New York State College of Human Ecology

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CEH 226: Household/Family Demography Professor Michael Rendall

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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

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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?

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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.

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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).


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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.



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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.


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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