1. Overview of Census Evaluation through Demographic Analysis Pres. 3

2. Uses of Demographic Methods of Evaluation
To complement results of matching methods of evaluation to provide further information on likelihood of errors in census data
To assess the quality of census data where no matching methods have been implemented
Data can be from a single or multiple censuses or in combination with other sources, e.g., surveys
Suitability of demographic methods depends on availability of information and on absence or presence of abrupt changes in population

3. Selected Demographic Methods
Presentation briefly covers five categories of methods
Analyses of Age and Sex Distributions
Stable Population Analysis of Age Distributions
Comparison of Successive Censuses using Actual Data on Components of Population Change
Comparison of Successive Censuses using Estimates of Components of Population Change
Analysis of Cohort Survival Rates

4. Analyses of Age and Sex Distributions
Reasonableness of the age-sex distribution of enumerated population provides information on quality of the census
Age-sex distribution for a given level of fertility, mortality and international migration follows a predictable pattern
Unexplained departures from expected distributions signify existence of errors in census enumeration
Limitation of age-sex analysis is difficulty to derive direct estimates of coverage and content error rates and often require use of other methods, e.g., PES to verify findings
It is also difficult to explain source of observed discrepancy between constructed and census enumeration distributions 4 4

5. Analyses of Age and Sex Distributions (Contd.)
Selected Methods:
Ratios and indices providing numeric departures of recorded age-sex distributions from expected distributions
Graphic presentation (population pyramid; cohort analysis)
Age ratios
Sex ratios
Summary indices
Whipples and Myers’ indices (digit preference/age heaping)
Age-sex accuracy index
Stable population theory (stable age distribution)
Quasi-stable population methods due to declining mortality
Internal consistency (e.g., age by marital status) 5 5

6. Analyses of Age and Sex Distributions (Contd.)
Population pyramid:
Example 1: Example 2: 6 6

7. Analyses of Age and Sex Distributions (Contd.)
Distortions in age pyramid could be due to:
Under/over enumeration
Age misreporting (including digit preference)
Changes over time in fertility, mortality, migration
Therefore, additional investigation required…… 7 7

8. Population Pyramid by Single Years of Age

9. Analyses of Age and Sex Distributions (Contd.)
Cohort Analysis:
Single census display
Multi-census display
Size of each cohort should decline in successive censuses due to mortality
Lines for successive censuses should follow same pattern and not cross (in absence of migration and errors in the censuses)
Line for earlier census should be on top of that for later census 9 9

10. Analyses of Age and Sex Distributions (Contd.)
Cohort analysis:
Example 1: Example 2: 10 10

11. Analyses of Age and Sex Distributions (Contd.)
Cohort analysis:

12. Analyses of Age and Sex Distributions (Contd.)
Cohort Analysis (Contd.):
Departure(s) from expected trend suggestive of age misreporting either under-reporting or systematic transfer to adjacent ages (most common at youngest and oldest ages)
Departures may also reflect historical events and not just misreporting (e.g., war resulting in small birth cohorts)
Do not “smooth” the data
Therefore, additional investigation required…… 12 12

13. Analyses of Age and Sex Distributions (Contd.)
Age and Sex Ratios:
Computations of quantitative assessment of “reasonableness” of census age-sex distributions through age and sex ratios
Ratios follow expected predictable patterns in human populations
Unexplained departures from predictable pattern indicative of census error
However, distinguishing effect on age and sex ratios of age and/or sex-selective migration (internal and international) from census error is difficult 13 13

14. Analyses of Age and Sex Distributions (Contd.)
Age Ratios:
Provide measure of “smoothness” of age distribution
In absence of sharp swings in fertility, mortality and migration, enumerated size of cohort equals average of two immediately preceding and subsequent cohorts (i.e., ratio of census count for a cohort to the average of the adjacent cohorts ≈ 1
Sex Ratios:
Number of males to females in an age group
Sex ratio at birth between 102 and 107 but declines with age due to higher male than female mortality 14 14

