When research agencies are pressed by politicians to quantify the economic value of scientific research, it is only natural that they reach for whatever numbers they can find and then repeat them as well-established fact. Natural, but wrong. The reality is that few of those numbers — typically, assertions that each unit of research investment will yield a certain amount of additional economic activity — rest on a secure basis (see page 682).

Economists can say with some certainty that basic scientific research plays a substantial role in fostering innovation — by which they mean new technologies, services and business methods. They also have good evidence that innovation is essential for strong economic growth, especially when society faces constraints on key inputs such as labour, capital and materials.

Beyond that, they can't predict which disciplines of scientific research will lead to future innovation — that would require a time machine. Nor, thus far, can they trace how additional research investment will influence a society's ability to innovate.

The problem is that innovation is not a simple, linear system in which basic research begets technology, and technology begets innovation — although that has always been the easiest model for policy-makers to envisage. Innovation is a complex, highly nonlinear ecosystem, full of interdependencies and feedback loops that aren't even completely mapped yet, never mind ripe for quantification. How do multiple basic-research findings accumulate into useful technology, for example? How do discoveries in one geographical region influence innovation in another?

Most of the attempts to count the economic benefits of investment in science have been derived from the efforts of lobbying groups and funding agencies to justify science spending. The few studies that have made a genuine attempt objectively to assess the economic outcomes of research — such as the 2008 UK study Medical Research: What's it Worth? — have highlighted vast swathes of uncertainty.

In the United States, there are moves afoot to do better. Physicist John Marburger, when he was running the White House Office of Science and Technology Policy during the George W. Bush administration, launched a number of measures to fill the gap, including an $8-million National Science Foundation programme to fund research into the science of science and innovation policy. But, as Marburger himself admits, this is a long-term research project; when officials claim that such investigations will next year yield useful data about the impact of President Barack Obama's 2009 stimulus package, they are promising more than what economics is likely to deliver.

That observation is reinforced by the experience of Europe, where economic competitiveness has been a constant concern for policy-makers, and where assessing the economic outcome of investments in science has been a major priority of research agencies for 20 years. That effort has led to a lot of interesting questions, but no solid guidance for policy-makers wondering how much to spend on research or what exactly they should spend their money on.

In time, the innovation ecosystem will be better understood. Meanwhile, researchers should do themselves a favour by cooperating with the good-faith efforts of economists and sociologists to improve that understanding. They should also comply with apparently tiresome demands from funding agencies for more complete information about how they spend their grants, their interactions with colleagues and their 'outputs' such as publications, patents and commercial benefits.

And in the public arena, scientists should talk like scientists and desist from using dodgy numbers to bolster the already powerful case for research spending to be maintained, or even increased, during difficult economic times.