---------------------------------------------------------------------------
CEH 226: Household/Family Demography Professor Michael Rendall
---------------------------------------------------------------------------
New York S
tate College of Human Ecology
A Statutory College of the State University
Cornell University, Ithaca, New York
IN
-
CLASS EXERCISES
IN
-
CLASS EXERCISE 1: Population Growth and its Components
I
N
-
CLASS EXERCISE 2: Mobility over Time and over the Life Course
IN
-
CLASS EXERCISE 3: Discussion of In
-
Class Exercise 2
IN
-
CLASS EXERCISE 4: Synthetic
-
Cohort Measures of Period Fertility
IN
-
CLASS EXERCISE 5: Children ever Born by Age and Race
IN
-
CLASS EXERC
ISE 6: Synthetic
-
Cohort Measures of a Non
-
Recurrent
Demographic Event: First
-
Birth
IN
-
CLASS EXERCISE 7: Marriage Markets for Black and White Americans
IN
-
CLASS EXERCISE 8: Widowhood and Widowerhood of Old
-
age Marriage Cohorts
IN
-
CLASS EXERCISE 9: Comparing
and Forecasting Disability
IN
-
CLASS EXERCISE 9: Comparing and Forecasting Disability
-
Model Answers
---------------------------------------------------------------------------
Last Modified Thursday, December 12, 1996
-
9:36:46 AM
USING CHIP TO
RETRIEVE 1950
-
90 CENSUS PUMS FILES FOR ANALYSIS
This document tells you how to access the specific set of data files
provided with your CHIPendale disk. They are data from the 1950, 1960,
1970, 1980, and 1990 Census PUMS (Public Use Microdata Sample) file
s. The
PUMS files contain data from households to whom the "long form" Census
questionnaire was given. This is a statistically
-
selected sample of all
Census households. The data from this sample have been statistically
"weighted" to represent all U.S. hous
eholds. The numbers and percentages
you will see when you use these data are therefore estimates for the whole
population of the U.S. The particular subset of PUMS data files on your
disk were created by Dr. William Frey at the University of Michigan.
Key
board and Mouse Commands to Access the Data Files
Insert the disk in the 3.25" drive (I assume here that it's the "a" drive).
To start CHIPendale from the DOS prompt,
1. Type a: < ENTER >
2. Type CHIP < ENTER >
Now you are in CHIPendale. You will s
ee a menu bar at the top of the
screen. From here, you will go into the directories that contain the Census
PUMS files created by Dr. Frey, and "open" data files in preparation for
subsequent data analysis operations.
1. Click on "File" at the top left
in the menu bar, and select "Open".
Select FREYCEN < DIR >, and then choose either CENTREND < DIR > for
the directory of 1950
-
90 Census files, or
CEN1990 < DIR > for the directory of 1990 Census files.
2. To go back and choose the other d
irectory (e.g., the 1990 files if you
first chose the 1950
-
90 files), select "Back one level".
3. Once you have made your choice of either the 1950
-
90 or 1990
directories,choose a file (e.g., BORN5090.DAT, and BORN9.DAT). To see
which dat
a variables are in this file, click on "Command" in the menu
bar, and select "Info". To see what are the categories of the data
variables, select "All Marginals" ("Marginals" are the totals of a
cross
-
tabulation).
4. To choose another fil
e, first clear the screen by clicking on "File"
and selecting "Clear". Then click again on "File", choose "Open", and
select the next file you want from the list. (Note: if you want to
next open a file that is in the alternate Census directo
ry, you must
first select "Back one level".
5. The last file that you opened will remain current (i.e., ready for
data analysis operations) until you open another file or quit from
CHIP. To find out which is the current file, click on "Co
mmand" and
select "Info".
To exit from CHIPendale, in the "File" menu, select "Quit".
---------------------------------------------------------------------------
CEH 226 Fall 1996
Professor Michael Rendall
-----------------------------------------
----------------------------------
New York State College of Human Ecology
A Statutory College of the State University
Cornell University, Ithaca, New York
IN
-
CLASS EXERCISE N
O. 1
For your group's state, do the following (refer to the Unit 1 notes on
POPULATION GROWTH and on CRUDE DEMOGRAPHIC RATES):
1. Compute the annual percentage growth and percentage growth rate between
1993 and 1994. Which is lower, and why? Show your eq
uations for the two
calculations.
2. Compute the doubling time from the percentage growth rate. Compute also
by what factor did the population increase in the 34 years between 1960 and
1994. Show your calculation. What can you say about your doubling time
versus this past growth?
3. Compute the Crude Birth Rate, Crude Death Rate, and Rate of Natural
Increase. Decompose the annual growth rate into that caused by natural
increase and that caused by net migration. Which is the more important
source of growth
, and by how much?
---------------------------------------------------------------------------
Last Modified Tuesday, September 03, 1996
-
10:22:21 AM
IN
-
CLASS EXERCISE 2: MOBILITY OVER TIME AND OVER THE LIFE COURSE
In this exercise, you will estimate c
hanges over time in migration and
residential mobility at different stages of life. You will do so by
computing synthetic cohort measures of mobility and migration expectancies
over multi
-
year periods of life. The class will estimate mobility of 1 to 9
yea
r olds; 10 to 17 year olds; 18 to 24 year olds; 25 to 34 year olds; 35
to 44 year olds; 45 to 54 year olds; 55 to 64 year olds; and 65 to 74 year
olds.
The period of life your group will study is:
Names of your group members:
The data you will use are f
rom the 1984, 1989, and 1994 Current Population
Surveys (CPS). The CPS is an annual survey conducted by the U.S. Bureau of
the Census.
1. For your particular 10
-
year age interval, calculate for 1984, 1989, and
1994 synthetic cohorts, the expected number o
f moves:
* within a county:
* between counties but within states:
* between states:
2. Calculate for 1984, 1989, and 1994, the percentage of all persons aged 1
and over who moved in the previous year:
* within a county:
* between counties
but within states:
* between states:
3. Summarize how the frequencies of these three types of move have changed
over the age interval of your study, and how this is similar to or
different from the overall population trend.
Note: please turn in your
printout with this page.
---------------------------------------------------------------------------
Last modified Tuesday, September 03, 1996
-
1:38:16 PM
IN
-
CLASS EXERCISE 3: DISCUSSION OF IN
-
CLASS EXERCISE 2 (MOBILITY OVER TIME
AND OVER THE LIFE COURS
E)
[Answers included here: partial only]
1. Methodological issues
Gill et al (p.64) present some statistics about what percentage of people
move within a five
-
year period. This can be calculated from the Census
question asking "where were you five years
ago?" How would this number,
asked of a twenty
-
five year old, compare to the expected number of moves
between the ages of 20 and 25 calculated by your synthetic cohort method?
ANSWER: the proportion who moved within a five
-
year period would be smaller
th
an the expected number of moves. The latter allows for more than one move
in the five
-
year period.
Do you think the synthetic
-
cohort method will over
-
or underestimate the
total number of moves a person might make between the ages of 20 and 25?
Why?
ANS
WER: underestimate, since people may also make more than one move per
year.
According to your calculations, in the 1994 synthetic cohort, the expected
number of within
-
county moves between ages 55 and 64 was 0.39, and the
expected number of within
-
county
moves between ages 65 and 74 was 0.33.
Does this mean that the average 55 year old can expect to move .72 times in
the next 20 years? Why or why not?
ANSWER: No. Death may occur before reaching 75, so .72 will overstimate
moves for the average 55 year ol
d.
2. Migration and the Family
How might the various trends in family formation, breakdown, and work in
the U.S. (many of which you raised in our first day of class) be expected
to affect mobility at different ages?
ANSWER: almost all family formation a
nd dissolution events are likely to be
associated with residential mobility at least. Think about this as we cover
the various family
-
change events during the course.
Are the measures you calculated for your particular age group consistent
with these spe
culations?
ANSWER: to answer this question, you should look for evidence of mobility
in the specific age groups at which the family
-
demographic event (e.g.,
getting married) is more common, and see how these have changed over time.
Type of move (e.g., res
idential mobility only versus interstate migration)
may give some clues (e.g., elderly persons might make interstate moves when
they retire, and then again when they need care from children).
---------------------------------------------------------------
------------
Last modified Thursday, September 12, 1996
-
11:09:18 AM
IN
-
CLASS EXERCISE NO. 4: SYNTHETIC
-
COHORT MEASURES OF PERIOD FERTILITY
Group Members' Names (For
-
Credit Ex. 1 group):
Years:________, ________, and _________ Race:___________
Note: sa
ve your spreadsheet on a disk (or on two disks for backup) after
the exercise.
