Transcript Evaluation of Census Data using Consecutive Censuses United Nations Statistics Division Demographic Statistics Section Sub-regional Workshop on Census Data Evaluation, Phnom Penh, Cambodia, 14-17 November.

Evaluation of Census Data using
Consecutive Censuses
United Nations Statistics Division
Demographic Statistics Section
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Methods for comparison of data from censuses
Three methods;
 Population balancing equation
 Cohort component method
 Intercensal cohort survival rates
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
If a country;
 Has a relatively complete systems of vital registration
 Has a fairly reliable estimate of the degree of underregistration
 Information on the number of intercensal births, deaths and
net international migrants can be used in conjunction with
the results of a previous census to evaluate the coverage of
a subsequent or current census.
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
P1 = P0 + B – D + M
Where:
P1=the population enumerated in the census being evaluated
P0= The population enumerated in a previous census
B = the number of births in the period between two censuses
D= the number of deaths in the period between two censuses
M= the number of net international migrants in the period
M = I (Immigrants) – E (Emigrants)
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
The logic underlying the balancing equation;
 The population of a country can increase or decrease
between any two points in time only as a result of births,
deaths and movement of population across national
boundaries
 Births and immigration add to the population
 Deaths and emigration reduce the population
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
 For census evaluation purposes, the “residual (e)”
quantity needed to make the equation balance exactly
 “e” in the equation is referred to as the “error of closure”
and represents an estimate of the relative coverage error
in the two censuses
P1 = P0 + B – D + M + e
 If a negative residual quantity e, P1 is underenumerated relative to P0
 If a positive residual is required to balance the
equation, P1 is over-enumerated relative to P0
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
Data required;
 The population enumerated for two consecutive censuses
 P1: the census under evaluation
 P0: previous census
 The number of births, deaths and net international
migration (immigrants-emigrants) during the intercensal
period, adjusted for under-registration (to the extent
possible)
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
Computational procedure
 Adjustment of registered numbers of intercensal births, deaths
and migrants
 Vital registration system
 Immigration record system (residence permit, border records, etc.)
 Adjustment based on under-coverage of these systems including
indirect estimates
 Computation of the “expected” census population
E(P1) = P0 +B- D + M
 Calculation of the residual error or error of closure
e = P1 – E(P1)
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
Interpretation of “e” :
 If P0 has been adjusted for net coverage error, the
estimated residual error (e) will represent an estimate of
net coverage error in P1
 If “e” is positive, P1 is overenumeration
 If “e” is negative, P1 is undercoverage
 If P0 is not adjusted, “e” will represent an estimate of the
relative level of net coverage error in P1 in comparison
with P0
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
Example: Sri Lanka, 1971 and 1981 census
E(P1) = P0 + B
adj
– Dadj + M
adj
= 12,689,897 + 3,716,878 – 1,002,108 + (-446,911)
= 14,957,756
e =E(P1)–P1=14,957,756–14,848,364=109,392 1% of E(P1)
E(P1) = P0 (adjusted)+B
adj
– Dadj + M
adj
= 15,17,655
e = E(P1) – P1 =269,291 1.8 % of E(P1)
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Population balancing equation
Limitations :
 Incomplete and defective data on the components of
population change are very common, therefore,
applicability of the method is limited.
 It is generally not useful for obtaining estimates of net
census coverage error for sub-national populations (for
example regions, provinces). In addition to the
components of population change considered, internal
migration also has to be considered.
 For most practical purposes, the use of the population
balancing equation is limited of net coverage error at the
national level.
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
 This approach is the “projection” of the population
enumerated in the first census to the reference date of
the second census based upon estimated levels and age
schedules of fertility, mortality and migration during the
intercensal period
 The “expected” population is compared with the
population enumerated in the second census
 Intercensal births, deaths and migration are estimated on
the basis of estimates and/or assumptions regarding level
and age schedules of these parameters rather than
directly available data based on registration systems
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Data required:

The population enumerated in two censuses by age and sex

Age specific fertility rates for women aged 15 to 49 (in 5-year
age groups) assumed to represent the level and age structure
of fertility during the intercensal period

Life table survival rates for males and females assumed to be
representative of mortality conditions during the intercensal
period

