1. Methodology for producing the revised back series of population estimates for 1992 - 2000 Julie Jefferies Population and Demography Division Office for National Statistics

2. Outline of Presentation 1. Why did the back series need to be revised? 2. The approach taken in 2001, compared to 1991 3. Explaining and quantifying the difference 4. The remaining difference 5. Possible methods for apportioning the remaining difference 6. Development of the final national method 7. The sub-national back series

3. 1. Why did the back series need to be revised? Population estimates provide estimates of the population in the years between censuses. Following each census there is a new base or starting point. A discontinuity occurs in the time series as a result of changing the base.

4. Population estimates for 1991-2001 (based on 1991 Census) and 2001 population estimate (based on 2001 Census)

6. 2. Approach taken in 2001 vs. 1991 Following the 1991 Census: A method for revising the 1980s back series had already been selected prior to the census –interim revised estimates produced using simple period method (easy and quick to calculate) –final revised estimates produced using the more sophisticated linear cohort method There was no …. examining of the reasons for the divergence evaluation of different methods … and the final method used was much simpler!

7. Approach taken in 2001 vs. 1991 In 2001, a three stage approach was used: 1. Examine the reasons for the difference 2. Quantify the impact of these reasons on the estimates over previous decade and adjust the back series 3. Apportion the remaining difference –Examine a range of methods –Select the most appropriate method

8. 3. Explaining and quantifying the difference The difference may be caused by: a) Issues with using the 2001 Census data (in its raw form) as a base for the mid-2001 population estimates. b) Accumulated error in the population estimates over the intercensal period – population drift. Possible causes - shortcomings in methodology or data sources, definitional issues.

9. Population estimates for 1991-2001 (based on 1991 Census) and 2001 population estimate (based on 2001 Census)

10. 2001 Census data A number of studies examining the reason for the difference were carried out. These included: –Demographic analysis of sex ratios, fertility, mortality and migration –Analysis of the Longitudinal Study –Comparisons with administrative sources –Investigation of census data and processes –Matching studies of address lists collected by local authorities and those held by census –The Local Authority Population Studies

11. Impact Conclusion: an adjusted Census base should be used for the mid-2001 population estimates. Hence the final rebased mid-2001 population estimate (September 2004) was 275,000 higher than the original rebased estimate: 193,000 due to LS adjustment and other adjustments in September 2003. 82,000 due to Local Authority Population Studies and consequential adjustments.

12. Intercensal population estimates Two quantifiable sources of error were also identified in the population estimates: 1. The mid-1991 population estimates were too high because they included too big an adjustment for undercoverage in the 1991 Census. 2. Difficulties in the estimation of international migration during the 1990s resulted in an overestimation of population growth.

13. Impact 1. Mid-1991 population was revised downwards and rolled forward over the decade. The rolled-forward mid-2001 population estimate was reduced by 351,000. 2. Following thorough methodological research, international migration estimates for the 1990s were revised. The rolled forward estimate for mid-2001 was reduced by 305,000.

14. Impact of quantifying these differences

15. 4. The remaining difference Remaining difference = 209,000 Possible causes e.g. issues to do with the concept and measurement of usual residence (including changes in residence status that do not involve a migration) remaining differences in estimating international migration births to non-resident mothers Not possible to separately quantify these causes at present.

16. The remaining difference

17. 5. Apportioning the remaining difference Two main methods: period cohort Within these methods, choice of: simple (linear) weighted (by…..)