I. Learning Objectives
After completing this exercise, you should be able to:
1. Understand the difference between the Total Fertility Rate (TFR) and
the General Ferti
lity Rate (GFR) as measures of amount of
childbearing, and be able to calculate both types of measure;
2. Understand the difference between birth
-
distribution measures of
fertility timing and synthetic
-
cohort measures of fertility timing,
and be able to calculate both types of measure;
3. Describe the effect of Baby Boom cohorts' aging on the distribution of
births by age of mother.
II. Calculations and Descriptions (fill in blanks, and write answers in the
spaces for descriptive an
swers)
1. Calculate the GFRs and TFRs for the two years, stating the unit (per
woman or per '000 women):
GFRs ________,________, and __________ per __________________
TFRs ________,________, and __________ per __________________
2. De
scribe similarities and differences in the changes over the three
periods in the GFR and TFR:
___________________________________________________________________
___________________________________________________________________
3. Calcu
late the percentage of all births that were to teenage mothers,
and the percentage of all births that were to over 30 year old mothers
for each of the three periods:
___________,____________, and _____________ under 20
___________,_____
_______, and _____________ over 30
4. Calculate the percentage of the synthetic cohorts' births that are to
teenage mothers, and the percentage of the synthetic cohorts' births
that are to over 30 year old mothers for each of the three periods
:
___________,____________, and _____________ under 20;
___________,____________, and _____________ over 30
5. Describe similarities and differences in the changes between the two
periods in the birth
-
distribution and synthetic
-
cohort
-
dis
tribution
measures of fertility timing (ages at childbearing):
6. State the two main assumptions of the synthetic cohort measures used
here:
IN
-
CLASS EXERCISE 5: CHILDREN EVER BORN BY AGE AND RACE
1. Learning Objectives
After comp
leting this exercise and the follow
-
up in
-
class discussion (and
for
-
credit exercise number 1), you should be able to:
1. Use the CHIPendale program to construct and interpret
cross
-
tabulations from Census data;
2. Define "birth cohort" from age a
nd period, and track a cohort's
progress across multiple Censuses;
3. Interpret the Children Ever Born (CEB) as a real
-
cohort measure of
cumulative and completed fertility;
4. Describe the past and projected future life
-
course fertility trend
s in
the United States, and what are the similarities and differences
across racial and ethnic groups.
2. Tasks
1. For 1990 (CENTREND subdirectory, BORN5090.DAT file), compute the
percentage of black and non
-
black women who have no child
ren at age
45
-
54 (i.e., at the end of childbearing).
Note: first use the "Modify", "Omit" commands to omit all age groups
except 45
-
54, and all years except 1990. Then use the "Modify",
"Combine" commands to combine the two categories o
f women with no
children (EM=ever
-
married and NM=never
-
married). Then use the
"Crosstab" command, selecting first "race" and second "child", and
selecting"percentage across" in the Crosstab menu.
Black percentage childless: ___________
____
Non
-
black percentage childless: _______________
This is a measure of completed fertility of the ___________ birth
cohort
2. Go back to the 1960, 1970, and 1980 Censuses to obtain your cohort's
cumulative fertility at ages ______
___, ___________, and ____________.
Again, calculate the percentage of Black and Non
-
black cohort members
who are childless at each age group, and calculate the percentage
differences in childlessness at each age group. Fill in the table
below.
Note: again, use the "Modify", "Combine", and "Modify", "Omit"
commands prior to the cross
-
tabulations of "race" by "child". You will
also need to choose the "percent diff" option under "Crosstab".
Age group ______ % Black Ch
ildless______% Non
-
black Childless_____ %
Difference
3. Go to the 1990 Census and obtain the percentages of all women aged 15
to 44 by race and ethnic group who have 0,1,2,3,...6+ children. Print
this table and bring it to the next class.
----------------------------------------------------------------------
Last modified Tuesday, September 24, 1996
-
1:59:31 PM
---------------------------------------------------------------------------
CEH 226: Household/Family Demography
Professor Michael Rendall
---------------------------------------------------------------------------
Group Members' Names (For
-
Credit Ex. 2 group):
Years: ________ and __________
IN
-
CLASS EXERCISE NO. 6: SYNTHETIC
-
COHORT MEASURES OF A NON
-
RECUR
RENT
DEMOGRAPHIC EVENT: FIRST
-
BIRTH
Note:
* 1. Please hand in this page, fully or partially completed, at the end of
class. It will be returned to your group on Thursday.
* 2. Save your spreadsheet on disk and bring it to class on Thursday.
(Bring also yo
ur IBM StudentChip disk to class on Thursday.)
Tasks and Questions:
1. Spreadsheet calculations: apply the single
-
decrement lifetable method
for non
-
recurrent events to construct a spreadsheet first
-
birth table
from the age
-
specific first
-
bir
th probabilities, beginning at age 15
and ending at age 44. Use the "Birth Probabilities by Parity" data
tables, "All Races"
---
use the "Parity
-
0" column. These are the
age
-
specific "exit rates" M(x) for this application, although you need
to divide them by 1,000 before you can use them. Construct one table
for each of your two years, with columns x, l(x), M(x), M(x)/1000, and
d(x).
2. Using your first
-
birth table's l(x) column, what percentage of your
two female synthet
ic cohorts initiate childbearing before age
20______and______, before age 30______and______, before age
40______and______, before age 45______and______? Formula you
used:__________________________________________________
3. What percentag
e of the synthetic cohort began childbearing in their
20s ______and_______, in their 30s _______and_______, and in their
40s_______and________? Formula you
used:__________________________________________________
4. What proportion of the
synthetic cohort who are childless at their
30th birthday("exact age 30") eventually bear at least one
child?______and_______ Formula you
used:__________________________________________________
5. Use the above results to compare the age
distribution of first birth
between the two periods.
---------------------------------------------------------------------------
Last modified Thursday, October 10, 1996
-
9:00:27 AM
------------------------------------------------------------------
---------
CEH 226: Household/Family Demography Professor Michael Rendall
---------------------------------------------------------------------------
New York State College of Human Ecology
A Statutory College
of the State University
Cornell University, Ithaca, New York
---------------------------------------------------------------------------
IN
-
CLASS EXERCISE NO. 7: MARRIAGE MARKETS FOR BLACK AND WHITE AMERICANS
LEARNING OBJECTIVES
Afte
r completing this exercise and the follow
-
up in
-
class discussion, you
should be able to:
1. Describe the differences in proportions of women currently married and
cohabiting by race/ethnicity, before and after controlling for
education;
2. D
escribe the extent of racial/ethnic group intermarriage, and so the
distinctness of racial/ethnic group marriage markets;
3. Describe the differences by race/ethnicity in men's and women's
education distributions, and in men's employment by edu
cation;
4. Use the family
-
economics framework and its theoretical applications to
formulate predictions and explanations of the marriage behavior of
women of each race/ethnic group, and compare to the empirical results;
INTRODUCTION
As stated
in lecture, black
-
white differences in marriage rates have
increased over recent decades. Two
-
thirds of Black children are now born to
unmarried women, compared to a fifth of White children (Gill et al,
pp.163
-
164). Sociologist William Julius Wilson (A. D
. White Professor at
Large at Cornell in the Fall of 1995) posits a marriage
-
market theory of
the low marriage rates and high marital dissolution among Black women (see
Gill et al, pp.264
-
266; and SOCIO
-
ECONOMIC THEORY OF MARRIAGE AND DIVORCE).
Dr. Frey's
1990 PUMS data give us the opportunity to empirically
investigate this and other marriage and divorce theories. We will compare
throughout, Black with non
-
Latino
-
White men and women 25
-
34 years old.
TASKS
1. Women's Marriage and Cohabitation
Using the
1990 MRRED9
-
25.DAT file, compute for Non
-
Latina White women and
for Black women: (1) the proportion of all women 25
-
34 who are (a)
currently married, and (b) married or living together; (2) the
living
-
together proportion of women 25
-
34 who are married or l
iving
together.
Question: Can the lower percentages married among Black women be partly or
fully accounted for by higher percentages cohabiting ("living together")?
Model Answer: Approximately equal percentages of black (6.0%) and
non
-
Latino white (5.7%)
women cohabit. Thus cohabitation differences cannot
account for the lower percentages married among black women.
2. Women's Marriage by Own Education
Using the 1990 MRRED9
-
25.DAT file, compute for 25
-
34 year
-
old Non
-
Latino
White women and for 25
-
34 year
-
old Black women: (1) the percentages married
by educational attainment (i.e., the percentages of women married among
women of each completed
-
education level).
