J Test).
1