ECON 7310: Elements of Econometrics
Tutorial 9: Instrumental Variables Regression
Fu Ouyang
University of Queensland
July 28, 2019
1. SW E12.1
How does fertility affect labor supply? That is, how much does a woman’
...
ECON 7310: Elements of Econometrics
Tutorial 9: Instrumental Variables Regression
Fu Ouyang
University of Queensland
July 28, 2019
1. SW E12.1
How does fertility affect labor supply? That is, how much does a woman’s labor supply fall when
she has an additional child? In this exercise you will estimate this effect using data for married
women from the 1980 U.S. Census.1 The data are in the file Fertility.dta and described in
Fertility Description.pdf. The data set contains information on married women aged 21–
35 with two or more children.
(a) Regress weeksm1 on the indicator variable morekids using OLS. On average, do women with
more than two children work less than women with two children? How much less?
(b) Explain why the OLS regression estimated in (a) is inappropriate for estimating the causal
effect of fertility (morekids) on labor supply (weeksm1).
(c) The data set contains the variable samesex, which is equal to 1 if the first two children are of
the same sex (boy–boy or girl–girl) and equal to 0 otherwise. Are couples whose first two children are of the same sex more likely to have a third child? Is the effect large? Is it statistically
significant?
(d) Explain why samesex is a valid instrument for the instrumental variable (IV) regression of
weeksm1 on morekids.
(e) Is samesex a weak instrument?
(f) Estimate the regression of weeksm1 on morekids, using samesex as an instrument. How
large is the fertility effect on labor supply?
(g) Do the results change when you include the variables agem1, black, hispan, and othrace
in the labor supply regression (treating these variable as exogenous)? Explain why or why not.
Solution: The answers below will reference regression results summarized in Tables 1 and 2.
(a) The coefficient is -5.39, which indicates that women with more than 2 children work 5.39
fewer weeks per year than women with 2 or fewer children.
(b) Both fertility and weeks worked are choice variables. A woman with a positive labor supply regression error (a woman who works more than average) may also be a woman who
is less likely to have an additional child. This would imply that morekids is positively
correlated with the error, so that the OLS estimator of βmorekids is positively biased.
(c) The linear regression of morekids on samesex (a linear probability model) yields
morekids d = 0:346
(0:001)
+ 0:068
(0:002)
× samesex
so that couples with samesex = 1 are 6.8% more likely to have an additional child that
couples with samesex = 0. The effect is highly significant (t-statistic = 35.2)
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