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PAM 305  Introduction to Multivariate Analysis
Fall 2006
Homework 5
Due date: November 17th
In this homework you will use the data set MROZ.dta to analyze the labor
force participation decision of married women in 1975. The relevant variables
for the analysis are:
•
inlf
: Binary variable that takes the value 1 if the woman participated
in the labor force, 0 otherwise.
•
nwifeinc
: Other sources of income, including husband’s earnings (in
thousands of dollars).
•
exper
: Labor experience
•
expersq
: The square of experience
•
educ
: Education
•
age
•
kidslt
6: Number of children less than 6 years old
•
kidsge
6: Number of children between 6 and 18 years old
Question 1
Estimate by OLS the following linear probability model (LPM)(ignoring that
the homoskedasticity assumption is violated)
1
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View Full Documentinlf
=
β
o
+
β
1
nwifeinc
+
β
2
educ
+
β
3
exper
+
β
4
expersq
+
β
5
age
+
β
6
kidslt
6+
β
7
kidsge
6+
u
and use the estimates obtained to answer the following questions:
a. Which variables are signiﬁcant at the 5% level?
All except kidsge6, see the STATA log ﬁle. The variable kidsge6 is the
only one with a value of the tstatistic smaller than 1.96, which is the
critical value for a t test with 745 degrees of freedom with 2sided signif
icance level of 0.05 (see the STATA log ﬁle on how to obtain this critical
value from STATA. In the exam you will need your tables.
b. Do the variables that are statistically signiﬁcant have the eﬀects we would
expect based on economic theory or common sense? Explain.
Yes they do. You just had to explain, based on your theory and common
sense, why you would expect the eﬀects you estimated. Here I am going
to give you a longer answer that explicitly proposes an economic model
to think about this issue and shows how the parameters you estimated
relate to the proposed model. This is to show you how economic theory
helps us to build a sensible model, which we can take to the data and
estimate its parameters.
A married female is assumed to value consumption and leisure. Her
preferences are represented by the utility function
u
(
c,l
) =
α
o
c
+
α
1
l
+
α
2
lc
where
α
1
is assumed to depend on kidsge6, kidslt6 and age. That is,
α
1
(
kidsge
6
,kidslt
6
,age
) =
α
1
o
+
α
11
kidsge
6 +
α
12
kidslt
6 +
α
13
age
This takes into account that the marginal utility of leisure for a female
is aﬀected by the ages of her kids, and by her own age.
A married female chooses the amount of consumption (c) and leisure (l)
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 Fall '06
 LUCARELLI

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