Wednesday 24 March 2010

The economics of optimal taxation applied to sport

It is now confirmed that Carl Hayman has signed with a French Club, and so will not be available to play for the All Blacks in next year’s world cup. This is obviously a big blow to the All Blacks. It is also unfortunate for rugby that international rugby, the showpiece of the sport, will continue to be without one of its genuine superstars.

Three common reactions to this are all wrong:

  1. Hayman should have put national pride ahead of financial return.
  2. The NZRFU should have matched the offer from Toulon.
  3. The NZRFU should abandon its rule about not selecting foreign-based players.

The first of these is ridiculous: Who among the rest of us base our personal employment decisions on considerations of the national good? The second would create an incentive for more players to leave in order to be enticed back. The third would have a similar effect on incentives, at a huge long-term cost to the base of the game in New Zealand. But a variant on it is worth considering.

This is where optimal tax theory comes in. The basic idea of this literature, see here, here, and here, is that there is no benefit from levying tax on income-generating activity if that tax will lead people to not undertake that activity, so taxes should ideally only be levied on activity that will take place even with the tax. The trouble is to find observable things that are correlated with tax-insensitive behaviour and not with tax-sensitive behaviour that still leave a progressive tax system. One example from the literature is that an optimal tax system has lower tax rates at higher incomes that at lower ones. (The vast majority of people will choose to continue to earn the first $10,000 of income; they may not choose to continue to earn the millionth dollar.)

The rugby analogy is that the NZRFU would be happy to select players from overseas who would be overseas whether they were allowed to be selected or not but also want to commit to not selecting players for whom that rule would be decisive in keeping them playing in New Zealand. So what they need is a rule that allows some players thought likely to be infra-marginal to be selected for the All Blacks if playing overseas while not others.

Fortunately, such a rule is possible. The vast majority of players who have gone overseas have not done so until they have played around 8 seasons of Super rugby (Hayman, himself played 8 seasons for the Highlanders), and typically, I would guess, the majority of high-profile players who can leave do so after that time. So the NZRFU should institute a policy that to be eligible for selection in the All Blacks, you must either be based in New Zealand or have played at least 8 seasons of super rugby. Indeed, once this rule were in place it might keep some players who now would leave before completing 8 seasons, as they would have the incentive to earn perpetual eligibility.


  1. I had a rough count and 8 out of 24 forwards who were selected for the All Blacks last year had played 8 or more seasons of super rugby. All 8 are still in NZ. Interestingly, only 1 out of 22 backs had played 8 or more seasons.


  2. "The third would have a similar effect on incentives, at a huge long-term cost to the base of the game in New Zealand. But a variant on it is worth considering."

    Why do we care? We just want the best players in the ABs, why should we care where they play their other rugby?All we need to be able to do is judge who the best players are, this may be more difficult if some are overseas. But other sports pick national teams from players all around the world, why can't rugby. The All Whites, for example, have players who play all over the world, why not the ABs?

  3. Paul: In the case of the All Whites, we need our best players playing overseas, as it is the only way they will get to play against decent opposition. For rugby, losing our top players would, reduce the quality of opposition for both them and the players left behind. And it would improve the quality of competitions that future international reps in the northern hemimsphere receive. (I readily concede that it is hard to make a claim based on empircial evidence that international signings in the Heineken leauge is helping the current England team.)

    Furthermore, a mass exodus would would heavily dent the popularity of Super 14, reducing the ability of the NZRFU to fund a professional competition, potentially with dire consequences for the future.

    Going back to a soccer analogy, I don't think Brazil are anywhere near the team they were back when most of their stars played in the home league.