Today's economic news has been mostly bad, with the Bank reporting (pdf) falls in mortgage approvals and non-financial companies' borrowing, and purchasing managers saying that manufacturing output fell last month. But there's one sign of hope. It's that non-financial companies' UK sterling bank deposits have risen quite sharply. They're up by 7.8% year-on-year, the biggest annual rise since December 2007.

My chart shows why this matters. There's a good correlation between companies' M4 growth (inflation-adjusted) and GDP growth. The best lag is two quarters, with money growth leading output growth.Eyeball econometrics - an under-rated discipline - suggests there's little sign of this relationship having broken down recently.

This relationship suggests that, at worst, the risk of serious recession is fading and, at best, that we're heading for recovery.

The obvious reason for such a link is simply that companies build up cash with the intention of spending it on capital or labour. If they were simply pessimistic about their prospects, they would not hold cash but rather hand it back to their owners.

There are, though, two caveats here. One is that the relationship between corporate M4 and GDP is stronger on the downside than upside; money predicts recessions better than booms. The other is that companies might be hoarding cash for precautionary reasons. The fear that credit lines might be withdrawn in future is causing them to have big bank balances as protection against this.

Two things, however, make me suspect these are no more than caveats:

1. Today's BCC survey shows a small rise in investment intentions, corroborating the message of M4.

2. There's recently been a decline in companies' financial surplus and a rise in PE ratios. Both are consistent with a pick-up in growth expectations and hence in the motive to invest.

The good news, then, is that the economy might be about to recover. The great news is that this might - only might - mean that the economy's long-term problem of a dearth of monetizable investment opportunities could be receding. The bad news is that, if the recovery does come, the Tories will claim this as vindication of its austerity policies.