Some terrible ideas are brand new, such as injecting disinfectant. But some bad policy plans are like zombies – however many times they are killed by the evidence, they just keep coming back.

And grammar schools are the zombie king. The grammars debate is usually about who gets in and the impact on social mobility. The evidence falls heavily on the “grammar schools are a disaster for social mobility” side of the argument. Only 2.5% of grammar school pupils are on free school meals v 13.2% in all state schools. And still the idea comes back.

But if demonstrating that grammars take the privileged, not the bright, hasn’t killed the idea, maybe a new approach is called for. That’s what recent research did by examining grammar schools’ impact on wage inequality.

The paper finds that it is significantly higher for those growing up in local areas where grammars are present – lower earners from grammar areas earn less than those elsewhere, while higher earners earn more.

This effect is big, with the school system explaining a quarter of the gap between low and high earners. So while the political consensus has been to raise the minimum wage and reduce earnings gaps, grammar schools push in the opposite direction.

The evidence from my household confirms that home schooling is a terrible idea, but that problem will disappear at some point. It’d be nice if the same could be said for grammar schools.

• Torsten Bell is chief executive of the Resolution Foundation. Read more at resolutionfoundation.org