Description
Question 1: Application of estimators based on treatment ignorability
This exercise asks you to implement some of the techniques presented in Lectures 6-7. The
goal is to estimate the causal effect of maternal smoking during pregnancy on infant birth weight
using the treatment ignorability assumptions.
The data are taken from the National Natality
Detail Files, and the extract “SMOKING_EDS241.csv”’ is a random sample of all births in
Pennsylvania during 1989-1991. Each observation is a mother-infant pair.
The key variables
are:
The outcome and treatment variables are:
birthwgt=birth weight of infant in grams
tobacco=indicator for maternal smoking
The control variables are:
mage (mother’s age), meduc (mother’s education), mblack (=1 if mother black), alcohol (=1 if
consumed alcohol during pregnancy), first (=1 if first child), diabete (=1 if mother diabetic),
anemia (=1 if mother anemic)
(a) What is the unadjusted mean difference in birth weight of infants with smoking and nonsmoking mothers? Under what hypothesis does this correspond to the average treatment effect
of maternal smoking during pregnancy on infant birth weight? Provide some simple empirical
evidence for or against this hypothesis.
(b) Assume that maternal smoking is randomly assigned conditional on the observable
covariates listed above. Estimate the effect of maternal smoking on birth weight using a linear
regression. Report the estimated coefficient on tobacco and its standard error.
(c) Use the exact matching estimator to estimate the effect of maternal smoking on birth weight.
For simplicity, consider the following covariates in your matching estimator: create a 0-1
indicator for mother’s age (=1 if mage>=34), and a 0-1 indicator for mother’s education (1 if
meduc>=16), mother’s race (mblack), and alcohol consumption indicator (alcohol). These 4
covariates will create 2*2*2*2 = 16 cells. Report the estimated average treatment effect of
smoking on birthweight using the exact matching estimator and its linear regression analogue
(Lecture 6, slides 12-14).
(d) Estimate the propensity score for maternal smoking using a logit estimator and based on the
following specification: mother’s age, mother’s age squared, mother’s education, and indicators
for mother’s race, and alcohol consumption.
(e) Use the propensity score weighted regression (WLS) to estimate the effect of maternal
smoking on birth weight (Lecture 7, slide 12).
Note: This homework is a simple examination of these data. More research would be needed to
obtain a more definitive assessment of the causal effect of smoking on infant health outcomes.
Further, for this homework, you can ignore the adjustments to the standard errors that are
necessary to reflect the fact that the propensity score is estimated. Just use heteroskedasticity
robust standard errors in R. If you are interested, you can read Imbens and Wooldridge (2009)
and Imbens (2014) for discussions of various approaches and issues with standard error
estimations in models based on the propensity score.