15. Analyses of Age and Sex Distributions (Contd.)
Age Ratio (contd.): 15 15

16. Analyses of Age and Sex Distributions (Contd.)
Sex Ratio: 16 16

17. Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.):
Sex ratios from current census can be compared to “expected” sex ratios based on previous census(es)
In absence of sex-selective mortality or international migration, sex ratios of total population and age groups/cohorts in successive censuses should be relatively stable from census to census 17 17

18. Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.):
Unexplained fluctuations in sex ratios by age are indicative of variations in coverage or accuracy of age reporting on a sex selective basis from census to census
In absence of census errors or other distorting factors, changes in sex ratios of birth cohorts from census to census should be consistent with sex mortality differentials under current mortality conditions
Where male mortality exceeds that of females, cohort sex ratios would decline from census to census and vice versa if female mortality exceeds that of males 18 18

19. Analyses of Age and Sex Distributions (Contd.)
Sex Ratio (Contd.): 19 19

20. Summary Indices of Error in Age-Sex Data
United Nations Age-Sex Accuracy Index
Whipple’s Index
Myers’ Blended Index
UN recommended index to measure relative importance of age overstatement and understatement in accounting for age heaping 20 20

21. Summary Indices of Error in Age-Sex Data (Contd.)
Since they are summary measures of error in census age and sex data:
Are not substitutes of detailed inspection of data as for the methods previously presented
Do not provide insight into patterns of error in data as is the case with methods just presented 21 21

22. Stable Population Analysis of Age Distributions
Recorded age distribution, by sex, compared to appropriately chosen stable population
Stable age distribution based on assumption of long-term constant levels of fertility and mortality, with no international migration
c(x) = b l(x) exp (-rx)
Where:
c(x) = the infinitesimal proportion of the stable population at age x
b = the constant birth rate
r = the constant rate of natural increase
l(x) = the probability of survival from birth to age x 22 22

23. Stable Population Analysis of Age Distributions (Contd.)
Required data for stable population analysis
The census count of population (which is to be evaluated) by single years of age or 5-year age groups by sex
Estimates of 2 of the following parameters – (a) the growth rate r in the population; (b) the birth rate b; and (c) the probability of surviving from birth to age x (lx function)
[Note that an estimate of the expectation of life at birth e, may be used to select a model life table to represent mortality conditions in the population under review] 23 23

24. Stable Population Analysis of Age Distributions (Contd.)
Few, if any, populations are genuinely stable
For many countries, there are no developed systems of vital and migration statistics
Therefore, parameters b, r, and l(x) used to derive stable age distribution for census evaluation are, for many countries, indirect estimates which are subject to error 24 24

25. Stable Population Analysis of Age Distributions (Contd.)
Computational Procedure:
Step 1 – calculation of proportional age distribution of the census population
C(x) = 5Nx / N *100
Where:
5Nx is the number of enumerated persons aged x to x+4
N is the total population enumerated 25 25

26. Stable Population Analysis of Age Distributions (Contd.)
Computational Procedure (Contd.):
Step 2 – Selection of a model life table
Model stable population chosen based on two of the parameters – r, b, or l(x) in the population
Model stable age distribution calculated by interpolating between print values in model life tables that correspond to two of the parameters – r, b, or l(x) in the population
Step 3 – Comparison of the recorded and stable age distribution, i.e., enumerated population by age/sex divided by stable population by age/sex 26 26

27. Stable Population Analysis of Age Distributions (Contd.)
Computational Procedure (Contd.):
Differences between the recorded and “expected” age distributions could be due to:
Changes in fertility/mortality in the population under study resulting in violation of notion of “stable population”
Age misreporting (overstatement, understatement)
Under-coverage of specific age group (e.g. children)
International migration of specific age segments (young adult males) 27 27

28. Comparison of Successive Censuses using Actual Data
“Expected population” derived using population enumerated at previous census plus information on intercensal births, deaths and net international migration
Population balancing method
P1 = P0 + B – D + M (Population balancing equation)
P1 = Population enumerated in census being evaluated
P0 = Population enumerated in previous census
B, D = Intercensual number of births and deaths
M = Intercensal number of net international migrants
Requires accurate vital statistics and information on international migration 28

