Immigration statistics and the UK census
Nigel Williams, 26 September 2013
The UK census is under threat. A massive effort on the part of volunteers, professionals and the public results in a detailed, valuable description of the country. For something so superficially dry and administrative, the census has triggered some important stories. Never mind the wags calling themselves Jedi (at least they filled in the form). The 1911 census recorded the unfranchised Emily Davison‘s address as the House of Commons after a night in the chapel and of course it was a census that sent Joseph and Mary to Bethlehem. It is a long and important tradition and suggestions to alter it need to be scrutinised.
As well as the detailed information that comes from it directly, the census serves to calibrate all the other more frequent surveys going on. They may feel like an imposition at the time but, without a census, surveys would happen more often and there would be wasted expenditure providing services for the wrong people. Stories about shortages of school places for rising fives or ghost patients registered for GP surgeries depend on the census to get at the true picture. Here is how it works, in microcosm:
Imagine your primary school wants to distribute some road safety advice to all children. Some of them, you understand, are red-green colour blind and will benefit from extra, more expensive material, but you have not time to test every child individually before the distribution. How many copies of the extra material should you order? You test a sample of 50 children and get one boy and no girls positive. Is that enough to go on?
From the test sample, you have an estimate of the proportion, with some idea that there will a margin of error. Before ordering the materials, you need to know how many children are in the whole school. Better still if you know the split between boys and girls. Population proportions depend on a numerator and a denominator. Extra surveys can provide extra numerators but the denominator needs the census, the equivalent of the school register in our example. Notice also that the extra information about gender can improve efficiency. Sometimes a question applies more to one group than another and our survey money is better spent interviewing more of that group.
Migration statistics offer a parallel. If local councils are providing support for women escaping from domestic violence, they may want to predict whether support staff will need to speak, say, Welsh, English, Polish or Urdu.
There is a second way in the which the census corrects what surveys can tell us. Well-designed surveys can infer remarkably accurately about people not in the sample provided they are similar to people that were included. The census includes everyone in its sample, so it provides the best possible data but it also improves the sample surveys in between by showing how they need to be adjusted.
The Office for National Statistics has published a reconciliation of migration statistics, showing what can get missed. “If the 2011 Census estimates had been unavailable the equivalent mid-2011 population estimate would have been 55,707,000, which is 464,000 (0.8 per cent) lower than the official figure.” The two largest components are 250,000 from the eight EU accession countries and 66,000 from the Republic of Ireland. With the regular census, that discrepancy gets eliminated or drastically reduced and there is potential to reduce the future divergence. Without it, divergence can only increase and remain uncorrected. Importantly, and contrary to some news coverage, the best information derives from the census. It is not the lowest but the best common denominator.