The Australian banks have a difficult decision to make after the rate rise: home lending, their most profitable business, isn’t doing well and housing approvals tanked in December.

The banks lifted mortgage rates by 0.12% to 0.20% in early January in response to higher funding costs caused by the subprime crisis and credit crunch (in which they had a tiny part, but it was a role nevertheless).

Now, do they follow the RBA increase and lift variable rates by 0.25%, or do they cut back any rise to try and steal a march over their competitors? Non-bank lenders aren’t very active, so the intensity of competition has eased. And the bank’s now the rate rise will give a boost to the demand for existing housing, while lifting rents and cutting demand for new homes.

But there’s the crunch in building approvals to think about. Building approvals in December fell sharply, much more sharply than even the most pessimistic economist had forecast.

It was another of what has become a feature of this series in the past year or so: big swings every month or so, driven mainly by a sharp rise or fall in approvals for what’s called “non-private dwelling units”, or units and apartments.

Total approvals fell a massive 16% to 12,263 units in December, seasonally adjusted, from a downwardly revised 14,601 units in November, according to figures from the Australian Bureau of Statistics.

Driving the fall was weakness in private sector housing where the number of approvals fell to 8,429 in December, from 9,426, seasonally adjusted in November. November approvals were up 8.2%, powered mainly by a strong rise in non-private dwelling approvals, and by a small growth in private houses. That was reversed in the latest figures.

The ABS said “The seasonally adjusted estimate for private sector houses approved fell 11.6% in December and is now showing a fall of 1.0% for November.”

The first announcement from the ABS said all approvals rose 8.9% and private housing, 0.3%. Non private dwelling approvals jumped 28.4, driving the overall figure higher.

But December saw a sharp fall in non private dwelling approvals according to the ABS: “The seasonally adjusted estimate for private sector other dwellings approved fell 24.5% in December.” and that very sharp 11%fall in private dwelling approvals.

Overall, approvals for the year to December fall 0.9%. Economists said it was the rate rises of August and December starting to bite, but that in turn has stimulated demand for existing houses.

On the non-residential side the figures are even more volatile, with falls of 11% in November and 24% in December unwinding a 36% surge in October.