Here is a puzzle that preoccupies futurologists, business strategists, economists and the world's foreign offices. Who is going to do best or worst economically over the next 15 years out of the world's current top 10 economies? In 2013, the US is comfortably number one, twice the size of China and two-and-half times the size of the number three, Japan. After Germany at fourth comes a cluster of countries with less than a trillion dollars of GDP separating them. France just pips Britain at sixth. Then follow Brazil, Russia, Italy and Canada with India, hurt by the collapse of the rupee, just outside the top 10 at 11.

The conventional wisdom, informed by conventional economics, is clear, represented faithfully by the conservative-leaning Centre for Economics and Business Research (CEBR) in its annual world economic league table released last week. The European economies, especially France and Italy, will sink down the league table, burdened by taxation, welfare and ageing populations. China is inexorably rising to take over the top spot, but in 2028, later than the CEBR thought last year. India will climb to number three. Russia will do well, as will Mexico and eventually Brazil. The UK, if it continues to shrink the state, keeps taxes low, deregulates its labour markets, continues to be open to immigration and disengages with Europe, may only fall one place in the 2028 ranking to seventh. But even though the UK and US will fare better than mainland Europe, the relative decline of the west will continue.

Britain's conservative press seized on the projections with glee, proof positive that George Osborne is on the right track and Euro-scepticism is triumphant. The Express trumpeted: "Booming Britain will be top dog as the rest of Europe stagnates", while one commentator in the Mail wrote of Britain's "renaissance": the CEBR had handed the chancellor a "weapon with which to attack Labour's agenda of despond and false promises".

Hmm. Booming Britain? Renaissance? The problem is that the economic theory that supports these predictions is itself in crisis. By prioritising the role of low taxes, deregulation, the inevitable efficiency of markets and the accompanying inevitable inefficiency of the state as drivers of growth, it assumes that the last 30 years – and in particular the 2008 financial crisis – had not happened. These are the terms in which UCL's Professor Wendy Carlin, leading the programme at the Institute for New Economic Thinking (INET) to reframe the economics curriculum to include economics' new advances, describes the state of much current teaching and debate, exemplified by both the CEBR report and the reaction to it.

For the best economics now has much more sophisticated understanding of what drives innovation, investment, productivity and growth than the simple faith in low tax and loosely regulated markets. It criticises the refusal to understand the complexity of how economies and societies create and assimilate paradigm-changing technologies. Nor is there room for assessing the quality of a country's entire institutional nexus – from company organisation to the accountability of government – in building inclusive, value-creating capitalism rather than extractive, value-capturing capitalism. The best brains in economics are now working on how economies work in reality, rather than as prospectuses for rightwing politicians and newspapers.

For example, in Why Nations Fail, MIT's Daron Acemoglu and Harvard's James Robinson present the results of 15 years of research into the rise and fall of countries and their economies. It is a far cry from the CEBR analysis, arguing that what differentiates countries is the quality and effectiveness of their economic and political institutions. Capitalism has to be shaped and governed to allow the new continually to reshape and even destroy the old: it has to allow multiple runners and riders, lots of experimentation and harness whole societies into accepting and taking risks. This happens best when economic and political institutions do not fall into the hands of one party or a group of self-interested oligarchs who essentially extract value; they need to be open and inclusive, constantly pushing back against the wealth extractors.

Acemoglu and Robinson are right, although inclusiveness and accountability go well beyond the democratic political institutions on which they focus – and for whose lack they doubt predictions of China's continuing inexorable rise. It extends to the integrity and soundness of the financial system, how effectively governments accept the risk of investing in frontier technologies that private entrepreneurs never undertake alone, how companies are prevented from falling into the hand of self-interested, overpaid boards and ensuring that workplaces are inclusive too. But they do recognise, along with the IMF and OECD, that growing inequality menaces vigorous societies. It is a proxy for how effectively an elite has constructed institutions that extract value from the rest of society. Professor Sam Bowles, also part of the INET network, goes further. He argues that inequality pulls production away from value creation to protecting and securing the wealthy's assets: one in five of the British workforce, for example, works as "guard labour" – in security, policing, law, surveillance and forms of IT that control and monitor. The higher inequality, the greater the proportion of a workforce deployed as guard workers, who generate little value and lower overall productivity.

The CEBR does warn that the break-up of the UK, if Scotland votes for independence, would qualify its optimistic predictions. But it never asks why Scottish voters might be so disillusioned if the Euro-sceptic, low-tax, low-regulation world it paints is so rosy: perhaps the Scots understand better than conventional economists what is really going on. More of what the CEBR recommends as the route to future riches – placing our faith in markets and individual incentives along with disregarding inequality and the dysfunctionality of our institutions – could break Britain up.

It is also reason to be sceptical about most of its projections. Will China, Russia and Mexico, governed by extractive elites, really do so well? Is Europe such a write-off? After all, Mr McWilliams, the affable Euro-sceptic who runs the CEBR, warned more than two years ago that European leaders had a month to save the euro.

I also bet that the US, if the destructive Tea Party can be held at bay, will hold on to the top spot. Britain, it is true, could catch up with Germany, but only if it builds on the effective industrial policy the coalition is developing and consigns small-state conservatism to the dustbin. Above all, I doubt the endless rise of Asian and Latin-American autocracies. The west is not dead yet.