Spare a thought for the homeowner trying to work out what is going on in the housing market, let alone the potential first-time buyer. If you’re buying, is it best to wait? And, if you’re selling, should you do so quickly?

It is a confusing time. The statistics are contradictory, the headlines scary. So it is useful to apply a bit of analytical rigour to where housing might be heading. This, I am glad to say, the economists at PricewaterhouseCoopers (PWC), the accountants and management consultants, have done. As a firm, it has no property axe to grind.

Let us start with the basics. By how much are houses overvalued, in Britain compared with their long-run average? PWC’s first answer, based on its housing model, is that prices are 20% higher than they should be. Bring in other factors, such as supply constraints – the lack of new houses relative to the rise in the number of households – and this figure drops to 10%.

An overvaluation is still an overvaluation, so what happens next? PWC has put probabilities on various outcomes. On the sensible assumption that no forecast is ever exactly right, and using a statistical technique known as a Monte Carlo simulation – not, as its name might suggest, a spin on the roulette wheel – the firm came up with some interesting results.

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There is, PWC says, a one in five chance that by the end of 2010, house prices will be lower in cash terms than now. This is split between a 15% probability of a cumulative fall of 0%-10% and a 5% chance of a drop of 10%-30%. Mainly, though, the odds favour continued, if more muted, house-price rises: a roughly 30% probability of an increase of 0%-10% over the next three years; a 32% chance of a 10%-20% rise; and a 15% probability of prices climbing 20%-30%. While PWC sees only a 3% probability that prices will go up by 30%-40% by 2010, it completely excludes a fall of more than 30%.

“There is clearly some risk of house prices falling over the next three years, but these risks are mitigated by continuing housing-supply constraints,” says John Hawksworth, PWC’s chief economist. “The most likely scenario is a slowdown in the housing market rather than an outright fall in prices.” The chances of a fall in “real” house prices – adjusted for inflation – are rather greater, but still only one in three, according to PWC.

People will have their own views on this, and any forecast is only as good as the assumptions on which it is based and the model used. On one thing, however, the forecast appears uncontentious: while there is a minority view around that house prices are about to enter a Rip Van Winkle slumber from which they will not emerge for years, it is a fact of economic history that, over time, house prices rise by more than inflation.

So, when PWC looks forward to 2020, it sees less than a 1% probability that house prices in cash terms will be lower than now, although there’s a one in six chance that they will not be any higher in real terms. More likely, they will continue to outstrip inflation even if the government provides the 3m extra new homes Gordon Brown promised last week. The question is by how much.

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