18. Period Period effect: where the error is related to a particular age, i.e. the estimates for those of that age are drifting further and further away from the truth E.g. Each year we were underestimating the number of students (age 18) leaving an area to go to university or leaving the UK on a gap year

19. Simple period example 1 For 20 year old males, difference between rolled forward 2001 estimates and rebased 2001 estimates is: 6240 Actual error each year: 1992199319941995199619971998199920002001 16437 17352 18911 191595 20624 21974

20. Simple period example 2 Accumulated error: This is what the existing back series estimate needs to be adjusted by. 1992199319941995199619971998199920002001 1643787413111748218526223059349639334370 1735270410561408176021122464281631683520 18911182227333644455554666377728881999110 1915953190478563807975957011165127601435515950 20624124818722496312037444368499256166240 21974194829223896487058446818779287669740

21. Cohort Cohort effect: where the error is related to a particular group of people i.e. the error for this birth cohort built up gradually over the decade as they got older. E.g. in the rolled forward 2001 estimates, we have too many 45 year old males. This could be because over the decade some people born around 1956 spent periods of time abroad and were not identified as out-migrants.

22. Linear cohort example 1 For 45 year olds, difference between rolled forward 2001 estimates and rebased 2001 estimates is: 2860. Actual error each year: 1992199319941995199619971998199920002001 36 286111223715127622101859195023231707 37 21428611122371512762210185919502323 38 2432142861112237151276221018591950 39 446243214286111223715127622101859 40 23744624321428611122371512762210 41 5712374462432142861112237151276 42 357571237446243214286111223715 43 368357571237446243214286111223 44 221368357571237446243214286111 45 241221368357571237446243214286

23. Linear cohort example 2 Accumulated error: 1992199319941995199619971998199920002001 36286222669286063801326013013156002090717070 372145723338923575765615470148721755023230 38243428858444111542908932176801673119500 39446486642114455513385005102081989018590 402378927298561430666156157201148422100 415714741338972107017167771784643512760 423571142711178412151284200288820077150 43368714171394822301458149822889992230 4422173610712284118526761701171225741110 4524144211041428285514223122194419262860 This is what the existing back series estimate needs to be adjusted by.

24. Period + cohort combination? Generally we pick whichever effect is likely to be dominant or best approximates the true situation. A combination of both the period and cohort effects may be closest to reality. Using a combination method is complex - need to decide for each age group what proportion of the error is due to a period effect and what is due to a cohort effect. Then need to apply constraints to ensure that the final error by age is correct. For the 1992 to 2000 back series we started out using a cohort method (more later)…..

25. Simple (linear) vs. weighted Examples so far have assumed a simple (or linear) effect A linear method: weights each year of the decade equally (divides difference by 10) is easier to calculate and understand than a weighted method assumes whatever is causing the difference will have an equal impact in each year, which may not be the case

26. The weighted method A weighted method: weights each year of the decade by a different amount i.e. allocates a varying amount of the difference to each year. may be appropriate if the difference is likely to be driven by or correlated with a quantifiable factor this factor varies over time or by age (or both) weighted methods are much more complex

27. Developing the final national method The intercensal drift was thought to be correlated with migration (in particular out-migration from an area). We know that: Propensity to migrate varies with age Levels of migration change over time Apportion difference back over cohort according to propensity to out-migrate by age (IPS data). In addition, weight the difference according to level of migration (all ages over time).

28. Calculating migration age weights 1 1992199319941995199619971998199920002001Total M40634183777921088906503305617452408397123930 M4116785705662017535571152159713317629168 M429084621258255948912421169360108347410003 M43182118254011410165859701805467232312307 M4478191177049210926983738864716146817 M45541142807252486123985317231239143811671 M46233258363044260911741658288895205910571 M4715991138114759838117511219210999007340 M4815404801154391063117148111873726768434 M49592870037362616811205904289296208 IPS out-migration data for males:

29. Calculating migration age weights 2 1992199319941995199619971998199920002001Total M40 2393 23930 M41 917 9168 M42 1000 10003 M43 1231 12307 M44 682 6817 M45 1167 11671 M46 1057 10571 M47 734 7340 M48 843 8434 M49 621 6208

30. Calculating migration age weights 3 1992199319941995199619971998199920002001Cohort Total M402393 23287 M41917 21078 M421000 19144 M431231 17458 M44682 15054 M451167 13772 M461057 12638 M47734 11872 M48843 11173 M49621 10645

