EurAsia Project Comparative Fertility Analysis: 
Specifications for Tables and Regression Models

Revised 16 August 2001

George Alter
Noriko Tsuya
Wang Feng

For more information about variables and models, interpretations, and ideas for country reports see "EurAsia Project Comparative Fertility Analysis: Suggestions and Interpretations for Country Reports"

CONTENTS

• Notes on final version of fertility models (4 April 2001)
• Summary of Changes Since Our Meeting in Fort Worth (15 September 2000)
• Summary of Changes Since Our Meeting in Beijing (13 August 1999)
• Descriptive Tables
• Event history models:
• Covariates for event history models (15 September 2000)
• Models for intervals between marriage and first birth (4 April 2001)
• Models for intervals following the first and higher births (4 April 2001)

Notes on final version of fertility models:

From: George, Noriko, and Wang Feng (editors of the fertility volume)

We are now sending the final version of the fertility specifications for descriptive tables and event history models. It is essential that all teams produce these estimates before our meeting in Florence (25-26 June 2001). We have done our best to reduce and simplify our requests. As the list below shows, each of the items listed here has been requested by the author of at least one of the comparative chapters.

After some discussion, we propose to run the models described here separately on
1. intervals between marriage and first birth, and
2. intervals following the first and higher births, but not on all intervals combined.

In previous specifications, we have asked all teams to estimate models separately for male and female births. Now, we are only requesting separate estimates for Model D1, which are needed for the chapter on infanticide. It will still be necessary for the Chinese and Japanese teams to do most of their estimates separately by sex, because of the prevalence of sex-specific infanticide. But it may not be necessary for the European teams. Previous results have suggested that little is gained by estimating separate models by sex of child. We now ask each team to evaluate this issue and reach their own conclusion. If the sex-ratio of births is close to the biological level (104-107 males per 100 females) and tests do not show differential responses to explanatory variables by sex, then most models can be estimated for males and females combined.

We also ask the European teams to simulate the data available to the Japanese team by estimating Model D1 for "pseudo-births." This means identifying children who would have been registered on an arbitrary annual enumeration day (e.g. April 1) and excluding infants that would have died without being registered. For the Italian case, this means using only children recorded in the status animarum and excluding births added from the birth register. Previous experiments have indicated that there are no systematic differences between results with all births and those with "pseudo-births," but we need a final set of estimates to discuss in Chapter 2.

In some samples, prices only affect fertility in certain sub-groups, such as unskilled laborers. Tommy has requested separate estimates focusing on these groups for the chapter on price effects. Teams should consult with Tommy to determine which models should be estimated on sub-groups.

Some teams (Sweden and perhaps Venice) have information about stillbirths. In general, research on fertility is limited to live births, but it would be quite useful to have comparisons of live births to live births+stillbirths. The models with biodemographic variables (especially C1, I1, I2, and I3) may be particularly useful here.

The fertility models have been revised and simplified. The following list explains the key variable in each model and the chapter in which it will be used. Each of these models is designed to focus on one variable or group of variables and to avoid confusion from collinear variables (such as "Children ever born" and "Sex composition of surviving children").

Event history models:

Model B (Chap 2 (George and Noriko); Chap. 9 (Tommy))
1. Expanded model with marriage characteristics.
2. Price interactions with age of mother

Model C (Chap 2 (George and Noriko); Chap. 9 (Tommy))
1. Children ever born. (1+ intervals only)
2. Price interactions with Children ever born (1+ intervals only)

Model D (Chap 2 (George and Noriko); Chap. 9 (Tommy); Chap. 10 (Renzo and Noriko))
1. Sex composition of surviving children. (1+ intervals only)

1. All births
2. Female births
3. Male births
4. All pseudobirths
5. Female pseudobirths
6. Male pseudobirths

Model E (Chap. 11 (Michel))
1. Woman's relationship to head.
2. Price interactions with Woman's relationship to head

Model F (Chap. 11 (Michel))
1. Household type.
2. Price interactions with Household type

Model G (Chap. 11 (Michel))
1. Household composition by age.
2. Price interactions with Household composition by age

Model H (Chap. 11 (Wang Feng))
1. Household composition by relationships.
2. Woman's relationship to head x Household type

Model I (Chap. 2 (George and Noriko))
1. Woman's age at first birth (1+ intervals only)
2. Woman's age at first marriage
3. Time since first marriage

We also want to remind you of the importance of the descriptive tables. We indicate here the chapters in which they will be used, so that you can send questions to the authors of those chapters.