[CHIP: After "Omit"ing males and all racial/ethnic groups except the two of
interest, "Cross
-
tab
"ulate "Educ" by "MarStus", "Control"ing for "RaceLat",
and choose the "percentages across" Option.]
Question: Are the lower percentages married among Black women due to their
different education levels? (I.e., within each educational
-
attainment
category,
do they have similar proportions married?)
Model Answer: At each education level, the proportion of black women who
are currently married is much lower. Overall, two thirds of white women are
married as compared to one third of black women. Among college
graduates
the differences are a little less (61.7% of whites and 42.3% of blacks).
However, differences among those with no more than high school education
are very great, e.g., 71.0% of white high school graduates vs. 34.8% of
black high school graduates
.
3. Separateness of Marriage Markets
Using the 1990 SPAGER9
-
25.DAT file, compute for Blacks and Non
-
Latino White
25
-
34 year
-
olds, the percentages of women and men marrying someone of a
different racial/ethnic group.
[CHIP: After "Omit"ing other ages, an
d all racial/ethnic groups except the
two of interest, "Cross
-
tab"ulate "WRaceLat" by "HRaceLat"]
Question: What percentages of Black and Non
-
Latina White women marry a man
of a different race?
Model Answer:
* 1.9% of black women and
* 0.4% of non
-
Latina
white women
4. The Marriage Markets: Male versus Female Education Distributions, and
Male Employment by Education
Using the 1990 MRRED9
-
25.DAT file, compute for 25
-
34 year
-
olds the
educational
-
attainment distribution by gender (i.e., the percentages of
women and men at each education level), for Blacks and Non
-
Latino Whites.
[CHIP: After "Omit"ing all racial/ethnic groups except the two of interest,
"Cross
-
tab"ulate "Gender" by "Educ", "Control"ing for "RaceLat", and choose
the "percentages across" Optio
n.]
Using the 1990 EMPED925.DAT file, compute for 25
-
34 year
-
old men the
employment distribution by educational attainment (i.e., the percentages of
men fulltime employed etc., at each education level).
[CHIP: After "Omit"ing women and all racial/ethnic
groups except the two of
interest, "Cross
-
tab"ulate "Educ" by "Hour", "Control"ing for "RaceLat",
and choose the "percentages across" Option
---
NA stands for Not Applicable,
and includes unemployed and not
-
in
-
labor
-
force categories.]
Question: Do Black wom
en of each education level face a worse marriage
market than do Non
-
Latina white women? (I.e., do Black women of each
education level have a higher ratio of men with lower education levels
relative to those with equal or higher education levels? Are Black
men of
given education levels less likely to be employed?)
Model Answer: Yes, black women face a worse marriage market. The
differences between males' and females' education distributions are small,
with both black and white women having slightly higher p
roportions college
educated than black and white men (47.8% of black women and 39.7% of black
men; 58.7% of white women and 55.8% of white men). However, the proportions
of black men employed are much lower than the proportions of white men
employed at eve
ry education level, and especially at lower education
levels. For example, while 88.5% of high school graduate 25
-
34 year
-
old
white men are employed, only 69.5% of high school graduate black men are
employed.
5. "Marrying Down" and Employment
Using the 1
990 SPED9
-
W.DAT file, compute for 25
-
34 year
-
old women the
distribution of husband's educational attainment for each married woman's
educational attainment level
[CHIP: After "Omit"ing other ages, men, and all racial/ethnic groups except
the two of intere
st, "Cross
-
tab"ulate "WEduc" by "HEduc"]
Question: What percentages of Black and Non
-
Latino White women, by own
education level, marry down (a man with a lower educational attainment) and
up (a man with a higher educational attainment)?
Model Answer: Amo
ng black women, 66.2% of college graduates marry down,
41.8% with some college, and 24.3% of high school graduates marry down.
Among white women, the percentages are respectively 34.5%, 31.1% and 13.8%.
Using the 1990 MRREMP9
-
W.DAT file, compute for 25
-
34
year
-
old women the
distribution of their employment status for each married woman's
educational attainment level.
[CHIP: After "Omit"ing all marital statuses except "Married" and all
racial/ethnic groups except the two of interest, "Cross
-
tab"ulate "Educ"
by
"Emp"]
Question: What percentages of Black and Non
-
Latina White women, by own
education level, are employed full time? are out of the labor force?
Model Answer: At every education level, married black women are more likely
to be full
-
time employed th
an are married white women, anad are less likely
to be out of the labor force. For example, while 19.7% of white college
graduates and 31.5% of high school graduates are out of the labor force,
and 61.2% and 45.7% are employed full time, among married blac
k women, only
9.7% of college graduates and 24.5% of high school graduates are out of the
labor force, and 76.8% of college grads and 52.6% of high school graduates
are employed full time.
6. Theoretical Interpretation.
Apply the Family
-
Economics framewo
rk (see SOCIO
-
ECONOMIC THEORY OF MARRIAGE
AND DIVORCE) to Black and Non
-
Latina White women's marriage behavior.
(1) Relate the empirical results to the theoretical concepts of the
framework: utility as a function of various valued goods; household
product
ion and division of labor; resource constraints.
Model Answer: The income of a married couple can be expressed as Y =
L(m)W(m) + L(f)W(f). Among black and white married couples, black women
contribute more hours in market work (L(f)) than do white women.
Given the
higher proportions of black women marrying down, they are likely also to
have higher wage rates (W(f)) relative to their husbands (W(m)) than do
white women. Futher, given the lower employment rates of black than white
men at each education level
(L(m)), a much greater proportion of total
family income L(f)W(f)/Y is likely to be provided by black wives than white
wives.
(2) Describe how the lower marriages rates of Black women might be
explained under each of the four "applications of the framewo
rk", making
reference to your empirical results wherever possible.
Model Answer (abbreviated):
1. Easterlin theory, Wilson's theory: black men's incomes are lower, and
so they are less able to marry.
2. Becker theory: black men's wages and earni
ngs are not high enough
relative to black women's to make gains to marriage through
specialization as great as for white women.
3. New Families theory: black men are not compensating for their lower
market productivity with higher producti
vity in household production.
---------------------------------------------------------------------------
Last modified Tuesday, November 05, 1996
-
1:27:14 PM
IN
-
CLASS EXERCISE 8: WIDOWHOOD AND WIDOWERHOOD OF OLD
-
AGE MARRIAGE COHORTS
LEARNING OBJECTIVE
S
After this exercise and follow
-
up class discussion, you should be able to:
1. Understand how to calculate and interpret the survival column of a
life table begun at age 65 (instead of at the usual age 0);
2. Understand how to use a female and
male lifetable survival column to
calculate the probabilities of joint and single survival of a couple;
3. Describe the effect of mortality reductions among the U.S. elderly
between 1970 and 1990 on widowhood and widowerhood.
INTRODUCTION
A
s you will later read in Gill et al (Ch.2 and Ch.22), mortality declines
among the elderly are continuing phenomenon of major demographic and
societal importance. Here we look at their importance for family
demography: in particular, for the proportions of
the elderly male and
female populations at various ages who will be widowed. To look at the
effect of mortality declines independent of trends in marriage and divorce,
you will construct two hypothetical 65 year old married
-
couple cohorts
(husband and wif
e both aged 65), calculating for them their proportion who
are both alive and proportion where one but not the other is alive
(widowhood or widowerhood) at ages 66 to 95.
The data you will use are from the 1970, 1980, and 1990 Vital Statistics
volumes (fr
om death registration statistics).
Your two synthetic cohorts are: _________ and _________.
Names of your group members:
Note: please turn in your spreadsheet printout and completed questions
(fully or partially completed) with this page.
