What if the problem with the economy is that good businesses can't grow and bad businesses can't shrink? Earlier this week one of the Bank of England's cleverest economists came up with an ingenious explanation for a big economic puzzle. If he's right, it has big implications for innovative businesses in the UK, and for what government can do to help them.

The puzzle is this. GDP - the value of goods and services we produce in the UK - has fallen. This is bad. But employment is going up. Normally this shouldn't happen. If the UK is not making as much stuff, normally there'll be more unemployed people. If lots of people are in work, normally they will be producing things and output will be high. There have been lots of attempts to explain this.

Maybe the Office for National Statistics has measured output wrongly. Maybe some of the people supposedly in work aren't actually doing much, either because they're part-time workers or "consultants" doing fewer hours than they'd like, or because businesses are holding on to idle staff in the hope that the economy will recover. Productivity - the relationship between hours worked and output produced - normally changes over long periods of time, not quickly.

The new paper by Ben Broadbent, a member of the Bank of England's Monetary Policy Committee, offers another explanation. It argues that the problem could be a failure of creative destruction. Or to put it another way, productivity is falling because across the economy, not enough resources are being invested in promising firms, and not enough bad firms are shrinking or closing.

What makes Broadbent's paper particularly interesting is the evidence he cites. First of all, he looks at the standard explanations for the output-employment puzzle and shows that none of them are major enough to account for the size of discrepancy we are currently seeing.

He looks at the performance of 81 different sectors in the UK economy. Before 2008, the disparity of returns between the best performing and worst performing sectors was relatively small. This is what the laws of economics would lead us to expect: some types of business do better than others, but on the whole investors respond by moving their money from poorly performing sectors to ones that are doing better. Good investments don't stay underpriced for long.

But since 2008, this has changed:

The difference in returns between high performing and low performing sectors has massively increased. This could be a sign of two things:

• Firstly, it could show that things are changing structurally in the economy. If consumers are feeling the pinch, consumer facing businesses are likely to be less profitable. New technologies could boost mobile phone operators, and hurt record shops. If sterling is worth less, exporters will do better. And so on. Perhaps since 2008, these sort of changes have got bigger. This gets close to the kind of arguments made by economists like Stiglitz, Brynjolfsson and Mandel, all of whom have argued that the economy is changing rather radically.
• Secondly, it means that for some reason, the UK economy is not reacting to these changes. One likely culprit is the financial system. It is widely believed that the UK's ailing banks are doing a poor job of financing business growth, and that UK financial markets do not support long-term bets or radical innovation. Another is low rates of bankruptcies. Low interest rates and banks worried about mean that failing businesses struggle on for longer than they would in better times (as Jon Moulton has been arguing for some time). We know that good businesses growing and bad ones going bust drives productivity.

If this is true, it suggests that the economy is suffering from a failure to innovate. Joseph Schumpeter, the granddaddy of innovation economics, first described the innovative process of one of creative destruction, of good ideas driving bad ones to the wall and of capital being reallocated, often rapidly and disruptively, from the old to the new. Broadbent's analysis suggests that we need more of this if the economy is to recover.

This strikes a chord with Nesta's new report, Plan I, which argues that innovation-led growth is necessary for economic recovery. One particular area of focus of Plan I is on investment, and what role public policy can play in creating the right climate for good ideas to scale up - and bad ones to fade away. It also reflects Nesta's work on High Growth Firms, which found that countries and sectors where good firms grew rapidly and bad ones shrank were more productive than those where companies were more stable.

There is one final implication of Broadbent's idea. If low growth is the result of capital accumulating in low productivity sectors, then getting the system working again could see not just recovery, but perhaps a period of higher than normal growth. Now there's a welcome glimmer of hope.