Some of the figures used to produce secret government modelling on university fees were “essentially invented by departmental officials”, a senior bureaucrat has said.

The education department’s associate secretary, Robert Griew, cast doubt over the calculations in a statement to the Administrative Appeals Tribunal (AAT) opposing the release of internal government documents on the impact of the government’s higher education reforms.

Griew’s statement – tabled in a Senate estimates committee hearing on Wednesday – argued the release of predictions about university fees could undermine “genuine price competition” and “have a potential dampening effect on the frankness of advice” provided to ministers in future.

Griew also noted that a series of spreadsheets depended on “a number of assumptions about relevant parameters such as student population, level of fees for various kinds of university courses at various locations, rates of completion of study and other factors”.

“In each case, while presented as assumed facts and informed by departmental analysis and research, these figures were essentially invented by departmental officials for the purpose of providing material for analysis based on assumed patterns of behaviour,” he wrote.

“In each case, the purpose of the analysis was to give the minister, and through him the government, advice that may help to provide an insight into how the reforms might play out given certain assumptions.”

Labor senator Kim Carr, who tabled Griew’s statement after referring to it during the education committee hearing, said it showed the department had conducted “extensive modelling” on the impact of its proposals.

The department’s work included providing the education minister, Christopher Pyne, with hypothetical scenarios before the May 2014 budget announcement illustrating the effect of changes to student loan interest rates.

Other documents that the government did not want to release under freedom of information laws included an assessment of the impact of deregulation on regional higher education, modelling of the effects on graduates in 2019, estimates about average student fees, and the potential cost of cuts on individual institutions.

Carr suggested to officials that they had previously created an “impression” in their testimony and answers to questions on notice that the government had done only a limited amount of modelling.

The secretary of the department, Lisa Paul, initially said she was not aware of Griew’s document. After taking advice, Paul told the committee the document may be subject to “sub judice” because it was a matter that remained before the AAT.

Carr said it was covered by parliamentary privilege and he tabled it because Coalition senators on the committee asked him to provide the document from which he was reading.

“The question I’m putting to you goes to whether or not this committee has been misled by the department on regular occasions,” Carr said.

Paul gave an undertaking to Carr to examine his questions about the modelling and to provide a response.