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Measuring Uncertainty inPopulation Estimatesat Local Authority Level

Ruth Fulton, Bex Newell, Dorothee Schneider

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Outline

• Project aim

• Overall method

• Method internal migration

• Method international migration

• Outputs

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Project aim

Improve understanding, measurement and reporting of the quality of population estimates at LA level

• Obtain overall quality measures for annual

population estimates at LA level

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Mid-Year Population Estimates

• Cohort component method

Pop.(t) = pop.(t-1) + births

+ internal net migration

• Determining associated uncertainty is complexMixed sources: Census, administrative sources, surveys

Different estimation methods

+ international net migration

– deaths

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Measuring uncertainty: Overall method

- Components with biggest impact:2001 Census-based estimate

Internal migration

International migration

- Estimate distribution of error for component - Combine error estimates into overall quality measure for MYE at LA level

Error (t) = error (t-1)

+ error (net internal migration)

+ error (net international migration)

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Internal migration

• Estimates based on GP registration data • Sources of uncertainty in estimates related to:

• Migrants missing from GP register

• Time lags between moving and re-registration

• Double counting of school boarders

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Method for internal migration

• Benchmark approach

• Uses adjusted 2001 Census data as benchmark

• Applies model from 2001 to subsequent years

• Limitation – does not cover all quality issues

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Method for internal migration (ctd.)

• Movers in Census: those with other address one year ago

• Movers in PRDS: those with different addresses in two downloadsCensus data adjusted to be as similar to PRDS data

as possible

• Compare observed number of migrants to a ‘true’ number of migrants

• Error represented by scaling factor of truth (Census)/PRDS

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Age pattern

• log(Census/PRDS)• shows double counting of school boarders• shows undercount of young male migrants

Mean log scaling factors for inflows by age and sex

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80

Mea

n ls

f

Males Females

Age

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Geographical variation

- Scaling factors vary by area

- Undercount in urban areas or areas with high proportion of students

- Cluster analysis

Mean log(Scaling Factors)Inflows

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Model

-.5

0.5

1M

ean

pre

dict

ed

log(

sf)

0 20 40 60age

group 1 group 2

group 3 group 4

Mean predicted log scaling factors, Inflows male

• Fit model to log of scaling factors of groups of LAs• Obtain predicted values and residuals

Error measure is obtained by simulating from this distribution

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Distribution of estimated inflows

05.

0e-0

4.0

01.0

015

.002

Den

sity

6000 6500 7000 7500 8000estimated 'true' flow

green: PRDS flow, red: Census (observed truth)example LA

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International migration

• Focuses on intentions-based IPS estimates• Multi-stage approach to distribute to national estimates

to lower levels of geography

IPS direct estimate

Calibrate to Labour Force Survey (LFS) 3 year average

Distribute using IPS 3 year average

Distribute using immigration model

National

Regional

Intermediate (NMGi)

Local Authority (LA)

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• Produce error distribution for statistical error

Bootstrapping approach

Resampling IPS

Resampling LFS (regional level)

Reproduce estimation method with new samples

International migration (ctd)

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Outputs

Outputs• Composite quality measure will be derived from the

overall error distribution• LAs will be banded based on this measure

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Questions?

Contact

dorothee.schneider@ons.gsi.gov.uk

imps@ons.gsi.gov.uk