Descriptive tables:

Summary of Changes Since Our Meeting in Fort Worth (revised 15 September 2000):

1. In Fort Worth we revised the covariates used to describe birth interval effects.  We combined the covariates describing the time in the current interval and fate of the previous child into a single covariate, which called "Time since last birth/Survival of previous child". One purpose of this covariate is intended to show the effects of lactation. If women were breastfeeding, fertility should be lower in the 2 years following a birth if the preceding infant survived. This change also eliminated the need for Model 4c, but we have kept the previous model numbers.

2. We have also renamed a related covariate called "Length of last completed birth interval."

Please note that these covariates refer to different birth intervals, and they also differ from the similar covariate used to analyze infant mortality. "Time since last birth/Survival of previous child" refers to the current birth interval. This begins as an incomplete birth interval which may be censored or completed by an event (birth). Thus, if a woman has n children at the beginning of the interval, this refers to time since the n-th child. "Length of last completed birth interval" refers to the previous completed interval, or time between birth n-1 and n.

3. We have added Table 8 to provide a descriptive analysis of the interval between marriage and first birth. It is also possible to construct Table 8 in a continuous form by calculating a Kaplan-Meier survival cuve.

4. In Fort Worth we also discussed the need for studies that examine the lag between prices movements and fertility responses. We have not added this below, but each team is encouraged to experiment with these models.

Summary of Changes Since Our Meeting in Beijing (revised 13 August 1999):

1. Time since last birth or latest marriageThis covariate is now included in all models. The Italian team showed that this covariate can be used very successfully in discrete-time models. Teams using continuous time (Belgium and Sweden) should use time since last birth or latest marriage as the time dimension of the baseline hazard.
2. Differences between intervals following last birth and intervals following latest marriageThe interval after a marriage needs special treatment for several reasons. In some of the European samples many brides were pregnant at the time of marriage. This means that the timing of births was quite different than in intervals following a birth. In contrast, Asian marriage practices may have made this interval unusually long. In addition, we have done experiments showing different responses to covariates in the interval after marriage than in intervals following a birth.


We handle this problem in two ways. First, we have modified the "time since last birth" covariate so that it is now "time since last birth or latest marriage." For discrete time analysis, the categories for time since marriage are separate from those for time since last birth, because the timing of fertility will be different in the interval following marriage. For continuous time analysis, the baseline hazard is measured from either last birth or from marriage, but these should be handled as different "strata". The Cox regression model allows different baseline hazards in different strata.

Second, we now request that models be estimated in three ways: all intervals, intervals after at least one birth, intervals between marriage and the first birth. We have done tests on the Belgian data that show very different results in the marriage-to -first-birth interval. In some cases, the inclusion of these intervals has a substantial effect on the estimated relative risks. Nevertheless, we believe that it is still important to estimate models of data that are pooled to include all birth intervals, because these give us our best estimates of the overall effects of economic and social covariates.

