A Grattan Institute analysis predicts removing the rebate would increase demand for public hospital services by between $1.5 billion and $3.8 billion a year, but suggests the increase would be at the lower end of the range because the Medicare Levy Surcharge (paid by middle and high-income earners who do not have private cover) and the Lifetime Cover policy (a penalty on those who first take out private cover after the age of 30) would provide incentives for people to keep their insurance.

The institute settles on an estimate of $2.5 billion in extra public hospital costs, projecting that scrapping the rebate would produce a net saving of $3 billion.

In a paper published last July, Terence Cheng, a research fellow at the Melbourne Institute of Applied Economic and Social Research modelled the impact of reducing the rebate by 5, 10, 15, 20 and 25 per cent on spending on rebates and on public hospitals.

He concluded in each case the government would save more than it would incur in increased public hospital costs. Dr Cheng said that cutting the rebate by 5 per cent would yield a net annual saving of $106 million, while cutting the rebate by 25 per cent would save $549 million a year.

Dr Cheng argued that private health insurance rebates were ''expensive and fiscally unsustainable''. He said while Labor's introduction of a means test on the rebate in July 2012 was ''a positive first step'', gradually removing the rebates would be a ''logically and fiscally responsible next step''. But Dr Cheng said this should not happen rapidly as the public hospital system would need time to expand its capacity.