29. Comparison of Successive Censuses using Actual Data
For census evaluation purposes, need equation
P1 = P0 + B – D + M + e
Where e is the residual that’s needed to balance the equation
However, values of e are affected by values of P0, B, D and M
Need to evaluate accuracy of data for balancing equation and to make adjustments as necessary before application to evaluation
However, adjustments for migration are problematic due to lack of comprehensive information
To obtain net coverage error in second census, need to adjust first census for net coverage error as well 29 29

30. Population Balancing Equation
Data required:
Population counts from census under evaluation, P1, and from a previous census, P0
If estimate of net coverage error is sought, previous census to be adjusted accordingly. Otherwise, resulting estimate represents relative coverage error of second to first census
Number of intercensal births, deaths, and net international migration, adjusted for under-registration 30 30

31. Comparison of Successive Censuses using Estimates
Where vital registration data are unavailable of very deficient
Indirect estimates of intercensal fertility and mortality levels are available for a demographic survey or current census can be used with previous census to derive an “expected” population
Use of “cohort component” method to project population enumerated at first census to reference date of second census based upon intercensal estimated levels and age schedules of fertility, mortality and migration 31 31

32. Cohort Component Method
Data required:
Population enumerated in two successive censuses by age (either single or five-year age groups) and sex
Life table survival rates by sex assumed representative of intercensal period
Age-specific fertility rate schedule for women years assumed to represent level and age structure of fertility during intercensal period
Estimate of sex-ratio at birth
Estimates of intercensal level and age pattern of net international migration 32 32

33. Cohort Component Method (Contd.)
Computational Procedure:
Step 1 – survival of population enumerated in first census on a cohort-by-cohort basis to second census based on age-specific survival rates from life table assumed representative of intercensal mortality conditions in population under study
Step 2 – Adjustment of “surviving” cohort populations to take into account intercensal migration
Step 3 – Estimation of intercensal number and timing of births on basis of assumed schedule of fertility rates and projected intercensal child-bearing age female population. Births are survived to second census to yield estimate of children under specified age at second census 33 33

34. Cohort Component Method (Contd.)
Concerns:
Like population balancing equation, estimates of error for cohort component method are “residual” estimates which are affected by accuracy of information on components of change and of first census.
Serious concern in countries with unreliable vital statistics where indirect fertility/mortality estimates are used
Indirect estimates may be unreliable due to violation of assumptions underlying techniques and errors in underlying data (age reporting, fertility, mortality data)
Estimating net migration is particularly problematic
Like for population balancing equation, estimates of error are estimates of relative or differential error between the two censuses 34 34

35. Analysis of Cohort Survival Rates
Based upon comparison of the size of birth cohorts enumerated in successive censuses
In population closed to migration, changes in cohort size between censuses is attributed to mortality
In absence of census errors, ratio of persons in birth cohort enumerated in census to those enumerated in first census should approximate survival rate based on prevailing mortality conditions
In closed populations, departures of observed from expected cohort survival rates should indicate census error in one or both censuses
Where net migration is significant, “expected” population should be modified accordingly 35 35

36. Analysis of Cohort Survival Rates (Contd.)
Data required:
Population enumerated in two successive censuses by age and sex
Life table by sex assumed representative of intercensal mortality conditions (based on estimate of level of mortality in population)
Information on volume of intercensal net migration by age and sex 36 36

37. Analysis Cohort Survival Rates (Contd.)
Computational Procedure:
Step 1 – Adjustment of one of the censuses to minimize distorting effects of migration on cohort survival rates (by adding or subtracting number of net migrants to one of the censuses)
Step 2 – Calculation of census cohort survival rates
Step 3 – Calculation of life-table survival rates
Step 4 – Calculation of cohort survival ratios 37 37

38. Analysis Cohort Survival Rates (Contd.)
Observations:
Method requires only two census counts and an estimate of level of mortality for selection of model life table
Knowledge of fertility not required as method does not assess coverage of population born between the two censuses
Where net migration is significant, estimate is required for adjustments to minimize distorting effects
Limitation of method is that when used on only two censuses, it is difficult to separate:
Census errors from other “factual” distortions
Coverage errors from content errors
Utility of method increases significantly when three or more censuses are compared 38 38

39. Thank You! 39 39