Changes to Internal Migration methodology for English Subnational Population Projections Robert Fry & Lucy Abrahams

Overview Introduction Background to subnational population projections Internal migration and the Rogers curve methodology Methodology Review of the Rogers curve Analysis of two subnational projections: With the Rogers curve Without the Rogers curve Conclusions

Background English subnational population projections project 25 years into the future Use trend data for each component to project current trends 25 years into future Cohort component method –Starting Population – mid-year population estimates 2006 –Remove the armed forces (static population) –Add births –Subtract deaths –Adjust for internal migration –Add net international migration –Add armed forces back in –This process is then repeated to give a 25-year projection

Background Developing a new production system for the English subnational population projections provided an opportunity to: Review & change elements of the methodology Build an efficient system with up-to-date software, which has the ability to cope with methodology changes. Focus on internal migration methodology Is using the Rogers curve still appropriate for the 2008-based English subnational projections?

Internal Migration Capture moves within England at the local authority level (broken down by age & sex) Data source: Patient Register data (PR) Calculate the probability of moving out of a local authority (LA): number of people moving out of an LA The total number of people living in an LA

Internal Migration 5 trend years of data ( ) Calculate the out-migration probabilities for each of the years individually and then take a five-year average a = Local Authority g = Sex i = Age T = First year of the projection j = Year MOUT(a,g,i,T-j)= Moves out of a local authority P(a, g, i, T-1)= estimated population in year 1 YR(a, g, i) = raw probability of migrating from a

Out-migration Probabilities Out-migration Probabilities for Males in Leicester

Out-migration Probabilities Out-migration Probabilities of Females in Gloucester

The Rogers Curve This out-migration profile was first described by Andrei Rogers in 1981 The out-migration profile shows: The pre-labour force curve The labour-force peak The post-retirement curve Different models of out-migration The Rogers curve with varying numbers of parameters describes four different models of out-migration

The Four Models of Out-migration

Current Methodology We apply a 13-parameter curve to the raw out-migration probabilities: The pre-labour force curve The labour force peak The retirement peak The post-retirement peak Origins of using the Rogers curve Applied originally to survey data The model produced more reliable out-migration probabilities than the survey data The out-migration profiles of the 1990s were modelled well by the Rogers curve

Methodology Review: Rogers Curve Change to the out-migration profile in many local authorities Out-migration Probabilities of Females in Mid Bedfordshire

Methodology Review: Rogers Curve Out-migration Probabilities of Males in Chiltern

Methodology Review: Rogers Curve The Rogers curve does not model the data well in these areas A ‘student peak’ appears at age 18/19 Applying the Rogers curve to the data means we are not projecting on current trends Improving Migration Statistics branch making improvements to the PR data – using Higher Education Statistics Authority (HESA) data to capture more student moves. Use of the Rogers curve would undo the effects of the additional HESA data What impact does removing the Rogers curve have on the projection?

Investigation In theory the current Rogers curve is no longer suitable for our application What effect would its removal have on the population projections?

Areas with out-migration student peaks What would we expect? Lower net migration when raw out-migration probabilities are used compared to when the Rogers curve is applied? Lower proportion of young adults in standardised age-profile?

Mid Bedfordshire (Females) – Out-migration probabilities

Mid Bedfordshire (Females) – Net internal migration numbers

Mid Bedfordshire (Females) – Standardised age profile – 2019

Harrow (Males) – Out-migration probabilities

Harrow (Males) – Net-migration numbers

Harrow (Males) – Standardised age profile – 2019

Areas with similar out-migration probabilities What happens in areas where the raw out- migration probabilities are similar to the Rogers curve probabilities? Somewhat dependant on the area. Does the area typically draw in young adults?

Origin-Destination Matrix Out-migration probabilities define how many people leave an area These migrants need a destination Origin-Destination matrix is a set of conditional probabilities giving the probability of someone moving to a destination dependant on that person leaving a given origin Generated using the same PRDS data No models used

Areas with similar out-migration probabilities Student area = significantly higher numbers of young adult in-migrants Non student area = modest increase in young adult in-migrants

Nottingham (Males) – Out-migration probabilities

Nottingham (Males) – Net internal migration numbers

Nottingham (Males) – Standardised age profile – 2019

Nottingham (Males) – In-migration standardised age profile

Plymouth (Males) – Out-migration probabilities

Plymouth (Males) – Net internal migration Numbers

Plymouth (Males) – Standardised age profile – 2019

Plymouth (Males) – In-migration standardised age profile

West Lancashire (Females) – Out-Migration Probabilities

West Lancashire (Females) – Net internal migration numbers

West Lancashire (Females) – Standardised age profile

West Lancashire (Females) – In-migration standardised age profile

What has this initial exploration shown us? Differences between projections using the two sets of probabilities are predictable Raw out-migration probabilities produce results that follow the observed trend data

Conclusions The use of the Rogers curve in its current form no longer seems appropriate to use in the English SNPPs for several reasons: We no longer use sample data (fewer problems establishing firm trends with our data) It no longer fits our current trend data HESA data supply Using raw out-migration probabilities appears to improve our projections

Further work Further explore differences between use of raw out-migration probabilities and Rogers curve (Come to firmer conclusions) Look at the possibility of extending the Rogers curve to include the student peak. Look at the possibility of using non- parametric techniques

Further work Explore the approach we take in small areas where the raw data doesn’t establish a trend (e.g. City of London and Isles of Scilly) Expert Panel (October) Publication (Spring 2010)

Questions?