A fresh analysis has cast doubt on the common assumption that lifting the rate of compulsory superannuation automatically leads to lower wages, finding that average pay growth was actually higher in years when the super levy increased.

The report, by the Centre for Future Work at the Australia Institute, finds there is no evidence for the prevailing view that there is an “automatic and complete tradeoff” between wages and super, and rejects calls from Liberal backbenchers to freeze in the superannuation guarantee at 9.5%, or even to make superannuation voluntary.

The compulsory superannuation guarantee is set to increase from 9.5% to 12% in five annual increases starting on 1 July 2021, but the government has refused to rule out freezing the increases as it reviews the retirement income system.

The report by Jim Stanford, the centre’s director and economist, argues that findings of the Henry tax review have been misconstrued by an echo chamber of stakeholders across the political spectrum – from the Grattan Institute to the Centre for Independent Studies, former Labor leader Bill Shorten and former assistant treasurer Kelly O’Dwyer.

Stanford’s report argues that the Henry tax review found that “in most circumstances most of the incidence” of payroll tax or superannuation will come from wages. That finding had been repeatedly misinterpreted in studies that assumed – rather than proved – a one-to-one trade-off to calculate how much workers would be worse off if superannuation increased, it said.

Meanwhile, a second report, by the Australia Institute’s Bill Browne, timed for “go home on time day” on Wednesday, found Australians were still working up to six weeks of unpaid overtime in a year, or up to an average of 4.6 hours a week.

Browne found the aggregate value of the “time theft” equated to about $80bn in lost wages, resulting in reduced “family incomes, [weakened] consumer spending and exacerbating the challenge of work-life balance”.

The reports aim to provide solutions and context to Australia’s stagnant wage growth.

Stanford conducted a historical analysis on earlier superannuation increases in Australia, and found “a surprising positive correlation” that annual wage growth was slightly higher in years in which the superannuation guarantee rate was raised, at 4.2%, than in years when it was unchanged (3.9%).

“Higher [super] payments are associated with faster growing wages, not slower, and in some specifications that finding is statistically significant,” the report said.

In six of 10 years when the superannuation guarantee was increased, wage growth exceeded its post-1992 average, while in only three years (in 1993, 1996 and 2014) was an increase accompanied by wage growth below that average.

In 18 years when the superannuation guarantee was not increased, it was “just as likely that wage growth fell below average as above. Clearly, therefore, freezing the [super] rate should provide no confidence of strong wage growth.”

Stanford conducted three further tests: a regression model that incorporated several other wage determinants, one based on inter-industry comparisons within Australia, and one based on international comparisons.

“In no case does the empirical evidence support the existence of a visible or statistically significant trade-off between wages and superannuation contributions … let alone the perfect one-to-one trade-off assumed by those opposing scheduled increases in [super] rates,” the report concluded.

“The assumption of a one-to-one trade-off between superannuation contributions and wage growth is not credible, and policy conclusions based on that assumption should be rejected.

“Canceling planned increases in the [superannuation guarantee] rate will not shift income from employers to workers; it would almost certainly lead to even further reduction in overall labour compensation relative to GDP.”

Stanford argued that a set of policies to boost workers’ bargaining power – including relaxing restrictions on collective bargaining – would allow workers “to demand and win both higher wages and higher superannuation contributions”.

Browne polled 1,464 respondents between 23 and 30 July for the 11th Go Home On Time Day initiative, and found growing evidence of “a sharp polarisation in Australian employment patterns”, between those in full-time, relatively secure work and the growing cohort of casual and part-time workers.

“At the same time as many Australian workers report they would prefer more hours of paid work, unpaid overtime is a frequent occurrence,” Browne reported.

“[It includes] coming in early, leaving late, working at home or on weekends, and working through regular breaks and lunch hours.

“In an era of wage stagnation underemployment, insecure work and significant cost of living pressures, Australian workers cannot afford to give their time away to employers for free.”