31. Calculating migration age weights 4 1992199319941995199619971998199920002001Cohort Total M400.2250.2140.2020.1890.1740.1590.1370.1250.1140.1031.000 M410.1000.0860.0820.0770.0730.0670.0610.0530.0480.0431.000 M420.1110.1090.0940.0900.0840.0790.0730.0660.0570.0521.000 M430.1430.1360.1340.1160.1100.1040.0970.0890.0820.0701.000 M440.0870.0790.0760.0740.0640.0610.0570.0540.0500.0451.000 M450.1470.1480.1360.1290.1270.1100.1040.0980.0920.0851.000 M460.1450.1330.1340.1230.1170.1150.0990.0950.0890.0841.000 M470.1120.1010.0920.0930.0860.0810.0800.0690.0660.0621.000 M480.1370.1290.1160.1060.1070.0980.0940.0920.0790.0751.000 M490.1070.1010.0950.0850.0780.0790.0720.0690.0670.0581.000

32. 1992199319941995199619971998199920002001 Total1068759615591957854309366892931103305108511133227123544 Factor1.0320.9280.8880.8250.9040.8970.9981.0481.2861.193 Calculate grossing factors to show how out- migration for each year compares to the average out-migration for the decade T otal out-migration for decade (all ages) = 1,035,604 Average migration per year = 103,560 Grossing factor for 1992 = migration in 1992 (106,875) 103,560 Calculating migration time weights

33. 1992199319941995199619971998199920002001 M400.2250.2140.2020.1890.1740.1590.1370.1250.1140.103 M410.1000.0860.0820.0770.0730.0670.0610.0530.0480.043 M420.1110.1090.0940.0900.0840.0790.0730.0660.0570.052 M430.1430.1360.1340.1160.1100.1040.0970.0890.0820.070 M440.0870.0790.0760.0740.0640.0610.0570.0540.0500.045 M450.1470.1480.1360.1290.1270.1100.1040.0980.0920.085 M460.1450.1330.1340.1230.1170.1150.0990.0950.0890.084 M470.1120.1010.0920.0930.0860.0810.0800.0690.0660.062 M480.1370.1290.1160.1060.1070.0980.0940.0920.0790.075 M490.1070.1010.0950.0850.0780.0790.0720.0690.0670.058 Age weightings: 1992199319941995199619971998199920002001 Factor1.0320.9280.8880.8250.9040.8970.9981.0481.2861.193 Time weightings:

34. Age weights * time weights 1 1992199319941995199619971998199920002001 M400.2320.1990.1790.1560.1570.1430.1370.1310.1460.123 M410.1030.0800.0730.0640.0660.0600.0610.0550.0620.052 M420.1140.1010.0830.0740.0760.0710.0720.0700.0740.062 M430.1480.1270.1190.0950.1000.0930.0970.0940.1050.084 M440.0890.0740.0670.0610.0580.0550.057 0.0640.054 M450.1520.1380.1210.1070.1150.0980.1040.1030.1190.101 M460.1500.1240.1190.1020.1060.1030.099 0.1150.100 M470.1160.0930.0820.077 0.0730.0800.0720.0850.074 M480.1420.1200.1030.0880.0970.0880.0930.0960.1020.090 M490.1100.0940.0840.0700.071 0.072 0.0870.070

35. Age weights * time weights 2 1992199319941995199619971998199920002001Cohort Total M400.2320.1990.1790.1560.1570.1430.1370.1310.1460.1231.000 M410.1030.0800.0730.0640.0660.0600.0610.0550.0620.0521.000 M420.1140.1010.0830.0740.0760.0710.0720.0700.0740.0621.000 M430.1480.1270.1190.0950.1000.0930.0970.0940.1050.0841.000 M440.0890.0740.0670.0610.0580.0550.057 0.0640.0541.000 M450.1520.1380.1210.1070.1150.0980.1040.1030.1190.1011.000 M460.1500.1240.1190.1020.1060.1030.099 0.1150.1001.000 M470.1160.0930.0820.077 0.0730.0800.0720.0850.0741.000 M480.1420.1200.1030.0880.0970.0880.0930.0960.1020.0901.000 M490.1100.0940.0840.0700.071 0.072 0.0870.0701.000

