America's economic debate is stuck in a time warp. On the one side, Mitt Romney's conservative advisers defend tax cuts for the rich and spending cuts for the poor as if we had not just seen 30 years of failed Reaganomics. On the other, Paul Krugman defends crude Keynesianism as if we had learnt nothing in recent decades about the limitations of short-term fiscal stimulus. Both sides merely raise their decibel levels at each announcement of bad news.

The two sides live in timeless and increasingly irrelevant ideologies. The prescriptions peddled by the Republicans - slash taxes and spending, end financial and environmental regulations - are throwbacks to the 1920s. Today's free-market ideologues pay no heed to recent history, to the financial crisis of 2008 or to the devastating and ever more frequent climate shocks that threaten far more than the economy. Their single impulse is the libertarianism of the rich: the liberty to enjoy one's wealth no matter what the consequences for society.

The other side is also wide of the mark. In Mr Krugman's telling, we are in the 1930s - even though the collapse of output and rise of unemployment then was incomparably larger and different in character from today's stagnation.

In his simplified Keynesian worldview, there are no structural challenges, only shortfalls in aggregate demand. There is no public debt problem. There is no global competitiveness challenge. Fiscal multipliers are predictable, timeless, persistent and large. All growth reversals can be solved with larger deficits. Politicians can be trusted to design short-term stimulus spending programmes of hundreds of billions of dollars. Tax cuts are about as good as increases in government spending, and short-term boosts in spending are about as good as long-term public investments. Not one of these conclusions stands scrutiny.

Why have we come to this empty debate that addresses none of the subtleties, trade-offs and uncertainties of the real situation? There are probably two main reasons. First, the world is noisy and overloaded with media messaging. Getting heard seems to require a short, sharp and exaggerated idea endlessly repeated. Second, the world is facing novel problems at the global level, and novelty is hard to factor into economics, which is a rigid, ideological, theoretically based, and largely backward-looking field.

Here are some of the new problems of macroeconomic significance.

First, the financial markets are global while regulation is at best national (and sometimes almost non-existent or criminal). This is killing the euro, but it is also undermining financial regulation and monetary policy everywhere. The US and UK are far more interested in defending Wall Street and the City than in fixing global regulation. Germany has been much more interested in coddling its errant banks than in fixing the eurozone banking system.

Second, the world of work is being transformed. Low-skilled work is for offshore workers, immigrants or machines. In high-income countries, the only route to middle class jobs is through education, skills and active labour market policies that match jobs and needs. Keynesian aggregate demand cannot create long-term employment for the low-skilled workers left to sink or swim in today's globalised labour market.

Third, tax collections on the rich and capital income are becoming little more than a Swiss cheese of tax evasion and tax havens. Value added tax and payroll taxes can still be collected but capital income of all kinds increasingly escapes taxation. These trends greatly exacerbate inequality of wealth and income.

Fourth, we are in the age of the Anthropocene, where global growth is limited by natural resources and climate change. If the world economy grows at 4 per cent or more, oil prices soar above $100 per barrel and food prices hit historic highs. This fact is not yet properly part of any country's economic strategy. America's hydrofracking of natural gas and offshore drilling will not solve the heatwaves, floods, droughts and other disasters hitting much of the world this year. Nor will it do much to ease the resource constraints that will squeeze economic growth until weshift to new, sustainable technologies.

Fifth, the combination of falling tax collections and rising pension and healthcare costs poses long-term solvency challenges for most of our governments. These can be met only by new, long-term policy approaches.

In short, we need new strategies to overhaul broken systems of finance, labour markets, taxation, ecological management, budget management and investment incentives. Those challenges cannot be fixed through lowering taxes on the rich or higher fiscal deficits to create aggregate demand. New approaches must be long-term, structural, sensitive to inequalities of skills and education, aligned with the need for more sustainable technologies and congruent with demographic trends. It is time we moved beyond the Republican party economics of the 1920s and the Democratic party economics of the 1930s, to a new macroeconomics for the 21st century.

The writer is director of the Earth Institute at Columbia University