3. Difference between the "Preceding birth" and the "Index child"Our previous specifications resulted in some confusion about the definition of the previous birth interval and the survival of the previous child. The confusion was created by our attempt to re-use variables created for the analysis of infant and chld mor tality. It may be possible to use those variables, but there is a fundamental difference between the fertility and the mortality analysis. In mortality analysis "survival of the preceding child" refers to the child born before the "index child". In fertil ity analysis "survival of the preceding child" refers to the survival of the most recent birth, and "preceding birth interval" refers to the interval before the birth of that child. Thus, if a woman has had 3 children, "survival of the preceding child" re fers to the survival of her 3rd child (not the 2nd child as in mortality analysis), and "preceding birth interval" refers to the interval between children 2 and 3.
4. New covariate: "Preceding child alive & less than 2 years since last birth"This new covariate was suggested by results presented by the Italian team at the last PAA meeting. They found an interaction between survival of the previous child and time since the last birth. Fertility was higher under 2 years when the previous child h ad died. It is likely that this result is due to termination of breastfeeding after the death of an infant. This covariate has been added to look for that effect.
5. New covariate: "Time since marriage"This covariate is an alternative to age at first marriage. It allows us to examine the possibility that fertility may be affected by recency of marriage, rather than age at marriage.
6. Model 1These model examines the overall effects of economic and social covariates (head's occupation, prices) without other controls. Following a suggestion of the Swedish team, we have added models with the age structure of the household using covariates develo ped for the mortality analysis.
7. Model 2These models focus on the sex composition of surviving children. The results presented in Bloomington showed some very strong effects of these covariates in some samples. If fertility varies by sex composition it is strong evidence of purposeful control.
8. Model 3These models involve several different measures of household structure and relationship to head of household. Since these measures are often correlated, we cannot use every variable in the same model. Interactions are included to help us to interpret thes e results.
9. Model 4These models of bio-demographic covariates have been changed in a number of ways. Our approach here is to test a number of different covariates. Since some of these covariates examine the same thing in different ways, they often cannot be included in the same model. Also, some of these covariates can only be computed for women who have had at least two children. However, teams are encouraged to estimate additional models that use the most promising combinations of these covariates.


See "EurAsia Project Comparative Fertility Analysis: Suggestions and Interpretations for Country Reports" for a longer discussion of these issues.

Model 4h has been added to look for an interaction between grain prices and parity (children ever observed).

10. Children ever bornChildren ever born should be constructed as a categorical variable, not a continous variable. When a population is practicing family limitation the effects of parity can be curvilinear, so it is important to allow for non-linear effects.
11. Male and Female Births and "Pseudo-births"European teams are requested to compute Table 2, Table 3, and Model 5a separately by the sex of the child and also using "pseudo-births" as well as observed births. "Pseudo-births" are children who would have been alive to be counted if an enumeration had been conducted on a specific date, such as April 1 or July 1. This computation simulates the situation in the Japanese population registers, in which children that were born and died between enumerations are not recorded.


Previous results from the European teams have shown that tables and event history models do not differ by sex. We have also seen that no biases are introduced by using pseudo-births instead of all births. These results are important to our Chinese and Japanese colleagues, but at this stage we only need one event history model to make these points.

DESCRIPTIVE TABLES

Table 1. Percentage Distribution of Marital Status by Sex and Age
________________________________________________________________ 
     Never    
Currently                   Marital Status
Age  Married    married  Widowed  Divorced  Unknown   Total      (N)
________________________________________________________________ 

Female
 under 10
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20-24
   .
   .
 45-49
 15-49


Male
 15-19
 20-24
   .
   .
 45-49
 15-49

SMAM:
    Female
    Male
________________________________________________________________ 

Table 2.  Age-specific and Total Fertility Rates for All Births 
and Separately for Male and Female Births by Period 
_____________________________________________________________________ 
Period     <15  15-19  20-24  25-29  30-34  35-39  40-44  45-49  TFR 
_____________________________________________________________________ 
All births
  1750-69
    . 
  1850-69
  1750-1869


Male births
  1750-69
    . 
  1850-69
  1750-1869


Female births
  1750-69
    . 
  1850-69
  1750-1869



Number of person-years observed
  1750-69
    . 
  1850-69
  1750-1869
____________________________________________________________________< 
NOTES: 
(1) Fertility rates are births per 1,000 woman-years.  TFR
is computed by adding the rates for ages 15-49.  Rates by period
should be computed only when there are enough person-years
observed.
(2) European teams are requested to compute this table using 
"pseudo-births," children who would have been alive at an 
enumeration on a specific day of the year.

