The total US force of military advisers in Iraq will be increased to only 1,700. According to CIA estimates Isis forces stand at more than 20,000 people and increasing rapidly. The extra $500m counterterrorism fund approved by Congress is less than 1 per cent of the total defence budget and there is no provision for a sustained air battle against Isis.

Isis is a military force whose leaders dream of creating a new caliphate by repeating the seventh-century sweep of forced Islamic conversions through the Middle East, north Africa and Spain. Although that may never happen, the Isis forces are conquering large amounts of new territory in Syria and Iraq and imposing their radical form of strict Islamic law. Isis leaders also have their sights on killing Americans in the US by encouraging US passport holders now fighting with them in Syria to commit acts of violence when they return home. It took only four gunmen in a Nairobi shopping mall to kill 47 innocent shoppers. The US fights Isis to protect Americans at home and not just our friends in the Middle East.

Mr Obama has recognised that we must destroy the Isis forces in their home base of Syria. But since those forces are commingled with the local population, doing so by air attacks would inevitably mean large numbers of civilian casualties. The US is therefore hoping for help from Iraqi national guard units, that have yet to be stood up, as well as from Kurdish forces and from Syrians who oppose both Isis and Bashar al-Assad of Syria. It is not clear how many of them will join the fight and not clear how well they will do in battle. American military leaders, both active and retired, warn that the time will come when US troops will have to become engaged.

The Arab countries of the Gulf Co-operation Council have agreed to assist American efforts but only “as appropriate”; meaning with finance and a Saudi training camp but not with troops because they fear the negative public reactions in their own countries. France and Britain have said they will join the US in air attacks; Germany and Turkey have said they will not. The administration claims that dozens of other nations will co-operate but it is not clear in what ways, certainly not with troops or aircraft. The coalition of the willing is very limited.

The global failure of US military leadership is not limited to the fight against Isis. Nato members recently refused to set a timetable for meeting their long-agreed obligation to spend 2 per cent of each country’s gross domestic product on defence. It is, of course, hard to persuade them to spend more when they see the US shrinking its planned defence budget to just 2.7 per cent of GDP, the lowest level since before the second world war. The recent events in Syria and Gaza show that the Obama administration’s “pivot” from the Middle East to the Pacific was a serious mistake and was essentially an excuse for reducing the overall size of the US defence budget.

As a result of our defence policies, America’s enemies do not fear us and our friends do not trust us. We have disappointed the Ukrainians, alienated the Israelis and the Egyptians, and left our allies in eastern Europe and in east Asia wondering how we would deal with future threats from Russia, North Korea or China.

Mr Obama is not likely to change his attitude about the effective use of America’s armed forces or his willingness to increase defence spending. But the next president should make it a central priority to rebuild our military budget and use it to strengthen our role in Europe, the Middle East and Asia.

The writer, a former chairman of the Council of Economic Advisers, is professor of economics at Harvard