Problem Set 2
Demog/Econ 175
Professor Ronald Lee
January 31th, 2012
DUE: February 15th, 2012 by 2:10 pm
**LATE ASSIGNMENTS WILL NOT BE ACCEPTED**
Please post your questions on the course’s Piazza site (search for Demog 175 on or send an email
with your question to 175gsi2012@gmail.com .
I
Demographic Concepts
In this exercise we will learn more about Iran, a country which has, in the past year, received
a great deal of attention in international news coverage. To learn more about Iran as well as
to familiarize yourself with sources of demographic data and facilitate a better understanding
of some of the concepts discussed in lecture, this question asks you to use the CIA World Fact
Book to locate some basic demographic information for Iran and to make a couple of key calculations.
(a) Please use the CIA World Fact Book : https://www.cia.gov/library/publications/the-worldfactbook/ to obtain the following information for Iran (2011 estimates). Note: The information is
located under the tab entitled “People” [1 point]
i. Population growth rate
1.248 percent
ii. Crude birth rate (per 1,000 individuals)
18.55/thousand
iii. Crude death rate (per 1,000 individuals)
5.94/thousand
iv. Net migration rate (per 1,000 individuals)
-0.13/thousand
v. Total fertility rate
1.88 children per woman
(b) Verify that the population growth rate can be recovered using only the crude death rate, the
crude birth rate and the net migration rate (please show your work). [2 points]
The population growth rate can be recovered by subtracting the net migration rate and the crude
death rate from the crude birth rate. Hence, the population growth rate = (18.55-5.94+(-0.13) =
12.48/thousand or 1.248 percent.
(c) Assuming that 49 percent of Iranian births are female babies, calculate the Gross Reproduction
Rate (GRR) for Iran. What does this number mean? [2 points]
The GRR is equal to the number of daughters per woman, not accounting for mortality (or, for
women who survive through childbearing). GRR = f f ab x TFR. Hence, GRR = 0.49 x 1.88 =
0.92
(d) Assume that 95.6 percent of women survive until the mean age at childbearing and continue
to assume that 49 percent of Iranian births are female. What is the (approximate) Net Reproduction
Ratio (NRR) for Iran? [2 points]
The NRR is the number of daughters per woman, accounting for mortality. NRR ≈ GRR x Pr[survival
until the mean age at childbearing]. Hence NRR ≈ 0.92 x 0.956 = 0.88
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(e) Continuing to assume that 95.6 percent of women survive through their mean age at childbearing,
estimate the Total Fertility Rate that Iran would need in order to achieve an NRR that, in the long
run, correpsonds to zero population growth? [2 points]
Since NRR ≈ GRR x Pr[survival until the mean age at childbearing], we can set 1 = GRR x 0.956 and
solve for the unknown GRR. Then TFR = GRR / 0.49. Hence, the TFR that satisfies this condition
is = 2.13
(f) Can the NRR for a given country in a given year be greater than the GRR? Briefly explain why
or why not. [2 points]
The NRR cannot be greater than the GRR because while the GRR does not account for mortality,
the NRR does. However, if there is no mortality in the population the two quantities will be equal.
In practice, GRR > NRR.
II
The Economics of Female Labor Market Supply
Thinking about the standard model of female labor supply discussed in lecture, consider a married
couple that consists of a husband and a wife who do not have children. Let
Y = family income that is not from the wife’s work
w = the wife’s potential wage (which does not vary with the amount of labor supplied)
T = total discretionary time for the wife
L = wife’s leisure (or home production) time
C = the family’s total consumption
(a) Write down a formula for the wife’s income derived from labor. [1 point]
w(T -L)
(b) Write down the household’s budget constraint. [1 point]
C = Y +w(T -L)
(c) Draw a diagram of the budget constraint with total family income, which is equal to consumption,
on the vertical axis and wife’s leisure or home production time on the horizontal axis. Mark the point
T on the horizontal axis and the point Y on the vertical axis (assume Y >0). Assuming that the wife’s
optimal arrangement is not a corner solution (i.e., she chooses some nonzero amount of both work
and leisure), draw a few indifference curves and indicate what combination of consumption and wife’s
leisure time maximizes the household’s utility by labeling the point on the budget constraint line. [2
points]
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(d) Suppose that the husband pays child support for his children from a prior marriage and that
the amount of child support he must pay increases as a result of a court order issued by a judge.
