There is some good and some bad news for the world economy coming out of the US. The good news is the US and Iran seem to be inching towards some sort of peace agreement that would allow for the opening of the Strait of Hormuz. The bad news is the Iran war has focused the market’s attention on the parlous state of US public finances. That has caused a spike in long-term US government bond yields in general, and in the all-important 10-year treasury bond yield in particular.It is difficult to overstate the economic importance of the Strait of Hormuz reopening. Not only does 20% of the world’s oil and natural gas production pass through the strait, so too does 30% of the world’s seaborne fertiliser trade, 30% of helium production — important for semiconductor production — and 10% of the world’s aluminum production.The three-month closure of the strait has contributed to a 60% spike in international oil prices to around $100 a barrel, and hence a worldwide increase in petrol and diesel prices, and to a more than 50% spike in a number of key fertiliser prices. Coming during the northern hemisphere’s planting season, this has set the stage for higher world food prices later this year.Such inflationary pressures are in evidence around the world and are inducing the world’s major central banks to consider interest rate hikes. A peace agreement would obviate the physical shortages of oil and natural gas-related products that have heightened the risk of a world economic recession.However, while the opening of the strait would clearly provide the US and world economies much-needed inflation relief, it is unlikely to lead to a material pullback in long-term US bond yields. Those yields could spike even higher than they are today because the need for increased defence spending might exacerbate an already unsustainable US public finance position. This has to be a cause for concern given the US government is already having to pay 4.6% for its 10-year borrowing and 5.2% for its 30-year borrowing, the highest rates since 2007.Before the war the congressional budget office projected the US budget deficit would remain above 6% of GDP as far as the eye can see. By the end of next year those deficits are expected to raise the public debt in relation to the size of the economy to a level exceeding that recorded at the end of the World War 2. Yet despite his country’s shaky public finances, President Donald Trump is proposing a 50% increase in the US defence budget from about $1-trillion a year to $1.5-trillion. He is doing so without giving any indication as to how this increased spending will be funded.It is difficult to overstate how big a headwind a further spike in US long-term government bond rates would pose to the US and world economies. In the US mortgage rates, vehicle loans and other key consumer and business borrowing rates are all keyed off the 10-year US treasury bond yield. At the same time, most emerging market borrowing rates are priced as a spread over US treasury bond yields. The last thing a world subject to an energy and food price shock needs is higher borrowing rates.All of this puts new Federal Reserve chair Kevin Warsh in a challenging position. Given the US government’s large budget deficit and the energy price inflation shock, the Fed cannot afford to let inflation expectations become unanchored. That would almost certainly lead to a further US government bond market rout. For the sake of the US and world economies we have to hope Warsh displays the same courage as his predecessor, Jerome Powell, in resisting Trump’s calls for premature Fed monetary policy loosening.• Lachman, a former deputy director in the IMF’s policy development & review department and chief emerging market economic strategist at Salomon Smith Barney, is a senior fellow at the American Enterprise Institute.