The government has released Treasury modelling showing a tax mix switch with a 15% GST and income tax cuts would deliver no gains to economic growth.

The modelling has been put out to back up Prime Minister Malcolm Turnbull’s decision to walk away from the GST change on the grounds that the option, as he told the Coalition party room on Tuesday, “does not offer the economic benefits that many have assumed”.

As a result of the modelling the government has refocused its work on its tax package towards other options.

The modelling, presented in a January 25 Treasury ministerial brief, assumed an increase in the GST from 10% to 15%, and broadening its base to include water and sewerage. This would raise $35 billion. It further assumed $6 billion in assistance to households automatically generated from indexed pension payments, leaving the rest for income tax cuts.

The higher GST rate would cut 1.2% off GDP, and the automatic CPI indexation of transfer payments and grants would slice off another 0.1%, according to the modelling. The modest base broadening to water and sewerage would add 0.07%, while the income tax cuts would add 1.3%. This left a bottom line of no addition to GDP.

The assumption in the modelling about compensation is minimalist – further measures would be needed in practice to compensate low income earners, which would mean less funds available for income tax cuts.

The government tested the Treasury modelling against that from two private sector firms – Independent Economics and KPMG. They came up with tiny increases to GDP from such a package.

Independent Economics estimated 0.18% gain to GDP in the long term, while KPMG’s estimate was 0.3% gain.

The brief says: “The estimates from the scenario testing are, of course, indicative and may change with further refinement.

“That said, they are all pointing to a small increase in GDP over time from personal income tax reductions that are funded largely by a GST hike. In essence, the models all suggest they are largely offsetting.”

The brief notes that the impact would be greater the more personal income tax cuts were combined with corporate income tax cuts – but the government could not, in political terms, skew its tax cuts to the corporate sector.

“The case [for a tax mix switch] will need to be made forcefully using broader arguments. These include the impetus to entrepreneurial behaviour, international competitiveness and reducing incentives to channel personal income into company and other structures,” the brief says.

Treasury also provided a brief on the economic and fiscal effects of rising average tax rates (bracket creep).

Dated February 1, it says that by the end of the forward estimates, about half of the fiscal consolidation relies on increases in average tax rates due to the tax scales not being indexed.

The average personal income tax rate is set to be 24.4% in 2016-17, rising to 26.6% by 2020-21.

Treasury has modelled the economic cost of allowing average tax rates to rise over the forward estimates period.

It shows that achieving a deficit reduction through an increase in the average tax rate, compared with a strategy of maintaining a constant average tax rate and cutting government spending, leads to a 0.35% contraction in GDP in the long term.

The long term economic cost of the increase in average tax rates (0.55% of GDP) is only partly offset by the lift in economic activity from government spending (0.2% of GDP).

The brief cautions that this modelling is indicative at best but says “it does illustrate the economic cost of relying on bracket creep, rather than spending cuts to close the budget deficit”.

“The economic cost of rising average tax rates is large (0.55% of GDP) because it creates distortions in all sectors of the economy. The economic distortion from all taxes increases as personal income tax rates rise.”

Industry Minister Christopher Pyne told Parliament on Thursday “there won’t be a [higher] goods and services tax”.