Assuming that the wife’s preferences are fixed, will the amount of labor the (rational) wife supplies
to the market increase, decrease or does the answer depend on the shape of the wifes utility function?
Use either words or a diagram to explain your answer. [2 points]
The husband’s increased child support obligation is equivalent to an increase in the tax rate on his
income. Thus we can model this as a decrease in the husband’s income. The husband’s decreased
income corresponds to a decrease in Y in the model. Hence, with regard to the wife, this is a pure
income effect which causes her to supply more labor to the market.
(e) Now suppose that in addition to the husband’s increased child support obligations, the wife
also receives a job promotion which results in a wage increase of 5 percent. Will the wife supply
more hours or fewer hours to market labor as compared to her labor supply choice in (d)? [2
points]
Now, in addition to an income effect that is positive in work (or negative in leisure) owing to the
husband’s child support obligation, the wife’s wage has increased. The substitution effect predicts
that the wife will supply more labor (and less leisure) to the market which the income effect predicts
that she will supply less labor (and more leisure). The income effect on husband’s income tells
the wife to work more. The substitution effect on the wife’s wage tells the wife to work more.
However, the income effect on the wife’s wage tells the wife to work less. The net effect is ambiguous.
III
Data Analysis Using IPUMS
The Goldin (2006) reading makes use of data on female labor force participation in the United States
over much of the 20th century. In this exercise, you will use Census data to examine changes in marital
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status among women aged 20-30 and changes in labor force participation rates among women, aged
45-59, by marital status. The data are available from IPUMS, which stands for Integrated Public Use
Microdata Series. (Note: This is an excellent source of data for your term paper. It will allow you to
analyze data and construct tables online so you do not need to know how to use statistical software.)
The following steps will walk you through creating the tables, and will give you a short introduction
to using Census data.
Be aware. Although the steps below are not difficult, they may take more time to complete than
you may anticipate. Especially if you anticipate that you might have some difficulty working with
data online, make sure to do this exercise early enough to allow you to go to one of the computer
sessions or office hours with any questions. Also, if you are currently looking at the problem set online,
we strongly suggest that you print out these directions before you go further, so that you can refer to
them step-by-step.PLEASE MAKE SURE NOT TO LEAVE THIS TILL THE LAST MOMENT!
(a) At which census is the proportion of women age 20-25 who are married with spouse present
the lowest? What is the proportion of women married at this time? [2 points]
2000. 25.9 percent.
(b) How much more likely was a single, never married woman aged 20-25 to be in the labor
market as compared to a married woman of the same age with a spouse present in 1880? [2
points]
In 1880, a married woman with spouse present had a 6.5 percent chance of working in the labor market.
In 1880, a single woman had a 42.8 percent chance of working in the labor market. Hence a single
woman was 6.6x more likely to be working than a married woman with spouse present. This is the
same as saying 558% higher or 36.3 percentage points higher.
(c) How much more likely was a single, never married woman aged 20-25 to be in the labor
market as compared to a married woman of the same age with a spouse present in 2000? [2
points]
In 2000, a married woman with spouse present had a 64.1 percent chance of working in the labor market. In 2000, a single woman had a 75.7 percent chance of working in the labor market.
Hence a single woman was only 1.18x more likely to be working than a married woman with spouse
present.
(d) Now consider women aged 45-59. Looking at the first table and graph which show trends
in female labor force participation for married women, what trend do you notice in female labor force participation among married women age 45-59 over time? During which decade (i.e.
1880-1890, 1890-1900, etc.) is the change in female labor force participation the greatest? [2
points]
Labor force participation among this group is fairly flat until 1940, increasing rapidly thereafter. The
decade with the largest growth rate is the 1950s.
(e) Looking at the third table and graph which show trends in female labor force participation for
unmarried women, what trend do you notice in female labor force participation across time? Has labor
force risen or fallen since 1960? [2 points]
Here, the trend is much flatter. Labor force participation among unmarried women was roughly the
same in 2000 as it was in 1960.
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