Table 3.  Age-specific and Total Marital Fertility Rates by Period 
_____________________________________________________________________ 
Period    <15 15-19 20-24 25-29 30-34 35-39 40-44 45-49  TMFR  TMFR20+ (N)
_____________________________________________________________________ 
All births
  1750-69
    . 
  1850-69
  1750-1869

Number of person-years observed
  1750-69
    . 
  1850-69
  1750-1869
_____________________________________________________________________ 


NOTES: 
(1) Marital fertility rates are marital (legitimate) births per
1,000 married woman-years.  TMFR is computed by adding the rates
for ages 15-49.    TMFR20+ is computed by adding the rates for ages 20-49.  
We include both TMFR and TMFR20+, because rates for ages 15-19 may be 
affected by small proportions of women who are married at those ages. 
(2)  Rates by period should be computed only when there are enough person-years.
(3) European teams are requested to compute this table using 
"pseudo-births," children who would have been alive at an 
enumeration on a specific day of the year.

Table 4.  Age-specific and Total Marital Fertility Rates by Age at Marriage
_____________________________________________________________________ 
Mother's
Age at
Marriage   <15 15-19 20-24 25-29 30-34 35-39 40-44 45-49  TMFR15+  TMFR20+ (N)
_____________________________________________________________________ 
All births
   under 15
   15-17
   18-19
   20-24
   25+
   Not available

Number of person-years observed
   under 15
   15-17
   18-19
   20-24
   25+
   Not available
_____________________________________________________________________ 


NOTES: 
(1) Marital fertility rates are marital (legitimate) births per 1,000 
married woman-years.  TMFR15+ is computed by adding the rates for ages 15-49.    
TMFR20+ is computed by adding the rates for ages 20-49.  We include both 
TMFR15+ and TMFR20+, because rates for ages 15-19 may be affected by small 
proportions of women who are married at those ages. 

(2)  Rates by period should be computed only when there are enough person-years.

Table 5. Number of Female Children by Age of Mother at Birth and 
          Number of Male Children by Age of Father at Birth 
___________________________________________________________________________

Mother's age      Number of female Children        Number of person years
under 15
15-19
20-24
...
45-49

Father's age      Number of Male Children          Number of person years
15-19
20-24
...
70-74
75+  
___________________________________________________________________________
Notes: 
1. If the age of the father is not observed, use the age of the
mother plus the average age difference between spouses.

2. If births are not observed, this table should be constructed 
by counting children who are observed at a specific age or range
of ages.  For example, in the Japanese registers, children
should be counted at their first appearance in the population register.  
Ages of parents should be adjusted so that they are ages at birth of the child.

Table 6.  Sex Ratio of Births by Number and Sex of
          Surviving Children
          (Males / 100 Females)
________________________________________________________________ 
Number of
Surviving           Number of Surviving Sons
Daughters    None     One    Two or more       All      (N)
_________________________________________________________________
None
One
Two or more
All
(N)
_________________________________________________________________
NOTES: 
(1) When information is not available, children who have left the
household (or village) are assumed to be alive for the purpose of
computing surviving children.

Table 7.  Proportion of Out-of-Wedlock Births by Birth Order,
           Mother's Age at Birth, and Time Period
___________________________________________________________
                    % out-of-wedlock      Number of Births
___________________________________________________________
All births
Birth order
  1
  2
  3+
Mother's age at birth
  15-19
  20-24
  25-29
  30-34
  35-39
  40+
Period
  1750-19
   .   .
  1860-19
___________________________________________________________
Notes: 
(1) European teams only.
(2) Birth order should only be computed for women who are
under continuous observation from age 15.

Table 8.  Number of Births by Months Since Marriage, Marriage Order, and Pre-marital Births
___________________________________________________________
                1st Marriage     1st-Marriage      Re-marriage
              No pre-mar birth   Pre-mar birth
___________________________________________________________
All births
Months since marriage
  1-3
  4-6
  7-9
  10-12
  13-15
  15-18
  19-21
  22-24
  25-27
  27-30
  30-33
  34-36
  37-42
  43-48
  49-54
  55-60
  >60
___________________________________________________________

BACKGROUND TABLES FOR EVENT HISTORY MODELS

Table 8. Means of Covariates Used in the Event History Models

Table 9. Correlation Coefficients among Covariates Used in the Event History Models

COVARIATES FOR EVENT HISTORY MODELS

DISCRETE TIME MODEL:

1a) Had a birth or not in an interval under consideration

1=birth

0=no birth

1b) Had a male birth or not in an interval under consideration

1=male birth

0=no male birth

1c) Had a female birth or not in an interval under consideration

1=female birth

0=no male birth

With the specification of:
2) Woman "at risk of a birth" if woman was alive and present in the village throughout the current interval, husband was alive and present in the village during the previous interval, and the next register is not missing.