TASKS
1. F
or each of your synthetic cohorts (put a Title with the Year of your
synthetic cohort in it), construct a joint life table with the
following columns:
Column 1: Age x (single
-
year ages 65,66,67,...,95)
Column 2: Male death rates Mm(x)
: [Enter these from the "All causes,
Male" row of the death rates table]
Column 3: Male survivors lm(x): [Set the age
-
65 value to 1, so that
you can calculate proportions
---
instead of the usual percentages
---
and
then calculate the next
columns with the formula lm(x+1) = lm(x)
-
((Mm(x)/100,000)*lm(x))]
Column 4: Male non
-
survivors {1
-
lm(x)}: [Calculate by entering the
formula 1
-
lm(x)]
Column 5: Female death rates Mf(x): [Enter these from the "All causes,
Femal
e" row of the death rates table]
Column 6: Female survivors lf(x): [Set the age
-
65 value to 1, and then
calculate with the formula lf(x+1) = lf(x)
-
((Mf(x)/100,000)*lf(x))]
Column 7: Female non
-
survivors {1
-
lf(x)}: [Calculate by entering
the
formula 1
-
lf(x)]
Column 8: Both alive: [Calculate by lm(x)*lf(x)]
Column 9: Widowhood (husband dead, wife alive): [Calculate by
{1
-
lm(x)}*lf(x) ]
Column 10: Widowerhood (husband alive, wife dead): [Calculate by
{1
-
lf(x)
}*lm(x) ]
Column 11: Widow proportion of all Women of the Marriage Cohort:
[Calculate by: Column 9 / (Column 8 + Column 9) ]
Column 12: Widower proportion of all Men: [Calculate by Column 10 /
(Column 8+ Column 10 ]
2. Census Widow
hood and Widowerhood Proportions Using the CENTREND
ELD5090.DAT file, compute the percentages widowed by gender and age
group for your two years. [CHIP: After "Omit"ing all years except the
one (you'll need to do this twice) of interest, "Cr
oss
-
tab"ulate
"AgeEldr" by "Marital", "Control"ing for "Gender", and choose the
"percentages across" Option.]
QUESTIONS
1. Describe from your lifetable results what has been the effect of
elderly mortality declines on proportions of wido
ws and widowers at
ages 65 to 95.
2. (a) Compare the proportions of widows and widowers from your
lifetables and your Census crosstabulations
---
choose the mid
-
point of
your Census age group to make the comparison to the lifetable (e.g.,
compare 70 year olds from the lifetable to 65
-
74 year olds in the
Census; compare 90 year olds to the 85+ Census category). Are the
trends the same? Are the levels very different?
(b) Describe what might account for the differences betw
een Census and
lifetable results.
---------------------------------------------------------------------------
Last modified Thursday, November 21, 1996
-
12:06:16 PM
Group Member names:
Note: Please turn this sheet in, fully or partially completed,
at the end
of class
IN
-
CLASS EXERCISE NO. 9: COMPARING AND FORECASTING DISABILITY
LEARNING OBJECTIVES
After completing this exercise and the follow
-
up in
-
class discussion,
you should be able to:
1. Use age
-
specific proportions in combination with p
rojections of the
population by age to project (forecast) numbers of persons in various
states or activities (i.e., functional projection);
2. Construct series of functional projections under different assumptions
about age
-
specific behav
ior.
3. Describe how the Baby Boom's forthcoming aging will effect the elderly
population's overall need for family caregiving, and how various
demographic, social and economic forces might affect how these needs
are met.
TASKS
1. Cho
ose two racial/ethnic groups among Hispanics (Latinos),
non
-
Hispanic whites, blacks, Asians and Pacific Islanders, and Native
Americans. Chosen two groups:
_________________and _____________________.
2. Comparing racial/ethnic
-
group
-
and
age
-
group
-
specific elderly
disability in 1990.
a. Using the ELDDSAB9.DAT dataset, compute for each of your two
racial/ethnic groups, by age
-
group and all 65+ year olds:
i. percentages unable to care for themselves (after
Omitting
racial/ethnic groups not of interest, CrossTabulate'RACELAT'
by 'SELFCARE' controlling for 'AGEELDR');
ii. percentages with mobility limits ('RACELAT' by 'MOBLMT'
controlling for 'AGEELDR').
b. Using the ELDDSAB9.DAT dataset, compute for each of your two
racial/ethnic groups, the age
-
group distribution ('RACELAT' by
'AGEELDR').
Questions: What are age
-
specific and all
-
elderly disability
differences betwe
en your two populations? What is the effect of the
differences in the elderly age distributions on the overall elderly
disability difference (65+ percentages disabled)?
Answer: Look at whether the (older) age groups with the higher
dis
ability rates are a higher proportion of their population
3. Projections of the numbers of disabled elderly in 2000 and 2040.
Choosing one of your disability types (self
-
care or mobility
impairment), for each of your racial/ethnic groups, proj
ect the
numbers of disabled persons. Use the 1990 racial/ethnic
-
and
age
-
group
-
specific disability proportions. Then calculate for each
racial/ethnic group the total number of 65+ year olds and the 65+
proportions. Your chosen disabilit
y type: ____________
Construct a spreadsheet for each of your racial/ethnic groups as
follows:
Column 1: Age Group (65
-
74, 75
-
84,85+, All 65+)
Column 2: Population in 2000 by age group, and total 65+. [From data
sheet, "Populati
on Projections of the United States..." You can
aggregate these data into your three age groups by, e.g., just typing
in =<number>+<number> in your spreadsheet]
Column 3: The disability proportion by age group, as calculated in
Task 2.
above.
Column 4: The (projected) number of disabled elderly by age group and
number and proportion disabled 65+ in 2000, using the 1990 disability
proportions.
Calculate this by first multiplying for each age group Column 2 by
Column 3, adding the projected numbers by age to get projected 65+
year olds, and then dividing this number by projected 2000 65+ year
olds to get the projected 65+ proportion disabled.
Column 5: Population in 2040 by age group, and total 6
5+.
Column 6: The projected number of disabled elderly by age group and
number and proportion disabled 65+ in 2040, using the 1990 disability
proportions.
Blacks 65 years and older
Column
1 2 3 4
5 6 7 8
populationdisab.prop. proj. # population proj. # alternate alt. proj.
in 2000 by age of in 2040 of projectionsof #s
disabled
disabled disab.
Age
Group
65
-
74 1631000 0.163 265853 3925000 639775 0.1467 575797.5
75
-
84 884000 0.236 208624 2758000 750888 0.21214 585799.2
85+ 326000 0.367
119642 1217000 446639 0.3303 401975.1
All
65+ 2841000 594119 7900000 1737302 1563572
proportion
proportion
proportion disabled
disabled: 0.209 0.220 under 0.198
disabled: alt.
assumption
Latinos 65 years and older
1 2 3 4 5 6 7 8
populationdisab.prop. proj. # population proj. # alternate alt. pro
j.
in 2000 by age of in 2040 of projectionsof #s
disabled disabled disab.
Age
Group
65
-
74 1135000 0.12 136200 5054000 606480 0.10
8 545832
75
-
84 578000 0.198 114444 3510000 694980 0.1782 625482
85+ 168000 0.37 62160 1365000 505050 0.333 454545
All
65+ 18810000 312804 9929000 1806510
1625859
proportion
proportion proportion disabled
disabled: 0.166 0.182
under 0.164
disabled: alt.
assumption
Questions: Describe the forthcoming trends in size and age com
position
of the elderly, 2000 to 2040, in terms of the birth cohorts they are
from (especially the age
-
group with the highest disability rate).
Describe similarities or differences between your racial/ethnic
groups.
Answer: The nu
mber of Blacks disabled over 65 will triple; the number
of Latinos disabled over 65 will quintuple. The percentages of over 65
year olds disabled will increase slightly, as the over 65 populations
of each get older.
4. Re
-
project the 2040
population using an alternate assumption about
proportions disabled (e.g., a 10 percent reduction in percent
disabled). For this create two new columns, one for the alternative
disability proportions, and one for the alternative projection
of the
numbers disabled (and 65+ proportion disabled).
Questions: Describe, drawing appropriately from the readings and class
work and lectures (give specific references), what demographic,
economic, and/or social forces might lead to
these alternative
assumptions.
Answer: The forecasted declines in age
-
specific disability rates would
result from a "morbidity compression", or from a shifting of the
disabled out of the community and into nursing homes. Lower
ava
ilability of "Baby Bust" children could lead to the latter.
---------------------------------------------------------------------------
Last modified Monday, December 16, 1996
-
12:18:44 PM
----------------------------------------------------------------
-----------
CEH 226: Household/Family Demography Professor Michael Rendall
---------------------------------------------------------------------------
New York State College of Human Ecology
A Statutory Colleg
e of the State University
Cornell University, Ithaca, New York
FOR
-
CREDIT EXERCISES
I. FALL 1996
FOR CREDIT EXERCISE 1: FERTILITY ACROSS TWO GENERATIONS
FOR
-
CREDIT EXERCISE 1: QUESTIONS AND MODEL ANSWERS
FOR
-
CREDIT EXERCISE 2: EXPLAINING RACIAL DIFFERENCES IN EARLY FIRST
CHILDBEARING
FOR
-
CREDIT EXERCISE 2: INDIVIDUAL ANSWER SHEET AND MODEL ANSWERS
FOR
-
CREDIT EXERCISE 3: INDIVIDUAL ANSWER SHEET
FOR
-
CREDIT EXERCISE 3: INDIVIDUAL ANSWER SHEET AND MODEL AN
SWERS
II. SPRING 1996
FOR
-
CREDIT EXERCISE 1: A CLOSER LOOK AT DIFFERENTIAL FERTILITY
FOR
-
CREDIT EXERCISE 1: QUESTIONS AND MODEL ANSWERS
---------------------------------------------------------------------------
Last modified Thursday, December 05, 199
6
-
10:29:28 AM
FOR
-
CREDIT EXERCISE 1: FERTILITY ACROSS TWO GENERATIONS
1. INTRODUCTION We know from period fertility measures such as total
births, the Crude Birth Rate, the General Fertility Rate, and the Total
Fertility Rate (see Gill et al, Figures 3
-
1, 3
-
2, and 3
-
3), that there have
been very large fluctuations in childbearing since World War II. These
"period" measures, however, do not tell us directly about women's
childbearing lifetimes. To do this, we construct real
-
cohort (or "cohort")
measures
of fertility. In the present exercise, we will construct
real
-
cohort measures from the same (birth registration) data from which
synthetic
-
cohort fertility measures are constructed. We will also see the
limitations of real
-
cohort measures, and learn how to
construct a part
real
-
cohort, part synthetic
-
cohort measure of lifetime fertility to address
these limitations.
