Homework 2 – due 3/7 before class
1. (Question 5.3 in the textbook) Consider the following model to estimate the effects of several
variables, including cigarette smoking, on the weight of newborns:
log(bwght) = β1 + β2male+ +β3parity + β4lfaminc+ β5packs+ u (1)
where male is the binary indicator equal to one if the child is male. parity is the birth order
of this child, lfaminc is the log of family income, and packs is the average number of packs of
cigarettes smoked per day during pregnancy.
a. Why might you expect packs to be correlated with u?
b. Suppose that you have data on average cigarette price in each woman’s state of residence.
Discuss whether this information is likely to satisfy the properties of a good instrumental
variable for packs.
c. Use the data in bwght.dta on icollege to estimate (1). Do the estimation using both OLS and
2SLS. For 2SLS, use cigprice as an instrument for packs. Discuss any important differences
in the OLS and 2SLS estimates.
d. Write out the reduced form for packs and estimate this reduced form (write out the formula
first and then use your formula to do calculations in R). What do you conclude about iden-
tification of equation (1) using cigprice as an instrument for packs? What bearing does this
conclusion have on your answer from part c?
Note: you don’t need to turn in your R code. Simply use R as a calculator to help you calcuate
the matrix product. For those of you who are not familier with R, you can follow closely with the
example code : OLS cps.R (for OLS estimation) and IV mroz.R (for 2SLS estimation). All of the
data files and R codes are posted on icollege.
Solution:
a. u might include omitted variables such as health status, whether she drinks alcohol, etc.
b. To be a good instrumental variable, Cigprice should satisfy the following contitions: 1. It is
uncorrelated with the error term. 2. In the reduced form: packs = δ1 + δ2male+ δ3parity +
δ4lfaminc+ θCigprice+ v should satisfy θ 6= 0. The influence...
