Local authorities have been urging people to complete their Census forms, warning them that a failure to do so will cost their local authority millions of pounds in lost grants.
 
But the claims vary widely. Liverpool, which believes its population was undercounted by 10,000 people in 2001, says a similar undercount this time would cost it at least £150 million in lost funding over the next ten years – that’s £15,000 per head, or £1,500 per head per year. (Source: Liverpool Echo)
 
Cardiff claims it was undercounted by 22,000 last time, and lost £85 million since: that’s around £4,000 per head, or £400 per head per year. (Source: Rodney Berman, leader of the council, on the BBC Politics show yesterday.)
 
Halton, the borough that covers Runcorn and Widnes, says that every completed return will benefit it by £5,000 over ten years, or £500 per head per year (Runcorn and Widnes World) while Maidstone claims that a 4 per cent undercount of its 140,000 population in 2001 cost the borough £30 million, or (by my reckoning) £535 per head per year.
 
Last year, a report from the London Councils, Counting the Cost, said an undercount of 10,000 could lose the borough suffering it more than £60 million over ten years, or £600 per head per year, counting only “formula grant” – the main but not the only grant affected by population numbers.    
 
Anything to encourage participation in the Census, but there is only a fixed sum of money available for distribution. If we managed to count an extra million people thanks to these initiatives, evenly distributed across the country, it would not produce an extra £5 billion of spending over the next decade. The count might be better but the distribution of the money would remain unchanged.
 
The strategy only has a chance of producing a benefit if your area was genuinely undercounted last time, which doesn’t appear to apply, for instance, to Maidstone. The citizens of Kent’s county town returned 96 per cent of their Census forms, well above the national average, in 2001. Raising that to 97 per cent wouldn’t have made any difference, because the missing 4 per cent weren’t simply forgotten. They were added by using estimated data. It is only if you believe those estimations have failed to do you justice that you have actually lost any money at all.
 
What is the evidence that the adjustments failed? Many local authorities are convinced if it. The 2001 Census counted 48.8 million people in England and Wales, and added another 3.2 million it estimated had been missed, to reach a population of 52 million. But this was still 1.1 million shy of the expected population based on births, deaths and migration monitored in the 1980s and 90s.  
 
The adjustment meant that for some local authorities, there were 20,000 people appearing in their local count who had not been counted at all, but had been estimated. But if 20,000, why not 30,000?  According to a report by Ludi Simpson, Professor of Population Studies at the University of Manchester, these adjustments were made by the ONS in a formulaic way and some are likely to be significantly wrong, by up to 10,000 in some authorities.
 
For areas with a large undercount, confidence in the final figures must be lower because they have been subject to a greater degree of correction. The chances are that the 2011 Census will show undercounts in the same areas as the 2001 Census – many London boroughs had a response rate of under 80 per cent last time – and among the same groups of people: those renting privately, minority ethnic communities, single-person households, those paying part rent, part mortgage, and those aged 23-34, especially men.
 
The principal method for filling the gaps will be the Census Coverage Survey, an independent re-enumeration of about 320,000 households - about 1 per cent of total households in England and Wales - during a four-week period between 9 May and 2 June. The households and people counted are then matched with those recorded in the Census, so an estimate can be made of the numbers and characteristics of those who were not counted by the Census.
 
The problem is that the very same people who are hard to reach with Census forms are also hard to reach in the Coverage Survey. The 2001 Census had a lower response rate than did the one in 1991, lower still in the hard-to-count areas, despite considerable efforts. The strategy adopted in 2001 was not effective in reducing differential undercounting, and it remains to be seen whether the 2011 strategy will do any better.
 
It will try to do so by making an estimate of the number of households and people missed by both the Census and the Survey. But at local authority level there may be too few households in the Survey to comprise a representative sample, and then statistical modelling techniques will be used, using data from other local areas, to top up the population estimates.
 
The final figure will come with a 95 per cent confidence interval around the Census population estimate. But that, of course, means that one in 20 may fall outside the confidence interval – 21 local authorities in the UK. There is no way of identifying which these are.
 
The local authorities who have reason to feel they were cheated in 2001 and are urging people to complete the forms are not necessarily wrong. The higher the count, the lower the degree of estimation needed, and the lower the final error is likely to be. But it won’t make a huge difference, and none at all to the likes of Maidstone.
 
Some people fill in the forms twice, possibly because they have two homes. Overcounting emerged in the 2001 Census, where the final estimate was that 0.4 per cent of the population were counted twice – and no adjustments at all were made. This time, with the opportunity to complete the form online as well as on paper, the chances of overcounting are much greater, particularly as the number of people with two homes is increasing.
 
But nobody, so far as I can see, is complaining that their population was overcounted.