An estimate of sex ratio at birth

Estimates of the level and age pattern of net international
migration during the intercensal period if the level of net
migration is substantial
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Description of the method: Females Only

“Survive” initial age distribution, 0-4 to 5-9, 5-9 to 10-14, and so
on; open-ended interval requires special handling
 Average initial and projected numbers in ages 15-19, ..., 45-49 to
estimate mid-period female population
 Apply age-specific birth rates to generate total numbers of births
during time period
 Apply sex ratio factor to get total female births from total births
 Apply life table survivorship ratio to determine number of survivors
of births
 Compare the estimated female population by age group with the
enumerated female population
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Computational procedure:
 Step 1:Population enumerated in the first census surviving to the
second census taking into account intercensal mortality
n
Sx 
L x i
n Lx
n
i: the length of the projection interval
nSx:
the life table survival rate for the cohort aged x to x+n at the time of
the first census
nLx:
nLx+i:
the number of life table person-years lived in the age interval x to x+n
the number of life table person years lived in the age interval x+i to
x+i+n
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
For the oldest age category (open-ended)
Tx i
w Sx 
wTx
w
W= the oldest age attainable in the population (exp.85 years and older)
i= the length of the projection interval
w Sx =
the life table survival rate for the population aged x and above
w Tx =
the number of life table persons lived in ages x and above
wTx+i=
the number of life table person-years lived at ages x+i and above
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
A preliminary expected population at the end of projection
period (nP1x+i)
1
nP x+i
=
0
nP x * nSx
Example: First census in 2000(P0) and second in 2005(P1), for age
10 at the time of first census
5 S10
L15

5 L10
5
5
1
105
P
5 P 5 S10
0
10
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 2: Adjusting for migration
 If net international migration is substantial, the “survived”
cohort population must be adjusted to reflect the effects of
migration
 The introduction of net migrants by age group at the mid-point
of the projection period and the survival of net migrants to the
end of the period:
1
1
ˆ
n M x  i  n M x 1 n S x   n M x  i 1 n S x  i 
4
4
Assumptions: i) An equal distribution of net migrants across years of the intercensal
period, ii) same fertility and mortality level as the enumerated population
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 3: Calculation of the average number of women of childbearing age
during the intercensal period in order to estimate the number of births
occurred during the projection period
0
1
P

P
x
x
n
n
n Px 
2
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 4: Estimation of the number of births during the projection
period
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 5: The estimated number of births disaggregated by sex

Proportion of female births =
SRB= Sex ratio at birth


Bf = B * prop. of female births
Bm= B-Bf
1
SRB
1  SRB
 If sex ratio at birth is 1.05
 Proportion of female births= 0.488
 Bf = B * 0.488
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 6: Surviving intercensal births to the end of the
projection period
f
5P 0
= Bf * 5S0

