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Overview of Census Evaluation through Demographic Analysis Pres. 3

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- 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

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

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

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)

Population pyramid:

Example 1:Example 2:

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……

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

Cohort analysis:

Example 1:Example 2:

Cohort analysis:

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……

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

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

Age Ratio (contd.):

Sex Ratio:

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

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

Sex Ratio (Contd.):

Indices:

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

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

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

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]

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

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

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

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)

“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

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

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

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

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 15-49 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

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

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

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

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

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

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

Thank You!