Politics thrives on myths and stories. One such is fast gathering pace in British politics. This claims that Labour, far from being radical, is actually not redistributive enough. The party’s commitment to universalism is derided as a sop to the well-heeled middle classes and its programme charged with a crime far worse than simply 1970s revivalism: that its policies are actually regressive and would worsen inequality.

Central to this claim has been the interpretation of a chart produced by the Institute for Fiscal Studies in their election manifesto analysis, which shows the distributional impact of all tax and benefit proposals from the Conservatives, Labour and Liberal Democrats. Strikingly, this chart suggests that not only was Labour’s offer almost perfectly regressive - from the second to the ninth decile, the poorer a family is, the worse off Labour’s plans would apparently make them – but that their policies were almost as regressive as the Conservatives, and far less egalitarian than the Liberal Democrats.

Unsurprisingly perhaps, this has been seized upon by commentators unsympathetic to the Labour leadership. In the Independent John Rentoul used the graph to describe Corybn as a ‘right-wing Red Tory’, while The Economist’s Jeremy Cliffe tweeted that Labour’s current programme would “slice the pie less fairly”, with little distributional difference between a Conservative and Labour government.

Powerful and counter-intuitive, but is this correct? Would the effects of implementing Labour’s manifesto be not only to take away from the poor, but to take away far more than they would from the rich?

The answer is either an unequivocal ‘no’ or ‘we don’t know because the analysis hasn’t been done’, depending on the meaning of ‘effect’. But the answer is certainly not ‘yes’.

Commentators have misinterpreted the IFS work in two important ways. First, by assuming it covered the whole of the manifesto (in fact only a fraction of the document was included: 8% of total spending and 16% of tax rises, to be precise). Second, by failing to distinguish sufficiently between the policies that were contained in Labour’s manifesto itself, and the Coalition and Conservative Government plans that they would be inheriting. IPPR have published a full analysis of these issues here, but it should be noted that the IFS themselves were entirely clear and accurate in their methods.

Addressing the faulty claims made on behalf of the IFS’s analysis is important. People who have raised concerns about the progressiveness of Labour’s programme are surely right to argue that reducing inequality and raising stagnant living standards should be a central goal of our politics, regardless of party. After all, we have the richest region in Western Europe – inner London – but nine of the 10 poorest. Median household disposable income has been flat since around 2005, with half of all UK households having seen no meaningful improvement in their incomes for more than a decade. Productivity, crucial to improving living standards over the long term, remains stubbornly sluggish. Looming over us is the monumental challenge of securing a fruitful new economic relationship with Europe, upon which so much rests.

Tackling these challenges, however, will require a more rigorous and candid conversation about progressive priorities. The election revolved around debates about the shape and scale of the state, the balance of public support between cash welfare or services in kind, the divide between young and old, between the super-rich and the rest, and on how principles of universalism, reciprocity and targeted redistribution should be brought to bear on the questions of precisely how an economy should be working for society. These are critical and require more thought. For a start, the absence of a more serious reversal of the Government’s welfare plans by Labour was conspicuous, and is rightly set to be an area of continued debate, not least because the Liberal Democrats committed to significant action in this area.

But there are other many areas where a deeper, more rigorous examination of institutional detail and policy design is needed by progressives. Here are just five.

First, Britain’s poor performance on investment, productivity and inequality stem in part from how – and in whose interest – British companies are governed. While Labour’s manifesto hinted at corporate governance reform, and Theresa May made company reform a signature issue when she first stood on the steps of Downing Street, a bolder agenda is needed to build more effective, equitable firms: company law should be reformed so that so that companies are governed on behalf of all their stakeholders, not just shareholders, and employee voice embedded in governance processes.

Second, how should we better finance investment? IPPR have long argued for public investment banks but this should be accompanied by reforming financial markets, which are key to upgrading the UK to a high-investment, high-productivity, high-paying economy. This includes hardwiring new incentives in stock markets through tax and legal reform so that they are better aligned with the imperative to create value for the long term.

Third, how can collective bargaining be strengthened in order to raise earnings and improve working conditions? While Labour committed to extending it in their manifesto, how would it be effectively institutionalised in a decentralised, liberal market economy? Should it be sectoral or firm-led? What co-ordinating institutions are required to bolster and support bargaining? And how can trade unions – whose density in the private sector is at near record lows – modernise and expand?

Fourth, progressives win when they have the future in their bones. While Labour committed to taking the utilities and rail companies back into public ownership, the commanding heights of the digital economy were left untouched. Yet with digital data a ubiquitous and essential source of value, absent policy intervention four or five ‘super star’ firms are set to harvest and monetise vast swathes of data creating huge concentrations of economic power. Given this, what does a democratically governed and owned data infrastructure look like that produces greater equity and genuine innovation? And should we regulate unaccountable, private algorithms, laced through with questions of economic power?

And fifth, if automation threatens to accelerate returns to capital and further polarise the labour market, new models of common ownership will be needed to ensure technological change doesn’t simply reproduce existing inequalities but expands and democratises its proceeds. Deepening and advancing the ideas laid out in the recent ‘Alternative Models of Ownership’ report could be one fruitful avenue but serious thought is required on all sides.

IPPR’s Commission on Economic Justice is examining these questions: how can you build an economy in which prosperity is underpinned by justice. What would an industrial strategy look that accelerates automation and supports good jobs? How can we work better but less? What steps can build a digital commons, broaden democratic ownership, and ensure equitable, sustainable economic development? And overarching all questions of domestic political economy, how can the UK secure a productive and prosperous economic relationship with the EU and wider world?

These are difficult and challenging questions but if we are serious about addressing inequality and raising stagnant living standards, it is what we should be debating.