CONTINUOUS TIME MODEL

1a) Had a birth or censored

1=birth

0=censored

1b) Had a male birth or censored

1=male birth

0=censored

1c) Had a female birth or censored

1=female birth

0=censored

With the specification of the origin point for time (i.e., t=0) for the Cox model. In the case of fertility this should be date of previous birth or marriage for first birth.

COVARIATES:

1. Individual demographic covariates:

Woman's current age (or age at childbirth)

(Reference: ages 20-24)

Under 15

15-17

18-19

20-24 (omit as reference category)

25-29

30-34

35-39

40-44

45-49

Interval after last birth or latest marriage

0 = interval after last birth

1 = interval after latest marriage

Time since last birth or latest marriage

Reference category: 1 to 2 years since last birth during current marriage

1. No information on date of marriage or last birth
2. Less than one year since marriage and no births since marriage
3. 1 to 2 years since marriage and no births since marriage
4. 2 to 3 years since marriage and no births since marriage
5. 3 to 4 years since marriage and no births since marriage
6. 4 to 5 years since marriage and no births since marriage
7. 5 to 6 years since marriage and no births since marriage
8. 6 or more years since marriage and no births since marriage
9. Less than one year since last birth during current marriage
10. 1 to 2 years since last birth during current marriage (Reference category)
11. 2 to 3 years since last birth during current marriage
12. 3 to 4 years since last birth during current marriage
13. 4 to 5 years since last birth during current marriage
14. 5 to 6 years since last birth during current marriage
15. 6 or more years since last birth during current marriage

Number of children ever-observed

(2 has been chosen as the reference category to avoid confusion with other effects operating in the interval between marriage and first birth.)

0

1

2 (omit as reference category)

3

4

5

6

7

8+

Current marriage is first marriage or remarriage

(Reference category: First marriage)

First marriage (omit as reference)

Remarriage

No data

Age difference between spouses

(Reference: Husband same age or less than 6 yrs older than wife)

Wife is older than husband

Husband same age or less than 6 yrs older than wife

Husband is older than wife by 6+ yrs

Migrant who arrived in previous three years

Reference: Non-migrant or migrated more than three years earlier.

Time since last birth/Survival of previous child

Length of last completed birth interval

0 = previous birth interval greater than 24 months

1 = previous birth interval less than or equal to 24 months

Woman's age at first birth

(Reference category: ages 18-19)

"No data" if first birth is unobserved

First birth under age 15

First birth ages 15-17

First birth ages 18-19 (omit as reference)

First birth ages 20-24

First birth age 25 or older

Woman's age at first marriage

(Reference category: ages 18-19)

"No data" if first marriage is unobserved

First marriage under age 15

First marriage ages 15-17

First marriage ages 18-19 (omit as reference)

First marriage ages 20-24

First marriage age 25 or older

Time since most recent marriage

(Reference category: 2 to 4 years)

"No data" date of marriage is unobserved

Less than 2 years

2 to 4 years (omit as reference)

More than 4 years

2. Household composition covariates:

Number in household ages 15-54

Percent of household ages 0-14

Percent of household ages 55+

Sex composition of surviving children

(Reference: at least one son and one dau alive)

No son alive, only daughter(s) alive

No daughter alive, only son(s) alive

No children alive

Woman's household relationship

Spouse of head or Head of household (Reference)

Household head

Stem kin of head

Spouse of stem kin of head

Non-stem kin of head

Servant

Other

Married child present

0 = No married child

1 = Married child present

Presence of parents (/or parents-in-law) in household

No parents present (reference)

Both parents present

Only father present

Only mother present

Household type

Simple household (reference)

Vertical -- stem (one married child of most senior person in household)

Vertical -- joint (2 or more married children of most senior person in household)

Horizontal

Diagonal

3. Economic and community covariates:

Socio-economic status

Grain price, logged values lagged by one year

Community/village

Time period dummy variables

EVENT HISTORY MODELS