36. Applying the weights 1 1992199319941995199619971998199920002001 Diff M40-15530 M41-8562 M42-2509 M431283 M441391 M45-2890 M46-275 M47-2168 M48-2738 M491270

37. Applying the weights 2 1992199319941995199619971998199920002001 Diff M40295-544-388-43-454198175-329-1251-1904-15530 M41-429102-199-138-18-1738471-155-444-8562 M42-262-421106-202-165-19-2099795-156-2509 M43-299-290-495121-273-202-27-2711461081283 M44126-149-154-25574-150-124-16-184751391 M45-1854194-244 -478125-285-223-33-292-2890 M46791-1511168-206-243-430126-271-248-27-275 M47520494-1003108-156-167-33292-231-160-2168 M48-479538543-1071136-178-214-400129-247-2738 M4985-317379371-864100-146-165-362881270

38. Applying the weights 3 1992199319941995199619971998199920002001 M40 295-835-874-130-1707956989-2130-7980-15147 M41 -429396-1034-1012-148-188010411059-2284-8425 M42 -262-849502-1237-1177-167-208911381154-2440 M43 -299-552-1345623-1509-1379-194-236012841262 M44 126-449-706-1599697-1659-1503-209-25441359 M45 -1854319-693-950-2078822-1944-1726-242-2836 M46 791-3365487-898-1193-2507948-2216-1975-269 M47 5201285-4369595-1055-1360-28391039-2447-2135 M48 -47910581828-5440731-1233-1574-32391169-2694 M49 85-79614362200-6304831-1379-1739-36011257

39. Applying the weights 4 1992199319941995199619971998199920002001 M40 298-849-887-132-17399791005-2189-8111-15530 M41 -434400-1051-1028-151-191510651077-2348-8562 M42 -264-861507-1257-1196-170-212911641173-2509 M43 -304-557-1362630-1534-1401-198-240413141283 M44 128-455-711-1620704-1686-1527-213-25921391 M45 -1880326-703-958-2105830-1976-1754-247-2890 M46 796-3411497-911-1202-2540957-2252-2006-275 M47 5331294-4429608-1070-1371-28761050-2487-2168 M48 -49410841840-5514747-1251-1586-32821181-2738 M49 87-82114722214-6391848-1399-1753-36481270 This is what the existing back series estimate needs to be adjusted by.

40. Story so far…. The 1992-2000 back series was revised using a: Cohort method Weighted by out-migration Migration weights varied by both age and time QA – weighted cohort method worked well for nearly all ages….. But still some issues with teenagers Following QA and further research, a period adjustment for teenagers was included …so the final method was a weighted combination method!

41. Period adjustment 1 Introduced to address a specific issue for 18 and 19 year olds Analysis of the results obtained using the weighted cohort method suggested that there was a significant period effect associated with these ages which had not been allowed for This is possibly due to people taking ‘gap years’ abroad at ages 18 and 19

42. Period adjustment 2 A proportion of the difference observed at age 18 and 19 was allocated using a time-weighted period method This proportion was determined by comparing the relative size of measured migration at 18 and 19 year olds with migration levels at younger ages The remainder of the difference was allocated using the cohort method

43. Final rebased back series (published Oct 04)

44. 7. Sub-national back series (published Oct 04) Each local authority calculated separately using method as for national estimate. –For the age weights, the national distribution was used. –For the time weights, both international out-migration (IPS) and internal out-migration were used. Final LA estimates for each year constrained to national estimate. QA – sex ratios and time series.

45. QA – sex ratios

46. QA – time series

47. Contact details: www.statistics.gov.uk/popest email: pop.info@ons.gsi.gov.uk tel: 01329 813318 Any questions?