ECON 7310: Elements of Econometrics
Tutorial 9: Instrumental Variables Regression
Fu Ouyang
University of Queensland
July 28, 2019
1. SW E12.1
How
... [Show More] 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).
1These data were provided by Professor William Evans of the University of Maryland and were used in his paper with Joshua
Angrist, “Children and Their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size,” American Economic
Review, 1998, 88(3): 450?477.
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(d) samesex is random and is unrelated to any of the other variables in the model including
the error term in the labor supply equation. Thus, the instrument is exogenous. From (c),
the first stage F-statistic is large (F = 1238.2 > 10) so the instrument is relevant. Together,
these imply that samesex is a valid instrument.
(e) No, see the answer to (d).
(f) See column (2) of Table 1. The estimated value of βmorekids = −6.314.
(g) See column (3) of Table 1. The results do not change in an important way. The reason is
that samesex is unrelated to agem1, black, hispan, othrace, so that there is no omitted
variable bias in IV regression in (f).
2. SW E12.2
Does viewing a violent movie lead to violent behavior? If so, the incidence of violent crimes,
such as assaults, should rise following the release of a violent movie that attracts many viewers. Alternatively, movie viewing may substitute for other activities (such as alcohol consumption) that lead to violent behavior, so that assaults should fall when more viewers are attracted to
the cinema. Find the data file Movies.dta, which contains data on the number of assaults and
movie attendance for 516 weekends from 1995 through 2004.2 A detailed description is given in
Movies Description.pdf. The dataset includes weekend U.S. attendance for strongly violent
movies (such as Hannibal), mildly violent movies (such as Spider-Man), and nonviolent movies
(such as Finding Nemo). The dataset also includes a count of the number of assaults for the same
weekend in a subset of counties in the United States. Finally, the dataset includes indicators for [Show Less]