Is the Group of 20 leading economies any longer fit for purpose? That depends on what you think its purpose should be.

At last week's meeting in St. Petersburg, Russia, the group had a lot to discuss. Officially, economic and financial coordination topped the agenda - remember, this is supposed to be an economic summit - but the crisis in Syria forced a different set of issues onto the participants.

President George W. Bush brought the grouping into the spotlight five years ago, when it played a crucial role in stabilizing a crashing world economy. British Prime Minister Gordon Brown then hosted a highly effective meeting in London in the spring of 2009. Since then, however, the G-20 has limped along. Many subgroups are beavering away on special projects, but each subsequent meeting has failed to deliver anything of note.

Like its predecessors the G-5 and the G-7, the G-20 needs a clear and pressing shared purpose to work to maximum effect. In 2008 and 2009 it had one - avoiding a repeat of the 1930s - and the grouping helped to avert that disaster. Almost five years on, as shown by the latest JPMorgan Global Purchasing Managers' Index, the world is mostly drifting along, without signs of a major acceleration or of falling back into the abyss.

Most developed countries are showing their first substantive signs of manufacturing recovery since 2008. As impressive and welcome as this is, it's being matched by significant slowing in most of the larger emerging economies including each of the BRICS countries - Brazil, Russia, India, China and South Africa. That's why the purchasing managers' index is generally flat-lining.

The world's economies seem to have difficulty prospering all at the same time. Perhaps that's not so surprising, given the connections - especially through commodity prices - among them. There are links between recovery in the advanced economies, slower growth in China, weaker commodity prices and the difficulties faced by many other emerging economies.

Broadly speaking, cheap commodities help advanced economies and put emerging economies at a disadvantage. The developed members of the G-20 have an economic interest in seeking an early solution to the Syrian crisis, because higher oil prices could set them back. As oil producers, many emerging economies - including the host country - might see short-term benefits.

Most of the time, finding a common purpose across such a wide span of nations is hard. Officials from more advanced countries complain that the whole idea is a waste of time. Their regard for the G-7 has risen: It's a more compact and therefore more manageable group, and its members have far more in common. Now that the BRICS group is up and running, and building the foundations of its own development bank, those countries too may see the G-20 as less and less useful.

Despite the challenges, the major global imbalances that existed on the eve of the 2008 crisis are gradually unwinding. The Chinese and U.S. current-account imbalances have declined to levels that no longer give cause for concern. This has happened even though the 2010 G-20 meeting in Seoul failed to establish targets for current-account imbalances, as some had proposed.

Is this good enough? I don't think so. The world still needs more effective economic leadership. The G-20 is representative - its members account for roughly 90 percent of global output - but it's far too unwieldy. The G-7 is compact but unrepresentative. What's required is a group of advanced and emerging economies that's slim enough to work well. Better economic governance demands that China and some of the other major emerging economies be given more voice at summit gatherings, and that some advanced economies - notably, members of the euro area - be given less.

Growth in the BRICS counties has slowed since 2010, but the increase in their aggregate output has been about $3 trillion nonetheless - more than the output of either France or Britain. Collectively, by the end of 2015, they are likely to be the same size as the U.S. In other words, the case for a realignment of global economic governance is strong. Moving that way would improve our chances of building a more balanced and stable global economic system.

Jim O'Neill, former chairman of Goldman Sachs Asset Management, is a Bloomberg View columnist.