Evaluation of Census Data using Consecutive Censuses United Nations Statistics Division Demographic Statistics Section

1. Evaluation of Census Data using Consecutive Censuses United Nations Statistics Division Demographic Statistics Section

2. Methods for comparison of data from censuses Three methods; • Population balancing equation • Cohort component method • Intercensal cohort survival rates

3. Population balancing equation If a country; • Has a relatively complete systems of vital registration • Has a fairly reliable estimate of the degree of under-registration • 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.

4. 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)

5. 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

6. 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 under-enumerated relative to P0 • If a positive residual is required to balance the equation, P1 is over-enumerated relative to P0

7. 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)

8. 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)

9. 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

10. 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)

11. 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.

12. 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

13. 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

15. 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

16. Cohort component method • Computational procedure: • Step 1:Population enumerated in the first census surviving to the second census taking into account intercensal mortality 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: the number of life table person-years lived in the age interval x to x+n nLx+i: the number of life table person years lived in the age interval x+i to x+i+n

17. Cohort component method • For the oldest age category (open-ended) • W= the oldest age attainable in the population (exp.85 years and older) • i= the length of the projection interval • wSx= the life table survival rate for the population aged x and above • wTx= 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

18. Cohort component method • A preliminary expected population at the end of projection period (nP1x+i) • nP1x+i = nP0x * nSx • Example: First census in 2000(P0) and second in 2005(P1), for age 10 at the time of first census

19. 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: • Assumptions: i) An equal distribution of net migrants across years of the intercensal period, ii) same fertility and mortality level as the enumerated population

20. 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

21. Cohort component method • Step 4: Estimation of the number of births during the projection • period

22. 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 • If sex ratio at birth is 1.05 • Proportion of female births= 0.488 • Bf = B * 0.488

23. Cohort component method • Step 6: Surviving intercensal births to the end of the projection period 5Pf0 = Bf * 5S0 • 5Pf0= the “expected” population of females aged 0 to 4 • Bf = female births during the projection period • 5S0 = life table survival ratio from birth to age 5

24. 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

25. 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

26. MORTPAK Software

29. COUNTRY EXAMPLES • Philippines • Indonesia • Turkey

31. 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.

34. 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

37. 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

39. 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

40. 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

41. Cohort survival rates • Intercensal cohort survival rates are defined as: i= length of the intercensal period nP1x+i=the population aged x+i to x+i+n years enumerated in the second census nP0x= the population aged x to x+n in the first census

42. Cohort survival rates • The ratio of the observed intercensal cohort survival rate to the corresponding life-table survival rate i= length of the intercensal period nP1x+i=the population aged x+i to x+i+n years enumerated in the second census nP0x= the population aged x to x+n in the first census nLx+i= 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

43. 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

44. 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

45. 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)

47. 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

48. 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

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