The use of real
-
cohort fertility measures also allows us to investigate
changes across generations of mothers and daughters. We will do this h
ere
for two generations
---
the generation that gave birth to the Baby Boom, and
the Baby Boom women themselves. Our purpose here is both descriptive
---
to
find out what happened
---
and theoretical, testing Easterlin's relative
income hypothesis of fertility.
Accurate description is a crucial function
of demographic analysis. When describing lifetimes, however, we will see
that one element of "description" involves the "projection" of current
trends into the future.
2. COMPUTATIONS
The basic idea is to descri
be fertility change by comparing fertility
across two generations: a "mother cohort" and a "daughter cohort". The
birth year defining your mother cohort is given to you. The birth year
defining your daughter cohort will be calculated by you. Measures of
fe
rtility over the entire reproductive lifetime of mother and daughter
generation cohorts form the basis for comparisons. The reproductive
lifetime is defined here as ages 15 to 44 inclusive.
A. For your "mother cohort", calculate measures of lifetime
fertility
by applying the appropriate five
-
year age interval, age
-
specific
fertility rate (ASFR) for every age from 15 to 44. This means that you
must use age
-
specific fertility rates for 30 consecutive years,
beginning 15 years after t
he cohort's year of birth. For example, if
your cohort is the 1940 cohort, you would apply the 15
-
19 year old
ASFR of 1955, 1956, 1957, 1958, and 1959, the 20
-
24 year old ASFR of
1960, 1961, 1962, 1963, and 1964, etc., through to the 40
-
44 y
ear old
ASFR of 1980, 1981, 1982, 1983, and 1984. The specific measures to
calculate are:
(i) Their mean number of children born (the Cohort Total
Fertility Rate), calculated exactly the same way as the period
Total
Fertility Rate
---
i.e., summing over all ASFRs;
(ii) The mean number, and proportion of lifetime mean number, of
children born (1) before age 20, (2) before age 25, (3) before
age 30, and (4) after age 30;
(iii) Th
e median age of childbearing, being the youngest age at
which less than half of lifetime childbearing occurs during all
subsequent ages.
B. Define your "daughter cohort" as the group of women born in the
year in which the mot
her cohort had borne half its children (i.e.,
when your mother cohort was at its median age of childbearing). For
this cohort, calculate the following measures:
(i) Their mean number of children born before age 20, (if data
p
ermit) their mean number born before age 25, (if data permit)
their mean number born before age 30, and the mean number of
children born up until the oldest age for which you have data
(call this "oldest observed age").
(ii) Now go back to the "mother cohort" and calculate the mean
number of children born up to the age given by the
daughter
-
generation's oldest observed age.
C. For your daughter cohort, estimate their childbearing that will
take place after their oldest observed age lifetime with the latest
period's age
-
specific fertility rates for their ages from that period
until age 44. For example, if your daughter cohort was born in 1965,
and your last available year o
f data is 1992, when your cohort was
aged 27, apply the 1992 25
-
29 year old ASFR for ages 28 and 29, the
1992 30
-
34 year old ASFR for ages 30 to 34, etc., up to age 44. This
is then a part real
-
cohort, part synthetic
-
cohort method. Now compu
te
all the same lifetime fertility measures which you computed for your
"mother cohort" (in part A above), but which you could not compute
from real
-
cohort data only.
3. WHAT TO HAND IN
Each person should hand in an INDIVIDUAL ANSWER SHEET
. Your designated
group member should hand in both the spreadsheet tables used to compute the
results, and the summary spreadsheet table(s) to present the results. On
the summary table(s), containing the mother
-
cohort measures and the
daughter
-
cohort measu
res, indicate which of the daughter
-
cohort measures
are real
-
cohort measures and which are part real
-
cohort, part
synthetic
-
cohort measures.
4. ASSESSMENT AND COOPERATION GUIDELINES
This exercise counts for 7 percent of final grades. You should work
toge
ther with members of your group to calculate the tabular results. You
may also consult each other (and other class members) with respect to the
written answers, and may construct the answers together or individually.
Whichever way you do your work, you mus
t each turn in an INDIVIDUAL ANSWER
SHEET in your own handwriting, and your designated group person must turn
in spreadsheet calculation tables and summary results tables. Your
individual grade will be based on both these (4 points) and your individual
ans
wer sheet (10 points), as indicated on the INDIVIDUAL ANSWER SHEET.
Due date: Thursday 26 September, in class.
---------------------------------------------------------------------------
CEH 226: Household/Family Demography Professor Michae
l Rendall
---------------------------------------------------------------------------
FOR
-
CREDIT EXERCISE 1: INDIVIDUAL ANSWER SHEET
Name:
Names of your other group members:
Name of group member handing in the group's summary results table(s) and
sprea
dsheet
-
calculation tables [worth a total of 4 points]:
Birth year of your mother cohort:
1933
-
39
Now answer the following questions in the spaces below:
1. According to Easterlin's "relative income hypothesis" (see Ch.3 of
Gill et al), which of
your mother and daughter cohorts should have
more children and why? [2 points]
The mother cohorts should have more children than the daughter
cohorts. The mother cohort is especially small, born in the Depression
years. The daughter co
hort is especially large, born between 1958 and
1962, at the peak of the Baby Boom. According to Easterlin, the size
of the cohort bears an inverse relationship to job and earnings
opportunities, which in turn have a direct relationship to l
ifetime
childbearing.
2. Compare the fertility of your mother and daughter cohorts using
real
-
cohort measures only. What evidence do you find to support or
contradict the relative income hypothesis, and what is your conclusion
about
the hypothesis from this evidence? In what way does the evidence
you present provide an incomplete test of the hypothesis? [2 points]
The fertility daughter cohorts through their early to mid
-
30s (the
oldest ages at which we can observe the
m) is much lower than that of
of the mother cohorts up to the same ages. The mother cohorts had
borne on average between 2.7 and 3.2 children each, compared to the
daughters'1.6 to 1.8 children. The Easterlin hypothesis is thus
strongly
supported by these results. The evidence is incomplete,
however, due to the lack of a comparison over the entire reproductive
lifetime of the mothers and daughters.
3. Compare the fertility of your mother and daughter cohorts using
real
-
cohort measures for your mother cohort and part real
-
cohort, part
synthetic
-
cohort measures for your daughter cohort. Describe to the
non
-
demographer reader what the part real
-
cohort, part
synthetic
-
cohort measures mean. What evidence do you
find to support
or contradict the relative income hypothesis now, and what is your
conclusion about the hypothesis? How dependent is your conclusion on
the synthetic
-
cohort part (what direction and magnitude of violation
of the main as
sumption of the synthetic
-
cohort part would be needed to
invalidate your conclusion)? Why is your evidence a better test of the
relative income hypothesis than would be measures based on completely
synthetic cohorts, such as Total Fertility
Rates at different periods?
[4 points]
The completed fertility of the mother cohorts is also much higher than
that estimated for the daughter cohorts, although the differences are
a little less than those seen from real
-
cohort measures
only. The
daughter cohorts' estimates were derived by filling in their remaining
lifetime fertility as at 1994, with the fertility rates estimated from
persons at those ages in 1994, the latest year for which we have data.
