Set Problem 2
Due: February 16, 2010 by 2:10 p.m.
Demog/Econ 175 Professor Ronald Lee February 3, 2010
1 If you have questions about this problem set
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2 Demographic Facts
On Tuesday, January 12th of this year, a devastating 7.0 magnitude earthquake struck Haiti causing widespread damage and untold loss of human life. To learn more about Haiti 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 online sources to locate some basic demographic information for Haiti and to make a couple of key calculations.
(A) Please use the CIA World Fact Book (https://www.cia.gov/library/publications/ the-world-factbook/) to obtain the following information for Haiti (2009
estimates). Note: The information is located under the tab titled people.: i. Population growth rate 1.838% ii. Crude birth rate (per 1,000 individuals) 29.1 per 1,000
iii.
Crude death rate (per 1,000 individuals) 8.65 per 1,000
iv.
Net migration rate (per 1,000 individuals) -2.07 per 1,000
v.
Life expectancy at birth
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60.78 years vi. Total fertility rate (TFR) 3.81 children per woman (B) Verify that the population growth rate can be obtained by subtracting the crude death rate and the net migration rate from the crude birth rate. What would the population growth rate have been if there had been no migration in this year? 29.1-(8.65+2.07) = 18.38 per 1,000 or 1.838% With no migration, 29.1-8.65 = 20.45 per 1,000 or 2.045% (C) Using the standard estimate for the fraction of births that are female presented in lecture, calculate the Gross Reproduction Rate (GRR) for Haiti. How much lower is the GRR than the TFR? GRR = TFR*0.488 = 3.81*.488 = 1.859 Using 0.493 (the actual estimate for Haiti). Then: GRR = TFR*0.493 = 1.878 The GRR is about 1.94 lower than the TFR [e.g., about 50% lower] (D) Assume that 88.8% of women survive until the age of 30 which we will assume is the mean age of childbearing and continue to use the standard estimate of births that are female. What is the Net Reproduction Ratio (NRR) for Haiti? NRR ~ GRR*survivorship to mean of childbearing years = 1.859*0.888 = 1.650. Using a GRR of 1.878, NRR ~ 1.878*0.888 = 1.668. (E) Continuing to assume that 88.8% of women survive through their mean age of childbearing, estimate the Total Fertility Rate that Haiti would need in order to achieve a net reproduction ratio (NRR) of 1, which corresponds to zero population growth. Assuming this target TFR was met this year, would the population growth rate become equal to zero immediately? Briefly explain your answer. NRR = 0.888*0.488*TFR
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1 = 0.888*0.488*TFR and solve for TFR = 2.307. Or using a GRR of 1.878, 1 = 0.888*0.493*TFR and TFR = 2.284. The population would continue to grow for a while due to population momentum. This is due to the fact that the previous population growth will cause a temporary rise in the number of births as those cohorts enter their childbearing years. (F) Referring again to the CIA World Fact Book, what is the adult prevalence rate of HIV/AIDS (2007 estimate)? Explain the difference between the incidence rate and the prevalence rate. 2.2% The incidence rate of HIV/AIDS is the rate at which new cases of the disease occur, typically in a given year. The prevalence rate is the proportion of the population that has a disease at a given point in time.
3 The Economics of the Family
Thinking about the standard model of female labor supply discussed in lecture, consider a married couple that consists of a husband and a wife. Let Y = family income that is not from the wifes work w = the wifes potential wage T = total discretionary time for the wife L = wifes leisure (or home production) time C = the familys total consumption (A) Provide a formula for the wifes labor income. W*(T-L)
(B) Write down the households budget constraint. 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).
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(D) Draw a few indifference curves and indicate what combination of consumption and women's leisure time maximizes the household's utility by labeling the point on the budget constraint line.
Note: Indifference curves do not turn up at the ends.
