Optimal tax rate for top one per cent may be as high as 83%

Paper suggests cutting taxes may divert attention to wasteful bargaining

Via Daniel Elton, a new(ish) paper (pdf) by economists Thomas Piketty, Emmanuel Saez and Stefanie Stantcheva makes the case for the optimal tax rate of the richest one per cent could be as high as 83 per cent.

The authors look at three possible ways in which top incomes respond to marginal tax rates.

The first is the "supply side" channel cited by Arthur Laffer when he developed his concept of the Laffer curve. Under this channel, marginal tax rates that are too high result in people doing less work than they otherwise would. Lower tax rates thus respond to more economic activity, and greater growth and higher tax revenue. Laffer's work was used by the Reagan administration to justify cutting the top rate in the US, from 70 per cent down to 28 per cent.

The second is the "tax avoidance" channel. This is the model cited by the Chancellor when he made the decision to cut the tax rate for top earners in Britain from 50 per cent to 45 per cent. The argument is that high tax rates increase tax avoidance, but the authors argue – in common with many of the Chancellors critics – that tax avoidance can be dealt with directly, writing that:

A better policy would be to first close loopholes so as to eliminate most tax avoidance opportunities and only then increase top tax rates.

The third is the "compensation bargaining" channel. The authors argue that:

While standard economic models assume that pay reflects productivity, there are strong reasons to be sceptical, especially at the top of the income distribution where the actual economic contribution of managers working in complex organisations is particularly difficult to measure.

As a result, top workers have ample opportunity to set their own pay, through bargaining harder or influencing compensation committees. The incentives for this economically wasteful activity are higher the lower tax rates are. Just as with the supply side model, tax cuts increase the wealth of the richest in society, but unlike that model they do not also increase growth; rather, the extra money for the rich comes from those poorer than them.

The authors, using their estimates of the elasticity of the various channels (that is, the magnitude of the effect), then calculate what the optimum rates would be. Under the first model, they find it to be roughly 57 per cent – 5 per cent higher than the top British tax rate is until the cut takes effect (National Insurance for top earners is 2per cent). Assessing the second model (Osborne's preferred argument), they find that the optimal tax rate would be 62 per cent, but argue that if the correct anti-avoidance and simplification measures were put in place, it would be 71 per cent.

The third model, however, outputs an optimal rate of 83 per cent. The authors still assume a minor supply-side effect, making up 40 per cent of the total elasticity, which is why it isn't higher. That is, they still assume that high tax rates will encourage the rich to work less, but they also assume that they will encourage the rich to put more of their effort into actual work, and less of it into "compensation bargaining".

How to decide between models one and three (the authors assume that once anti-avoidance measures are put in place, model two is the same as model one)? The former predicts that lower tax leads to more work, the latter that it merely leads to higher pay. As a result, tax cuts should be correlated with higher growth. Are they? Well, no:

As a result, the bargaining model can at least be said to be as realistic as the supply-side model; and if that's the case, the optimal top tax rate for most nations is likely to be far in excess of where it is set now.

For more, see the authors in the Boston Review, VoxEU, or their original paper (pdf).

Pictured: Laffer. No, wait, laughers. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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Rarely has it mattered so little if Manchester United won; rarely has it been so special they did

Team's Europa League victory offers chance for sorely needed celebration of a city's spirit.

Carlo Ancelotti, the Bayern Munich manager, memorably once said that football is “the most important of the least important things”, but he was only partly right. While it is absolutely the case that a bunch of people chasing around a field is insignificant, a bunch of people chasing around a field is not really what football is about.

At a football match can you set aside the strictures that govern real life and freely scream, shout and cuddle strangers. Football tracks life with such unfailing omnipresence, garnishing the mundane with regular doses of drama and suspense; football is amazing, and even when it isn’t there’s always the possibility that it’s about to be.

Football bestows primal paroxysms of intense, transcendent ecstasy, shared both with people who mean everything and people who mean nothing. Football carves out time for people it's important to see and delivers people it becomes important to see. Football is a structure with folklore, mythology, language and symbols; being part of football is being part of something big, special, and eternal. Football is the best thing in the world when things go well, and still the best thing in the world when they don’t. There is nothing remotely like it. Nothing.

Football is about community and identity, friends and family; football is about expression and abandon, laughter and song; football is about love and pride. Football is about all the beauty in the world.

And the world is a beautiful place, even though it doesn’t always seem that way – now especially. But in the horror of terror we’ve seen amazing kindness, uplifting unity and awesome dignity which is the absolute point of everything.

In Stockholm last night, 50,000 or so people gathered for a football match, trying to find a way of celebrating all of these things. Around town before the game the atmosphere was not as boisterous as usual, but in the ground the old conviction gradually returned. The PA played Bob Marley’s Three Little Birds, an Ajax staple with lyrics not entirely appropriate: there is plenty about which to worry, and for some every little thing is never going to be alright.

But somehow the sentiment felt right and the Mancunian contingent joined in with gusto, following it up with “We’ll never die,” – a song of defiance born from the ashes of the Munich air disaster and generally aired at the end of games, often when defeat is imminent. Last night it was needed from the outset, though this time its final line – “we’ll keep the red flag flying high, coz Man United will never die" – was not about a football team but a city, a spirit, and a way of life. 

Over the course of the night, every burst of song and even the minute's silence chorused with that theme: “Manchester, Manchester, Manchester”; “Manchester la la la”; “Oh Manchester is wonderful”. Sparse and simple words, layered and complex meanings.

The match itself was a curious affair. Rarely has it mattered so little whether or not United won; rarely has it been so special that they did. Manchester United do not represent or appeal to everyone in Manchester but they epitomise a similar brilliance to Manchester, brilliance which they take to the world. Brilliance like youthfulness, toughness, swagger and zest; brilliance which has been to the fore these last three days, despite it all.

Last night they drew upon their most prosaic aspects, outfighting and outrunning a willing but callow opponent to win the only trophy to have eluded them. They did not make things better, but they did bring happiness and positivity at a time when happiness and positivity needed to be brought; football is not “the most important of the least important things,” it is the least important of the most important things.

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