The mother c
ohorts' completed fertility was between 2.9 and 3.3
children each, as compared to the daughter cohorts' 2.0 children. This
evidence still provides firm support for the relative income
hypothesis. This conclusion is not highly dependent on th
e
part
-
synthetic cohort assumption. For the daughter cohorts to attain
lifetime fertility equal to their mothers', their ASFRs in their
mid
-
late
-
30s and early 40s would have to be as much as three times
higher than those assumed from 19
94 data. Our evidence is a better
test than completely synthetic cohort measures because the Easterlin
theory is explicitly about cohorts. Completely synthetic cohort
measures are based entirely on data of a single period, whereas our
m
easures rely largely on real
-
cohort data.
4. Using the same method as you used to define the daughter cohort, when
will your granddaughter cohort be born or when was it born? What would
Easterlin predict about their fertility, and why? [2 poin
ts]
The granddaughter cohorts will be born between 1984 and 1988,
calculated from the median ages (in all cases 26) of the 1958
-
62
daughter cohorts. Easterlin would predict that their fertility will be
higher than that of their mothers
(our "daughter cohorts"), since they
are granddaughters are a small cohort relative to their mothers, and
so will experience better economic conditions as they enter their
childbearing years.
-----------------------------------------------
----------------------------
Last modified Wednesday, October 02, 1996
-
2:14:25 PM
---------------------------------------------------------------------------
New York State College of Human Ecology
A Statutory College
of the State University
Cornell University, Ithaca, New York
---------------------------------------------------------------------------
Group Members' Names:
Group Member Turning in Group Work:
First
-
birth Table Cohorts: _________a
nd __________
FOR
-
CREDIT EXERCISE NO. 2: EXPLAINING RACIAL DIFFERENCES IN EARLY FIRST
CHILDBEARING
INTRODUCTION
In this exercise, you will investigate the extent to which White and Black
fertility has converged or diverged over the last decade with resp
ect to
the timing of first childbearing. First, you will calculate first
-
birth
lifetables for two White and Nonwhite cohorts who attain age 25 at
approximately 1980 and 1990 respectively. Next you will use 1980 and 1990
Censuses to calculate first
-
childbea
ring percentages of Nonblack and Black
cohorts who attain ages 15
-
24 in those years. For these Census cohorts, you
will further investigate their childbearing by education level and look at
employment levels of 15
-
24 year old men of the same race. You will
then use
these Census data to investigate different explanations for these trends
and racial differences.
WHAT TO HAND IN
Each person should hand in an INDIVIDUAL ANSWER SHEET. Your designated
group member should hand in both the spreadsheet tables used
to compute the
results, and a summary table or tables to present the results.
ASSESSMENT AND COOPERATION GUIDELINES
This exercise counts for 7 percent of final grades. You should work
together with members of your group to calculate the tabular results.
You
may also consult each other (and other class members) with respect to the
written answers, and may construct the answers together or individually.
Whichever way you do your work, you must each turn in an INDIVIDUAL ANSWER
SHEET in your own handwriting
, and your designated group person must turn
in spreadsheet calculation tables and summary results tables. Your
individual grade, calculated out of 21, will be based on both the group
work (8 points) and your individual answer sheet (13 points).
Due date:
Tuesday 10/22/96, in class.
COMPUTATIONS:
A. First
-
birth Table [5 points]
Apply the single
-
decrement lifetable method for non
-
recurrent events to
construct a spreadsheet first
-
birth table from the age
-
specific first
-
birth
probabilities, beginning at ag
e 15 and ending at exact age 25 (i.e.,
include l(25), but not M(25) or d(25)). Use the Birth Probabilities by
Parity data tables, White, All Others
---
use the Parity
-
0 column. These are
the age
-
specific exit rates M(x) for this application, although you nee
d to
divide them by 1,000 before you can use them. Up to 1976 use the
appropriate 5
-
year age group. From 1977 onwards, use the 1
-
year ages.
Construct two tables (one for Whites, one for All Others) for each of your
two cohorts, with columns x, l(x), M(x),
M(x)/1000, and d(x). Hand in these
four tables, one set per group.
2. Using your first
-
birth table's l(x) and/or d(x) column, compute for
Whites and NonWhites the percentage of your two female cohorts that
initiate childbearing (i) by age 20, (ii) by age
25, and (iii) between 20
and 25. Compute also (iv) of those not giving birth before age 20, the
percentages that give birth before age 25, and (v) of those giving birth
before age 25, the percentages that give birth as teenagers. State the
formulas you use
d to calculate each of these and tabulate these results.
Hand in one per group.
1980 and 1990 Census PUMS (StudentChip) Cross
-
tabulations [3 points]
Using the BORN5090.DAT dataset, compute (i) for Blacks and NonBlacks the
percentage of 15
-
24 year olds wh
o have had a first birth, for 1980 and
1990; and (ii) for Blacks and NonBlacks of each education level the
percentage of 15
-
24 year olds who have had a first birth, for 1980 and
1990.
Using the EMP5090.DAT dataset, compute the male employment to populatio
n
ratio for 15
-
24 year old Black and NonBlack males in 1980 and 1990 (as in
Table 15
-
2, p.265, of Gill et al). This ratio is simply the percentage of
Unemployed and NILF (Not in Labor Force) among all 15
-
24 year old Black or
NonBlack males.
--------------
-------------------------------------------------------------
Last modified Monday, October 14, 1996
-
3:44:43 PM
---------------------------------------------------------------------------
CEH 226: Household/Family Demography Professor Micha
el Rendall
---------------------------------------------------------------------------
New York State College of Human Ecology
A Statutory College of the State University
Cornell University, Ithaca, New
York
---------------------------------------------------------------------------
FOR
-
CREDIT EXERCISE 2: INDIVIDUAL ANSWER SHEET:
1. [4 points] Use your results calculated from your first
-
birth tables
for Whites/Nonwhites, together with your Black
/NonBlack results
tabulated from the 1980 and 1990 Censuses, to describe any convergence
or divergence of timing of first birth between Blacks and Whites
(before controlling for education). [Note that Blacks make up a large
majority of
NonWhites and Whites make up a large majority of
NonBlacks.]
Model answer: Differences between the proportions of black and white
women commencing childbearing in their teens and early 20s changed
little across cohorts of the 1950s, 19
60s, and early 1970s. From first
birth tables, the proportion of nonwhites commencing childbearing in
their teens fell from about 40% of the 1950s cohorts to 33% of the
1960s cohorts. Meanwhile, the proportion of whites commencing
child
bearing in their teens fell from about 20% of the 1950s cohorts
to 17% of the 1960s cohorts. Thus a ratio of 2 to 1 between nonwhites
and whites was maintained. A similar picture is seen from the
percentages of 15 to 24 year old black and no
nblack women having
already had a first birth respectively in 1980 and 1990
---
a comparison
of the 1956
-
64 and 1965
-
74 cohorts. The black proportion fell from
34.4% to 31.6% while the nonblack proportion fell from 19.4% to 18.0%.
2. [6 poi
nts] Gill et al (pp.434
-
436) discusses the
social
-
characteristics and minority
-
group hypotheses as explanations
for completed family size. We will apply these two competing
hypotheses here to early first childbearing, since this is strongly
associated with larger completed family size. (i) Using Johnson's
social characteristics hypothesis ("strong form" and "weak form", Gill
et al, pp.435
-
436), explain what predictions would you make about
differences in the percentages ha
ving already given birth between
Blacks and NonBlacks aged 15
-
24? (ii) Explain what prediction would
you make based on the minority group status hypothesis as used by
Farley and Allen (Gill et al, p.435)? (iii) Which hypothesis or
hypot
heses appear to be better supported by your data. In your
answers, note any changes over time in support for one or other
hypotheses.
Model answer: (i) Johnson's social characteristics hypothesis ascribes
racial differences in fertilit
y to differences in socio
-
economic
status, which may be represented by differences in women's education
level. Using the strong form, I would predict no differences within
education group in the percentages of 15
-
24 year old blacks and
nonblacks having already having given birth; using the weak form, I
would predict higher percentages of blacks having already given birth
up to perhaps high school graduates, but no differences between women
with some
-
college or college
-
grad
uates. (ii) The minority group status
hypothesis asserts that cultural differences and the majority
-
minority
relationship leads to fertility differences even between women of
similar socio
-
economic status. Farley and Allen use this hypothesi
s to
explain higher fertility of black women at all education
levels
---
hence a prediction of higher percentages of 15
-
24 year old
blacks and nonblacks having already having given birth, at all
education levels. (iii) The minority group
status hypothesis is better
supported by the data, since in both 1980 and 1990, black 15
-
24 year
old percentages having already given birth are consistently higher
than nonblack 15
-
24 year olds. For example, 54.7% of black high school
g
raduates and 19.3% of black college graduates in 1980 and 45.8% and
13.4% respectively in 1990 had a first birth, compared to 34% of
nonblack high school graduates and 6.1% of college graduates in 1980
and 30.7% and 5.6% respectively in 1990
. These results, however,
suggest greater declines within education level for blacks than
nonblacks, and so some convergence towards the results that would be
predicted by the social
-
characteristics hypothesis.
