The Labour leadership contest began in earnest with the New Statesman debate at Church House in Westminster on 9 June. In retrospect, all the themes of this summer-long contest were apparent that evening: the rivalry between the Miliband brothers, the pugnacity of Ed Balls, the boldness of Diane Abbott and the positioning of the underrated Andy Burnham as the voice of working-class aspiration. But it was the clashes between the Milibands - as Ed attempted to define himself against David and the New Labour establishment - that were the most fascinating and offered a clear sense of the direction of travel.

Many of our readers despair of Labour and will never forgive the authoritarian tendencies of Tony Blair, or how he allowed the party to be drawn into a fatal and militaristic alliance with the neoconservatives of the Bush administration. Nor will they forgive the neoliberal market dogmatism that resulted in the British economy becoming so unbalanced and so over-reliant on reckless financiers.

We empathise with them. In our first issue, of 12 April 1913, we outlined our founding mission as being the creation of a state in which "health, comfort, culture and personal freedom are the rules instead of the exception". The New Statesman would be "an independent journal in the fullest sense of the word". That remains as true today as it was then. Above all, we remain beholden to no one political party - including the Labour Party.

Indeed, there are many aspects of the coalition government's programme of which we approve, notably its commitment to constitutional reform and enhanced civil liberties, and the willingness of the Work and Pensions Secretary, Iain Duncan Smith, to make poverty and dispossession a defining issue of our political discourse. Yet we still believe that Labour is the party that offers the best hope of achieving the progressive transformation of British society that we seek, perhaps one day in coalition with the Liberal Democrats.

However, we do not agree with the caricature that the leadership contest has done little more than dramatise the dilemmas of a directionless party speaking only to itself. It takes time to recover from the trauma of defeat after 13 years in office. It takes time to understand how the party that preached "prudence with purpose" left government with the largest Budget deficit in our peacetime history. First, there is shock, and then the reckoning begins. In many ways, because Labour knew it could not win with Gordon Brown as prime minister, the party was collectively mourning its defeat long before the general election was called. This has been liberating: a period of mourning can be that much longer if a death is unexpected. But New Labour's obituary has been happily written during this campaign as all five candidates - the Milibands in particular - elaborate on their vision of a transformed party.

Now, slowly, we are witnessing the first signs of renewal. There has been a preparedness to admit mistakes and ask painful questions about why so many of its natural supporters ended up feeling so betrayed by or isolated from Labour. So far, of all the candidates, it is Ed Miliband who has been most prepared to challenge New Labour orthodoxies, to use a different kind of language. He advocates a Labour agenda that is confident, forceful and empowering, committed to greater freedom, social justice and, above all else, reducing inequality.

The primary task of the next Labour leader has to be to develop a political economy that addresses the fundamental inequalities and inequities that have blighted British society for so long - and which will only worsen as the Con-Lib coalition's doctrinaire spending cuts begin to bite. To talk of tackling social mobility, as coalition ministers do, without addressing the ever-widening gap between rich and poor, is disingenuous. The fight for a more equal society has to become a priority again and Ed Miliband understands this (see his column on page 21). Witness his living wage campaign, his proposal for a high pay commission and his insistence on keeping the new top rate of tax for high earners.

Ed Miliband also understands that the Labour Party must once more become part of a much larger and wider movement for change - a true movement, transcending class divisions and geographical boundaries. Rightly or wrongly, he is less contaminated than his brother and Ed Balls by the fall-out from the radioactive Brown-Blair wars. With the exception of Diane Abbott, he has been most robust in denouncing the Iraq war as a great wrong, a moral failure. He has placed civil liberties and the restoration of freedoms lost during Labour's 13 years in office at the centre of his campaign. On constitutional reform, he supports the Alternative Vote, if not full proportional representation, and is an instinctive pluralist. However, he needs to think harder about the relationship between the individual and the state and accept that we are grappling with not only market, but state, failure, too. It would be wise to incorporate the ideas of groups such as Compass and London Citizens because, as pluralists, they are seeking to reconnect Labour with an older and deeper tradition of mutualism, reciprocity and association.

Our endorsement of Ed Miliband is not a rejection of his brother, nor indeed of Ed Balls. Mr Balls in particular has been impressive during this contest. As an astute and experienced economist, he is the most numerate of all the candidates. As the coalition has already discovered, he is a formidable opponent, unrelenting and forensic. Like Robin Cook when he was in opposition, Mr Balls has the potential to destroy the careers of Tory ministers. But he is a victim of his unquestioning loyalty to Gordon Brown and his statist instincts. Of all the candidates, unfairly or otherwise, he has a reputation for political thuggery. Yet he would make an excellent shadow chancellor; certainly he has a more sophisticated understanding of economics than George Osborne. As Irwin Stelzer - no leftist - writes on page 22, he and Mr Brown made the right decisions in response to the financial crisis. The Conservatives did not.

The contest, however, is a two-horse race. David Miliband deserves his title of "front-runner". Despite his mistaken support for the catastrophic invasion of Iraq, the elder Miliband has the intellect, eloquence and experience to be Labour leader and prime minister. When his stock was low in the party following his bungled bid for the leadership in August 2008, we refused to believe that he lacked political courage or was merely a Blairite stooge, and published an 8,000-word interview-profile of him in January 2009.

So we supported David Miliband when his reputation was at its lowest and we have not been disappointed by his leadership campaign - his Keir Hardie Lecture was powerful and persuasive, and he is correct to remind us all that if Labour is to win again, it must appeal to affluent voters in the south of England. He has been caricatured as a Blairite, but his call to abolish the charitable status of private schools in order to pay for free school meals for the poorest children in our society, and his support for a mansion tax, reflect his strong social-democratic credentials.

There have been whisperings to the effect that if he does not win the leadership, he will leave politics altogether. That would be a tragedy: David Miliband is an outstanding politician and a man of integrity. He has a major to role to play, either as Labour leader or his brother's lieutenant-in-chief.

The elder Miliband remains the bookies' favourite, the best-funded candidate, with the support of the New Labour establishment and much of the right-of-centre commentariat. For all of this, the race is open. Voting begins on 1 September and we urge all undecided MPs and MEPs, and Labour Party and trade union members, to vote for Ed Miliband. He is the "change candidate" who has the greatest potential to connect with a wider electorate and especially with those politically engaged young people, internationalist in outlook, who have lost faith in conventional Westminster politics but yearn for a more democratic, fairer and freer Britain. Labour needs a bold, charismatic, compassionate and visionary leader to renew the party and begin the journey back to government. Ed Miliband has shown us he could be that leader.