f
5P 0=
4
the “expected” population of females aged 0 to
 Bf = female births during the projection period
 5S0 = life table survival ratio from birth to age 5
5
S0 
1
L0  4 L1
5  l0
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Step 7: Comparison of the expected and enumerated
census populations
 Final step in procedure is to compare the enumerated
population by age and sex in the second population with
the expected population
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Software packages (MortPak, DemProj, etc.) are available
for application of cohort component method
 MortPak has many modules for demographic methods on
fertility, mortality, indirect techniques and population
projection
 Single year projection program will be used in the
exercise
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
MORTPAK Software
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
COUNTRY EXAMPLES
Philippines
Indonesia
Turkey
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Main findings from Philippines example
 Overall difference between the expected and observed populations
is very small for both sexes
 Expected population of females in 15 to 34 age range consistently
exceeds the enumerated population, while the opposite true for
males. This pattern raises the possibility that the migration data
used in deriving the expected population may not be reliable.
 Enumerated population of aged 0 to 4 is likely to reflect under
counting while the same population of aged 10 to 14 reflects over
counting as compared to the expected 1980 population. This may
have shown under enumeration for young population in the 1970
census
 Large excesses of population at age 60 years and over are likely to
reflect highly age misreporting.
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Main findings from Indonesia example
 In terms of overall coverage, the 1980 count was under
enumerated by around 6% for both sexes
 With regard to age;
 The results suggest an under-enumeration of children aged
0-4 years of about 10 % (which may be accounted for
partially by the transfer of population into the 5 to 9 age
category due to age misreporting
 A significant under enumeration of young adults aged 15 to
30 particularly among males
 A significant over-enumeration of population at ages 60 and
above
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Main findings from example of Turkey
 The results suggest 1.5 % (around 1 million)
overenumeration of total population
 With regard to age;
 around 15% overcounting of children aged 10 to 14
 A significant overenumeration of population at ages 80
and over
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort component method
Uses and limitations:
 It is applicable when registration data are not-existent or
deficient to such an extent that satisfactory adjustment is not
possible
 Sufficient information to derive indirect estimates of fertility and
mortality levels should be available
 Lack of information on international migration is the most
problematic aspect of the application of the cohort component
approach
 In case where sufficient information exists to derive reliable
estimates of demographic parameters, the method is perhaps
the most powerful among the alternative demographic
approaches for the evaluation of censuses, since it provides age
and sex specific estimates of net census error
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
 It is based on the comparison of the size of birth cohorts
enumerated in successive censuses
 In the absence of census errors, the ratio of the number of
persons in a cohort enumerated in the second census to the
number enumerated in the first census should approximate the
survival rate that would be expected on the basis of mortality
conditions
 In populations which have experienced significant net
intercensal migration, the “expected” survival rates must be
modified to reflect the effects of migration on the relative size of
cohorts as enumerated in the two censuses
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
 Intercensal cohort survival rates are defined as:
1
P
x i
n
n Sx 
0
P
x
n
i= length of the intercensal period
1
nP x+i=the
census
0
nP x=
population aged x+i to x+i+n years enumerated in the second
the population aged x to x+n in the first census
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
 The ratio of the observed intercensal cohort survival rate to
the corresponding life-table survival rate
1
P
x i
n
n Rx 
0
n P x
Lxi
n Lx
n
i= length of the intercensal period
1
nP x+i=the population aged x+i to x+i+n years enumerated
0
nP x= the population aged x to x+n in the first census
nLx+i=
in the second census
the life table number of person-years lived in the age interval x+i to
x+i+n years
nLx
= the life table number of person-years lived in the age interval x to x+n years
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
 In the absence of census error, the expected value of the
ratio (nRx) would be 1.0
 Ratio values for any particular cohort which exceed 1.0
would indicate overenumeration of the cohort in the
second census relative to the first census
 Ratio values of less than 1.0 would indicate
underenumeration of the cohort in the second census
relative the first census
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
Computational procedures:
Step 1: Adjustment for migration
 In countries experiencing net immigration significant levels of net
intercensal immigration, the number of net immigrants in each
cohort may either added to the cohort enumerated in the first
census or subtracted from the cohort enumerated in the second
census
 In cohorts experiencing net intercensal emigration, the number of
net intercensal emigrants can either added to the second census or
subtracted from the first census
 To eliminate the effects of international migration on the
cohort population for application of cohort survival rates
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Cohort survival rates
Step 2: Calculation of census survival rates using two consecutive
censuses
(nP1x+i
/ nP0x)
Step 3: Calculation of life table survival rates based on the
expected level of mortality
nSx=
( nLx+i/nLx)
Step 4: Calculation of cohort survival ratios (nRx)
n
Rx
1
P
x i
n

0
P
x
n
Lxi
n Lx
n
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Uses and limitations
 It is widely applicable approach for examining error in
consecutive censuses
 It is required relatively little information
 Information on the level of fertility is not required since
the method does not assess the coverage of the
population born between two censuses
 However, for countries which have experienced significant
levels of intercensal migration, an estimate of the volume
and age pattern of net migration during intercensal period
is needed to calculate survival rates
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
Uses and limitations
 When only two censuses are available, the method suffers from
the limitations shared by the demographic methods namely
difficulties involved in separating census errors from other real
distortions
 The utility of census survival approaches increases significantly
when three or more censuses available
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011
THANK YOU …..
Sub-regional Workshop on Census Data Evaluation,
Phnom Penh, Cambodia, 14-17 November 2011