3. [3 points] What is the
pattern of difference in Black to NonBlack
employment? Is this similar or opposite in direction to the difference
in Black
-
NonBlack first childbearing. Use Wilson's hypothesis
(discussed in Gill et al, pp.264
-
266) to interpret this associati
on.
Model answer: In 1980 and 1990, the percentage of employed black males
aged 15
-
24 was 40.9 and 40.0% respectively, much lower than the 59.1%
and 60.0% of employed nonblack males aged 15
-
24 in 1980 and 1990. This
is opposite to the
difference between percentages of black and
nonblack 15
-
24 year old women who had already had a first birth in
1980 and 1990. Wilson uses differences in the male employed
percentage
---
the lower percentage of blacks than whites
---
to explain
the higher rates of black single mothers, whether through divorce or
non
-
marital childbearing. With poor marriage prospects, black teenage
girls have less reason to postpone childbearing until they are
married
---
hence a higher percentage
commence childbearing in their
teens.
----------------------------------------------------------------------
Last Modified Monday, November 04, 1996
-
11:15:18 AM
---------------------------------------------------------------------------
CEH 226: Household/Family Demography Professor Michael Rendall
---------------------------------------------------------------------------
New York State College of Human Ecology
A Statutory College of the St
ate University
Cornell University, Ithaca, New York
---------------------------------------------------------------------------
FOR
-
CREDIT EXERCISE 3 INDIVIDUAL ANSWER SHEET [12 points.]
Your Name:
Names of group members:
Name of g
roup member handing in spreadsheet [3 points]:
Your "reason for leaving" and two education levels:
GROUP TASKS
Use the synthetic
-
cohort method for non
-
recurrent events to calculate a
"home
-
returning life table" for your two education levels, constructin
g a
separate table for each (for your assigned "reason for leaving" (total of
two life tables).
Each lifetable should have the following columns:
Column 1: duration x, from 0 to 10
Column 2: M(x)
---
return rate
Column 3: l(x)
---
"survivors" from the
original 100 of the synthetic
cohort
Column 4: d(x)
---
"returners at duration x"
Column 5: 100
-
l(x)
The designated group member is to hand in the lifetables on spreadsheet (no
summary table necessary).
INDIVIDUAL QUESTIONS (Hand in handwritten answers
on these pages; you may
work together on your answers)
1. What descriptive title would you give to your two synthetic cohorts?
[1 point]
Nest
-
leaving cohort with <education and reason/circumstance for
leaving home>
The following q
uestions must be answered for each of your two
education levels (i.e., using both life tables)
---
show any
calculations:
2. What percentage of the synthetic cohort return within (a) 1 year; (b)
2 years; (c) 5 years?
[1 point]
(
a) d(1); (b) 1(1)
-
1(6)
3. Assuming that persons who don't return within 10 years never return,
what percentage of your two cohorts ever return? [1 point]
100
-
1(10)
4. Of all who return, what percentage return within the first 2 years? [1
point]
d(1)/[100
-
1(10)] (or d(1) + d(2)/[100
-
1(10)])
5. State the assumption(s) of these synthetic cohort measures. [1 point]
(1) duration
-
specific home
-
returning rates will remain constant;
(2)no other exits (e.g., by death)
from the "living independently"
population occur.
6. What advantages are there to calculating duration
-
specific rates
synthetic
-
cohort (life table) measures, as compared to using the "All
durations" home
-
returning rates only? [1 point]
(1) lifetable measures give us life
-
course type measures such as the
percentae of home leavers who will return home within a given period;
(2) lifetable measures allow us to better compare groups' home
-
leaving
behavior, because they co
ntrol for duration
--
the "all durations"
home
-
returning rate will be affected by how long people have been away
from home.
7. Drawing appropriately from the readings (particularly Goldscheider and
Goldscheider) on leaving and returning h
ome, and combining this with
the family
-
economic framework for analyzing household composition and
change (see WWW document):
(i) construct "Resource Constraints" and "Household Production
Functions" for both parents and children under
the alternatives of (1)
the children's continuing to live independently; and (2) the
children's living back with their parents again;
(1) children independent:
(a) Resource constraints
children's: F = L(n)*W(n) + H(n) * W(n)
parents': F = L(h)*W(h) + H(h) * W(h)
(a) Household production functions
children's: Z(n) = Z[C(n), H(n)]
parents': Z(n) = Z[C(h), H(h)]
(2) children move back home:
(a) Resource constraint
children's and parents': F
= L(n)*W(n) + H(n)*W(n) + L(h)*W(h) +
H(h)*W(h)
(b) Household production function
children's and parents': Z(h,n) = Z[C(n), C(h), H(n), H(h)]
(ii) use these to derive explanations for the differences you found by
education leve
l of children;
Children with higher education are likely to have higher wages and
thus be able to pay for the privacy afforded by independent living. If
they are married, the number of hours available for both employment
and household
production are higher, making them more able to live
independently. If they are unmarried with a child, more
home
-
production hours and income are needed, making it more likely
they will return home.
(iii) use them to derive predictions
of possible effects by level of
parents' income.
[3 points
---
continue your answer on a separate page and staple it to
this page]
From the children's perspective, richer parents may mean a greater
reduction in the children's reso
urces when they are away from home,
and thus more incentive to return home. From the parents' perspective,
their higher income may allow them to afford to subsidize their
children's independent living, so giving the parents more privacy.
This would lead to the opposite prediction that children would be more
likely to have enough income to stay living away from their parents.
----------------------------------------------------------------------
Last modified Thursday, Dec
ember 05, 1996
-
10:27:02 AM
---------------------------------------------------------------------------
CEH 226: Household/Family Demography Professor Michael Rendall
--------------------------------------------------------------------------
-
New York State College of Human Ecology
A Statutory College of the State University
Cornell University, Ithaca, New York
FOR
-
CREDIT EXERCISE 1: A CLOSER LOOK AT DIFFERENTIAL FERTILITY
1. INTRODUC
TION
Gill et al (p.431 and pp.434
-
438) raise the issue of higher fertility
among Black and Hispanic Americans as a possible impediment to the
narrowing of the economic
-
status gap between them and non
-
Hispanic
White Americans. In making
the connection between fertility and
economic status, they cite Kuznets' concern (p.431) that higher
fertility implies more children per family, and so a smaller
proportion of total family income per child. Indeed, many studies find
th
at a larger number of children in the family leads to lower economic
success as adults. Later (p.437), Gill et al use the total fertility
rate as their measure of higher Black fertility, and so also larger
family size.
But does a highe
r total fertility rate mean more children per family?
Not necessarily. We must also know how many women have any children at
all, since family size is relevant only when there is at least one
child. To use an extreme example to illustrate th
e point, if the White
TFR was 2.0 but only half of White women had children, then there
would be on average 4 children per family. Childlessness has indeed
been increasing in the U.S. (Gill et al, pp.162
-
163). In this
exercise, we will
therefore investigate racial differentials not only
in total fertility rates, but also in proportions of women remaining
childless. Further, we will use our estimates of TFRs and childless
proportions to construct an approximate measure of a
verage family
size.
Differentials in how many children women bear in their lifetimes are
not the only fertility differentials of interest, however. As
throughout this course, we are also interested in timing of
family
-
demographic
events. A first
-
birth, for example, signals the
beginning of a child
-
raising stage of the life course. We will
therefore also estimate in this exercise, measures of fertility timing
for White and Nonwhite women.
The data we will use ar
e from the National Center for Health
Statistics' Birth Registration System. The particular data we need are
published only for Whites and All Others. Therefore we will be
restricted to White/Nonwhite empirical comparisons of fertility.
2
. COMPUTATIONS
In order to answer the questions in this exercise (see separate
"ANSWER SHEET"), you will first need to construct four spreadsheet
tables as follows:
(1) apply the synthetic
-
cohort approach for recurrent events to
construct a spreadsheet Total Fertility Rate (TFR) table. Construct
this table from the age
-
specific fertility rates (called "central
birth rates" in your data tables
---
use the "Total" column). Construct
one such table for Whites and one for
Nonwhites ("All Others").
(2) apply the synthetic
-
cohort approach for non
-
recurrent events to
construct a spreadsheet First
-
Birth table from the age
-
specific
first
-
birth probabilities (from the "Birth Probabilities by Parity"
data tab
les
---
use the Parity
-
0 column). Again, construct one table for
Whites and one for Nonwhites.
