There has been much discussion of the qualifications and nationality of the next head of the International Monetary Fund. This talk is insufficiently ambitious. The fund's next head must be a genuine economic architect capable of helping to design an entirely new international monetary framework.

The defining truth of our time is that the US-led international order - the one that gave birth to the IMF - is over. The problems in Greece, Ireland and Portugal are serious, but Europe can largely manage them itself. The IMF's new leader must be chosen to address longer-term and more complex global challenges.

The end of the cold war was widely expected to result in stronger global leadership. Instead the period has been marked by rising financial instability, an explosion of tax evasion and corruption, and a ludicrous breakdown of policymaking in the US - where politicians now spend 90 per cent of their time fundraising and campaigning and only 10 per cent of it governing.

The IMF is not responsible for this mess, but it has not been effective in fixing it either. It has seen its role as lending to smaller economies. Its advice has been uneven and largely absent on the big issues of global monetary reform, financial regulation and tax policy when capital is highly mobile. The fund's main task in the coming years should be to create a monetary and financial system that causes fewer international shocks - not to clean up after each debacle.

For at least two decades the US has been unable to provide monetary stability, financial regulation and fiscal rectitude. Now we need to find a new architecture for a globally interconnected economy - with the US as one important actor but no longer the global leader.

So what must the new IMF head do? Managing the declining role of the dollar will be a core task. If it remains the sole key currency the world will suffer the repeated spread of America's woes across its national borders, as occurred in the 2008 Wall Street meltdown. The answer for the next couple of decades is likely to be a new system built on a handful of currencies of regional significance: the dollar, euro and renminbi, along with possibly the Brazilian real, Indian rupee, and one or two others.

To make this work, regional groups must strengthen co-operation and assume greater responsibility for producing the public goods needed to underpin strong regional currencies. These include effective monetary policy, financial regulation, tax harmonisation and enforcement, fiscal policy co-ordination and physical infrastructure. The eurozone can and should look after itself. Helping Greece through the current crisis raises political problems in Germany, but the IMF is not the appropriate body to solve Angela Merkel's domestic political problems.

Other regions can and should do more to solve their own economic problems. The Arab world, for example, should act on recent upheavals to strengthen economic co-operation - not least because the Gulf is enjoying a $150bn oil windfall this year. China, Korea and Japan are well-placed to help the weaker economies of south-east Asia - especially if east Asia can begin to act as a political grouping, rather than nursing past grievances. The IMF chief should have the vision and mandate to support these regional approaches above US-led solutions.

There would still be plenty to do at IMF headquarters. The world economy is rife with lawlessness and recklessness, with tax havens and regulation-free zones catering to the avarice of globally mobile capital. The fund's new head should be given the task of systematically shutting these venues down and, with global co-operation, to reverse the race to the bottom in tax and regulatory policies that threatens the world economy.

I have no illusions about the limits of human-built currency systems and financial regulations. Nor do I imagine any IMF managing director will be empowered by sovereign states to make crucial decisions over tax, currency and regulation. My point is the quality of leadership needed at the IMF. We do not need a financial mechanic or mere politician. We need a managing director with monetary expertise, and the vision and capacity to guide a crucial process of global change.

The process of selection matters: a rushed appointment, as now seems likely, will deliver the wrong message, wrong ethics, wrong objectives and will overlook many exciting world-class candidates. A good search takes time. New and unexpected names should come to the fore; candidates should be vetted, not anointed; their opinions should be heard; their qualifications should be reviewed and, this time, any well-whispered weaknesses should not be ignored. The IMF search should be a chance to hear from every region on the challenges of a fast-changing and crisis-prone world economy.

To argue that we need a European to handle the European crisis gets everything backwards. We need a global citizen who understands the priority of building a new global system, not somebody selected to patch the old one or to keep Europe in charge. But most of all we need a leader of supreme integrity, who will help to clean up a financial system that has become increasingly unstable, unfair and beyond the law.

The writer is director of the Earth Institute at Columbia University