(E) Suppose that the wife's potential wage decreases. Draw a new budget constraint
line that reflects the shift in the wife's potential wage. Indicate which point on the
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new budget constraint optimizes utility. In your diagram, does the wife end up taking more leisure time or working more as a result of the wage increase (remember this answer is sensitive to how you draw the indifference curves).
3 Data Collection
The Goldin (2006) reading discussed female labor force participation in the United States over time. We will be creating tables using US Census data from 1880-2000 to examine changes in marital status among women aged 20-30 and changes in labor force participation rates among women, aged 45-59, by marital status. 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 you 30 to 60 minutes to complete. MAKE SURE NOT TO LEAVE THIS TILL THE LAST MOMENT! 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. Finding the data: First, go to http://usa.ipums.org/usa/, the home page for downloading public-use microdata from the Census and several other sources. We will be using their online data analysis system to create tables. From the links on the left-hand column, choose 'Analyze data online' from the Data section.
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We will be looking at data from multiple censuses simultaneously. Choose the section Use data from multiple samples 1850-2008. A page now opens which asks you which variables you would like in the table it will build for you.
Understanding the variables: Now that we have selected the data that we are interested in, we need to figure out which variables from the data set we want to use for our analysis, and also how to use these variables to restrict our sample to the people we want to study. The first step is to determine the variable names of the data you would like to look at, and the relevant values. We will need to know the variable names and how the data are coded. age (we are interested in women 20-30 and women 45-59) sex (we want to look at data for women) labor force participation rate marital status (we will look at work patterns separately by marital status) year (we will look at data from every census between 1880-1990) From the top, left-hand corner, choose the link "Codebook". This will open a new window or tab, depending on your browser. Choose "Sequential Variable List", and a set of headings will come up. The first are 'Household variables', the second 'Person variables'. From Person variables, click "Core Demographic". You will now see that two of the variables that we care about are right at the top of the list age and sex. Click "age". The codebook expands to tell us that the named variable "age" stands for age. (Not too surprising!) It tells us that there are 26,737,559 person records in the database, and that the valid range of age codes is between 0-125. The topcode (highest value) for age changes across censuses, but since we are only interested in 20-25 year olds and 45-59 year olds this should not be a problem for us. 20 year olds are conveniently given a code of 20. Below you will see the codebook entry for "sex". We see that the value for men is 1 and for women is 2. Namely, in the data, it does not say "Male" or "Female", it says 1 or 2, and from the codebook we know that sex=1 means the person is male and sex=2 means the person is female. Hit the back arrow of your browser. From the Core Demographic box under Person Variables, select the marital status variable marst. You will see that there are six possible marital status codes. Married, spouse present (marst=1), Married, spouse absent (marst=2), Seperated (marst=3), Divorced (marst=4), Widowed (marst=5) and Never married/Single (marst=6). Hit the back arrow of your browser again twice, and from the listing of Person Variables choose "Work". Now choose the variable labforce, which is an indicator for whether someone is currently in the labor force. (Be aware that 'labor force status' and 'employment status' are distinct. Employment status is based simply on whether you are currently working, but the labor force includes both those who are working and also those who would like to be working, but are not. Thus if you are currently unemployed but looking for work, you are a member of the labor force but you are not currently employed. In order to examine trends in female labor force participation, we will use labor force status (whether a person is working or would like to be working), not employment status (whether a person is currently working). From the codebook data we see that
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labforce=1 means "no, not currently in the labor force", labforce=2 means "yes, currently in the labor force", and labforce=0 means "not applicable". Hit the back arrow of your browser twice again, and choose the Technical category under the Household Variables Click on the variable yearp. We are interested in the years 1880-2000. We now know the variable names and values for all the factors we care about, so we can close this window.