3. ASSESSMENT AND COOPERATION GUIDELINES
This exercise counts for 5 percent of final grades. You may work
together with members of your group (a
nd other class members) to
calculate the results. You may also consult each other with respect to
the written answers, and may construct the answers together or
individually. Whichever way you do your work, you must each turn in an
answ
er sheet in your own handwriting. One member of your group must
turn in a copy of the four spreadsheet tables. Your individual grade
will be based on both this and your answer sheet.
Due date: .
----------------------------------------
------------------------------
Last modified Tuesday, September 10, 1996
-
8:02:17 AM
---------------------------------------------------------------------------
CEH 226: Household/Family Demography
----
Professor Michael Rendall
------------------
---------------------------------------------------------
New York State College of Human Ecology
A Statutory College of the State University
Cornell University, Ithaca, New York
FOR
-
CREDIT EXERCISE 1:
MODEL ANSWERS
Name: Michael Rendall
Names of your other group members: The Whole Class
Name of group member handing in the spreadsheet tables: The Groups'
Designated People
Year of your fertility data: 1984
-
1991
Now answer the following questions:
I
. DIFFERENTIALS IN NUMBER OF CHILDREN BORNE
1. Calculate the absolute and relative differentials (Gill et al, p.437) in
the Total Fertility Rate (TFR) between Whites and Nonwhites (show
calculations), and compare these results to those displayed in Figure
24
-
6b
to show whether Black
-
White fertility differentials can be reasonably
approximated by White
-
Nonwhite fertility differentials (write either one or
two sentences).
Answer: The white
-
nonwhite fertility differential increased over the
1984
-
91 period, w
ith non
-
white women estimated in 1984 to bear over their
lifetimes 0.51, or 30 percent, more children than white women, and in 1991
to bear 0.79, or 42 percent, more children than white women. These
white
-
nonwhite differentials approximate reasonably well
Gill et al's
estimates of black
-
white differentials, which appear to be in the range of
.5 to .65 in absolute terms and 30 percent in relative terms over the
mid
-
to
-
late 1980s.
Calculations: TFR is calculated as the sum of age
-
specific fertility rates
ove
r the ages 14 to 49. Absolute differential is calculated by Nonwhite TFR
-
White TFR; relative differential is calculated by Nonwhite TFR / White
TFR.
[Give numbers.]
2. Calculate from your first
-
birth table the percentages of White and
Nonwhite women bea
ring children (show calculations), and describe this
fertility differential between Whites and Nonwhites (one sentence).
Answer: Very large differentials in the proportions of white and nonwhite
women ever having chidren are estimated, with increases from
94.5 percent
of nonwhite women in 1984 to 98.3 percent in 1991, versus from 77.3 percent
of white women in 1984 to 80.1 percent in 1991.
Calculations: percentage ever having children = l(15)
-
l(50) = 100
-
l(50)
[Give numbers.]
3. Divide the TFR by the pro
portions (not percentages) of White and
Nonwhite women bearing children and calculate the absolute and relative
fertility differentials according to this new measure (show calculations).
Write a sentence describing the results.
Answer: much smaller fertil
ity differentials are seen between nonwhite and
white women who have children, the absolute differential increasing from
.13 more children in 1984 to .39 more in 1991, or from 6 percent more in
1984 to 17 percent more in 1991. Calculation: Average number o
f children
per woman bearing children = TFR / {[100
-
l(50)] / 100}
[Give numbers.]
4. What condition about with which parent or parents the children live is
necessary to interpret your results of question 3 as representing
family
-
size differentials (one se
ntence)?
Answer: That the children live with the mother (irrespective of whether she
still lives with the father).
[Note: this answer takes "family
-
size" to mean number of children per
family; I also accepted interpretations of number of children plus
pa
rents.]
5. Using the results you presented above (and noting in your answer any
problem of using only the two broad racial categories for which we have
data available), evaluate Gill et al's use of the Total Fertility Rate to
approximate differences in th
e family sizes of Blacks and Whites.
Answer: The relative differential in Total Fertility Rates between blacks
and whites will greatly overstate relative differentials in their family
sizes. Using white
-
nonwhite as a reasonable approximation to black
-
whit
e
comparisons (as shown above), we find that average family sizes are between
6 and 17 percent higher for nonwhites, as compared to average Total
Fertility Rates that are between 30 and 42 percent higher.
II. FERTILITY TIMING DIFFERENTIALS
6. Use your fi
rst
-
birth tables to calculate the percentages of White and
Nonwhite families begun between the ages 15 to 19, 20 to 29, and 30 or
above (show your calculations).
Answer: see "Synthetic
-
cohort measures for non
-
recurrent events: first
birth" on the Web. Div
ide d(x) summed over the x's of each age range by
d(x) summed over all the x's (which equals 100
-
l(50)).
7. Use your TFR tables to calculate the percentages of all children borne,
alternately by White and Nonwhite women, between their ages 15 to 19, 20 to
29, and 30 or above (show calculations).
Answer: M(15)+M(16)+...+M(19) / TFR
M(20)+M(21)+...+M(29) / TFR
{TFR
-
[M(14)+M(15)+...+M(29)]} / TFR
[Note: a better classification of the youngest age group would have been 14
to 19, as some of you did.]
8. Use
the results calculated in questions 6 and 7 to describe
differentials in fertility timing between White and Nonwhite women (one or
two sentences).
Answer: Nonwhite childbearing women begin their childbearing earlier than
do white childbearing women, and h
ave their families on average at
significantly younger ages. While consistently around 35 percent of
childbearing nonwhite women begin their childbearing before age 20 and only
14 percent after age 30, for example, around 20 percent of white
childbearers b
egin their childbearing as teenagers while almost as many
(around 18 percent) begin their childbearing after age 30. On the other
hand, the percentage of all children born after age 30 differs
comparatively little between white and nonwhite women (around 2
8 percent
and around 24 percent respectively).
[Note: "questions 5 and 6" should have read "questions 6 and 7". I accepted
either interpretation in your answers. Also, in retrospect,"two to three
sentences" would have allowed for more adequately descripti
ve answers. I
have indicated what such a "two to three sentence" answer might look like
above.]
III. METHODOLOGY
9. What are the main assumptions behind the synthetic
-
cohort approach you
have used to calculate your TFR and first
-
birth tables?
Answer: 1.
women live through the childbearing years (to age 50); 2. the
age
-
specific birth rates (for the TFR calculations) and age
-
specific
first
-
birth rates (for the First
-
Birth Table calculations) will remain
constant at their current
-
year levels.
EXTRA NOTES O
N THIS EXERCISE
1. When rounding your answers to present numbers that include a decimal
point, a good rule of thumb is to present three informative digits.
You would, for example, round percentages to one digit after the
decimal place (e.
g., 14.8 percent), and round a TFR expressed in
per
-
woman units to two digits after the decimal place (e.g., 1.78
children per woman). The same TFR expressed in per
-
thousand
-
women
units, however, would have four informative digits: 1,781 per
haps.
Rounding should be done after calculations, not before, to increase
the accuracy of the results you present.
2. When using your calculated numbers to tell something about the real
world, try to bear in mind the distinction between
what you want to
measure and the measures you are using to estimate or approximate
this. Typically, our data and measures do not allow us to exactly
measure what we would like to measure. So we must use them
intelligently. For example,
in question 5., we are using a
white
-
nonwhite comparison of family
-
size differentials as measured by
TFRs (the average lifetime fertility of all women in a cohort) versus
as measured by the average lifetime fertility of women who have
c
hildren. The differences between these two types of measure are so
great that it is highly unlikely that they could be accounted for by
our failure to more finely classify our racial/ethnic groups. Our
comparison of our nonwhite
-
white TFR di
fferentials with those of Gill
et al's black
-
white differentials give us important further
reassurance on this point.
When describing the results you have calculated, try to express them
in terms of what they mean in addition to expres
sing them correctly as
numbers with appropriate units. For example, use "we estimate that the
78.5 percent of white women have children" instead of "...have
children by age 50." We chose age 49 to be the maximum age of
childbearing (and
our "central birth rates" data in the late 40s
affirm that choice). It is not too bold in this case to be claiming to
be estimating lifetime fertility. Similarly, even though we know some
childbearing occurs before age 15, we believe it is
small enough for
our 15
-
19 year old category to be used to describe "..the percentage
of childbearing women who begin their childbearing as teenagers." On
the other hand, you must also be careful not to leap too far from the
data, as we
saw in this exercise with respect to Gill et al's use of
TFR differences to equate to family
-
size differences.
---------------------------------------------------------------------------
Last modified 2/21/96 3:50 pm
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