THERE MAY not seem to be much of an immediate connection, but the news that the Bradford & Bingley is being forced reluctantly to demutualise seems a good moment to revisit the strange and so far unexplained mystery of the divergent house price indices. For many years there have been two prominent indices that track changes in house prices in England & Wales.

Both are prepared by prominent mortgage lenders - one by the Halifax, the other by the Nationwide Building Society. For many years, it was difficult to find much daylight between the results. Suddenly, about two to three years ago, something strange occurred. The two indices began to march at a quite different pace. For most of the past two years, house prices as recorded by the Nationwide have been growing substantially faster than those recorded by the Halifax.

In the third quarter of 1997, the Nationwide index recorded that prices were 12.5 per cent higher than they had been 12 months previously. According to the Halifax, however, the annual rate of increase was barely half that amount, 6.6 per cent. For three quarters in a row the rate of increase shown by the first index was more than double that shown by the second.

Although the gap has narrowed a little more recently, the divergent readings of the Halifax and Nationwide indices continues. Confused? You are not the only one. The divergence between the two indices is noteworthy because the two series had so closely tracked each other before. The fact that they are now marching in different directions casts an obvious doubt over their reliability as an indicator of what is happening to prices and economic activity in this country.

The difference is important, not just to impatient homeowners, but to economic policymakers as well. House price inflation is one of the key indicators the Bank of England monitors in setting interest rates. Having been embarrassed a year ago into a misguided interest rate change by rogue readings from the statistics on average earnings, the Bank's monetary policy committee has been concerned to try to find out what has gone wrong with the house price indices on which they were once happy to rely.

As I discovered last week, when I dropped in on a Bank-sponsored seminar on this issue, the house price issue has prompted a feverish bout of analysis and soul-searching by the country's statistical profession. The two rival indices have been taken apart and backtested repeatedly, both internally and by independent experts, to try to eliminate all the most obvious reasons why they might suddenly have started to diverge. We now have it on the best statistical authority that many of the explanations simply don't hold water.

For example, one popular view has been that the difference simply reflects the fact that the Nationwide typically lends money on more properties in the richer South, whereas the Halifax is more heavily concentrated in the North and Midlands. The statistical analysis is quite conclusive, however, that this is not the cause of the divergence in the price indices. (Common sense would suggest that if this were the cause, it would have shown up before the 1997 hiatus.) Both indices, it should be said, were constructed with the advice of outside experts and are based on sufficiently large samples to produce statistically significant results.

The conclusion of the various expert speakers at the seminar was that the divergence in the house price indices remains, officially, a mystery. So concerned has the Bank itself become that it has started its own house- price index, based on data held at the Land Registry. The advantage of this data is that it is based on actual prices paid for properties, including those bought with cash. The Halifax and Nationwide indices by contrast are based on the prices borrowers have agreed to pay at the mortgage application stage.

By definition, the data in their two indices excludes the 25 per cent or so of properties that are bought without a mortgage each year. The drawback of the Bank index is that the Land Registry data does not include the detailed breakdown of transactions by type and size of house that the two building society samples provide. So it provides very few meaningful explanations of how and why house prices are changing. For the record, however, the Land Registry data suggests that house prices are, in fact, rising at a rate which is about halfway between that recorded by the Halifax and the Nationwide.

The one surprise to me in this great debate is that all the statisticians are failing to use the one faculty that might help them to unravel the mystery, which is common sense. It is surely more than coincidence that the divergence arises during the period when Halifax was preparing to demutualise and Nationwide was stepping up its campaign to remain the leading mutually owned building society.

We know that the Halifax's share of the mortgage market has fallen sharply since its flotation, while that of the Nationwide has increased. The gap between the two lenders' mortgage rates has suddenly become very wide. The two lenders are pursuing very different lending strategies. At the same time, the market has been experiencing an unprecedented degree of competition, with the widescale use of cashbacks, discounted mortgages, flexible loans and all the rest of it.

In other words, we have been witnessing unique and unprecedented behavioural changes on both sides of the lending equation. The moral is: don't put too much reliance on any indicator of prices until the war between mutuals and demutualisers has run its course.