Making the tables: Now that we have our dataset and know which variables we want, we are ready to extract the data to make the tables. Now we want to be back at the original page where we chose the "Codebook" link. (This screen has a set of boxes titled "Row", "Column", "Control". If the codebook opened in a new window, when we closed it the page we want should be up on your screen. If the codebook instead opened in a new tab, simply look at the other open tabs. In my browser (Firefox), the tab I want is labeled "SDA Web Application".) We can now tell the IPUMS online data analysis system what type of table we would like it to build. First, we will build a table displaying the distribution of marital statuses for women age 20-25 at each census from 1880-1990: (NOTE: the words in bold are the things you will type into the screen; the rest is just an explanation of what we are telling the computer to do.) In the first box labeled "Row:" enter marst In the box labeled "Column:" enter yearp "Control:" leave blank "Selection Filter(s):" enter sex(2), year(1880-2000), age(20-30) (For "Selection Filter(s):" type ALL of the bolded text above in the line for 'selection filters', sex(2) ensures that the table will only include females, age(2025) indicates that only 20-25 year olds should be included in the tabulation and year(88-99) restricts the census years used to those between 1880 and 1990. weight: (leave as is it should say "perwt - Person weight") percentage: 'column' should be selected color coding: unselect 'color coding' type of chart: choose 'Line Chart' (the rest of the settings are fine as they are) Hit "Run the Table". Notice that it will create the tables in a new window or tab, depending on the browser you are using. At the top of the output it will tell you the variables used in the tables and the ranges included. Below it will give you a table of the distribution of marital statuses for women age 2030 at each census. Make sure not to close this window, as you will be referring to it to answer some questions below. Now we will look at differences in female labor force participation rates of women age 45-59 by marital status for the census years between 1880 and 2000. Now go back to the previous window/tab where we filled in the variables for the table. The changes we will now make are: row: labforce column: yearp
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control: selection filters:
marst (this will stratify the results by marital status) sex(2), age(45-59), yearp(1880-2000), marst(1,4,6) (Notice that we are looking at women age 45-59 who are Married with spouse present, divorced, or never married) Hit "Run the Table". Now we have four new tables, which display the proportion of 45-59 year old women in the labor force by marital status at each census between 1880 and 1990. The fourth table and corresponding graph show the results for married, divorced, and never married women combined.
Answering some questions based on our tables: NOTE: The students are allowed to answer this question either using ages 20-30 or ages 20-25. Accordingly there are two sets of answers, both of which are similar. (a) At which census is the proportion of women age 20-25 who are married with spouse present the highest? What is the proportion of women married at this peak? AGES 20-30: 1960. Between 70-75%. AGES 20-25: 1960. Just over 65%. (b) Define the term gains to marriage. Gains to marriage is defined as the difference between the combined utility of two married people and the sum of their separate utilities if they were single. Measuring the gains to marriage in this way allows you to determine whether the couple is better off in the marriage compared to if they both remain single. If the gains to marriage are positive, then the couple will experience higher utility if they are married. (c) State whether you think that gains to marriage have been declining or increasing for women age 20-25 since 1960. Gains to marriage appear to be declining for women age 20-30 (20-25) since 1960 since a greater proportion are remaining single while they are in their early twenties rather than getting married. (d) Give two reasons why the gains to marriage have changed for women in this age group between 1960 and 1990. Gains to marriage decreased for women 20-30 (20-25) between 1960 and 1990 for a variety of reasons. For instance, over the time period 1960-1990, women had increasing access to higher education and better paying jobs. This increases their utility when they are single and reduces the gains to marriage that might come from specialization of labor within the home (i.e. wife specializes in domestic labor while husband works in formal labor market).
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Other possible answers: increased access to contraceptives, increase in cohabitation, reduced fertility, market goods that make home production easier (e.g. dishwashers, microwaves, etc.). (e) 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 across time? During which decade (i.e. 1880-1890, 1890-1900, etc.) is the change in female labor force participation the highest? The percentage of married women in the labor force has risen. The change in LFP is highest between 1950-1960. (f) 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? LFP has risen over time but has leveled off and has actually fallen since 1960.
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