Lee Williamson CCSR Cathie Marsh Centre for Census & Survey Research The University of Manchester

1. Deriving age-specific fertility rates by ethnic group at the ward level for Bradford: an assessment of 6 promising strategies PhD title:Population projections for small areas and ethnic groups - developing strategies for the estimation of demographic rates Lee Williamson CCSR Cathie Marsh Centre for Census & Survey Research The University of Manchester lee.williamson@postgrad.manchester.ac.uk

2. Background to research project • The PhD is CASE partnered with Bradford MDC using data provided by Bradford MDC • Core problem of creating demographic rates to be used in population projections where there is very little data available (small areas, ethnic groups or both) • Different strategies of both methodological approach and data sources will be used to provide the estimates of the demographic rates • The impact of the demographic rates will be assessed by implementing the rate estimates in projection software Popgroup provided by Bradford MDC. • This presentation will focus only on fertility rates

3. Overview of Presentation Overview: • Introduction to the Bradford district • Introduction to the 6 different sets of age-specific fertility rates (ASFRs) • Assessing the 6 different sets of rates by using them in population projections and comparing projected births against actual births (1) ethnic group at the ward-level for 1991-1998 (2) at the ward-level only for 1991-2000 • Discussion of findings Overall to compare the 6 sets of ASFRs in population projections in order to assess whether using detailed ethnic-specific ward-specific information produces the more accurate projected births

4. Bradford Metropolitan District in 1991 • Bradford is a multicultural district • 30 wards • Ward sizes range from 13,000 to 23,000 • Total population 480,000 (1991)

5. The 6 different sets of age-specific fertility rates (ASFRs) I. GAD England rates for 1991 (Government Actuary Dept. from the England national-level population projections) All other sets of ASFRs were created with using maternity records that record ethnic group, using an average of 5 years worth of births (1989-1993) for 1991 rates II. Bradford district rates III. Ethnic group only rates at the district level (smoothed by the Hadwiger function due to ragged ASFRs) IV. Ward only rates equal across all ethnic groups (smoothed by the Hadwiger function) The final sets of ASFRs are based on a ‘grouping’ strategy which, overall, grouped wards together based on cluster analysis using fertility level (TFR) and 1991 Census variables which have been used in many deprivation measures and also considering the 1991 ONS classifications for wards. Thus, the ‘groupings’ ASFRs were based on more events (births) and larger populations of childbearing women V. The ‘grouping’ rates specific for each ethnic group (smoothed by the Hadwiger function) • The ‘combined best method’, where there were over 100 births recorded in the 1989-1993 period (average of 20 births) using that ward-specific ethnic group rate and, if not, alternatively using the ‘groupings’ rate (all smoothed by the Hadwiger function) The ‘combined best method’ will either be the ward-specific ethnic group rate, or a ‘grouping’s’ ethnic-specific ward-level fertility rate.

6. 1991 ASFR curves: GAD England and Bradford district Fertility schedules for Bradford district and GAD England in 1991

7. 1991 ASFR curves: ethnic group rate at the district-level Fertility curves for all ethnic groups at the Bradford district-level

8. 1991 ASFR curves: ethnic group rate at the district-level smoothed by the Hadwiger function Fertility curves for all ethnic groups at the Bradford district-level

9. 1991 ASFR curves: ward-level rates smoothed by the Hadwiger function low TFR and high ward TFRs compared with Bradford district (1.98)

10. 1991 ASFRs: the ethnic-specific ‘groupings’ rates *rounded to nearest hundred

11. 1991 ASFR curves: the ethnic-specific ‘groupings’ rates smoothed by the Hadwiger function • 19 sets of fertility rates were smoothed using the Hadwiger curve • Some sets of ASFRs are still very ragged White Indian Suburbia Suburban more established areas

12. Comparing the 6 different sets of ASFRs using projected births against actual births • The different set of age-specific fertility rates being tested for accuracy are: I. GAD England rates II. Bradford district rates III. Ethnic group only rates (smoothed by the Hadwiger function) IV. Ward only rates (smoothed by the Hadwiger function) V. The ‘grouping’ rates specific for each ethnic group (smoothed by the Hadwiger function) VI. The ‘combined best method’ rates (smoothed by the Hadwiger function) • The ‘combined best method’ will either be: ethnic-specific ward-specific rates if over 20 births occurring on average (1989-1993) or the ethnic-specific ‘grouping’ fertility rates

13. Error measure is the Mean Absolute Percentage Error (MAPE) mean absolute percentage error the percentage error (PE) (Makridakis 1998:44) • The problem with using the MAPE is that there must be at least 1 observed birth (Yt) occurring, otherwise it cannot be used (cannot divide by zero). • For example, for ethnic group Black there were 9 wards where there were births occurring, however, due to the small numbers of births occurring the MAPEs could only be calculated for 7 wards.

14. Comparing projected births to actual births for period 1991-1998using the MAPE (for wards with at least 1 birth per year occurring) Ethnic group White Ethnic group Indian

15. Comparing projected births to actual births for period 1991-1998 using the MAPE (averaged over the number of wards, with at least 1 birth per year) Ethnic group White Ethnic group Black Ethnic group Indian

16. Comparing projected births to actual births for period 1991-1998 using the MAPE (averaged over the number of wards, with at least 1 birth per year) Ethnic group Pakistani Ethnic group Bangladeshi Ethnic group Other

17. Considering the results at the ward-level only (for period 1991-2000 from VS data)

18. Conclusions for investigation • The six different sets of rates were first considered by ethnic group at the ward-level. The results differed from what was expected; that is, for some ethnic groups, using the ethnic-specific fertility rates produced the smallest average MAPE. • Second, when considering the errors at the ward-level, results were generally as expected, which is reassuring. Overall, using the ‘combined best method’, 22 of the wards were found to have both an MPE and MAPE of under 10%. It was also discovered that the method which produced the largest number of wards with both MPEs and MAPEs of under 10% (24 wards in total) was using ward-level ASFRs. However, this finding is not the same as the one reported when the births were investigated by ethnic group at the ward level. • In concluding on which method to recommend and when, it is very difficult to make an objective assessment of the findings considering all the different data limitations in both creating the ASFRs and assessing the projected births. For example, the revisions of the ONS population estimates from 1991 onwards, in the light of the 2001 Census results and problems in that the maternity records can be up to a few percent lower than the VS data for which they were compared to at the ward-level.

19. Conclusions for investigation • In discussing more detailed subnational rates, with reference to the migration of the foreign born population in the US by regions, which was what the research paper was focused on, Rogers and Raymer comment: “High levels of disaggregation permit a greater flexibility in the use of the projections by a wide variety of users; they also lead to a detection of greater consistency in patterns of behaviour among more homogeneous population subgroups. But greater disaggregation requires the estimation of even greater numbers of data points, both those describing population stocks and those defining the future rates of events and flows that are expected to occur. The practical difficulties of obtaining and interpreting such data soon outstrip the benefits of disaggregation”. Rogers and Raymer (1999)