Economists Andrew Leigh, from the Australian National University, and Professor Joshua Gans, from Melbourne University, will write to the minister warning her to expect another bout of unhealthily heavy babies if the increase goes ahead.

Babies born weighing more than 4kg are statistically more likely to have low scores on the Apgar scale which measures muscle tone, heart rate, reflexes and respiration.

The economists will tell the minister that in July 2004, the month the baby bonus was introduced, 680 babies were born weighing more than 4kg 140 more than in a typical month.

"People are aware that premature babies are unhealthy," Dr Leigh said yesterday.

"They are less aware that overcooked babies are unhealthy." Dr Leigh and Professor Gans' research suggests that about 1000 babies that would have been born in June 2004 had their arrival delayed until July, mainly by postponing caesarean sections and inductions.

Only 42 per cent of births in the final week of June were caesareans or inductions. The rate jumped to 52 per cent in the following week.

Data from the Bureau of Statistics suggested that the rate of infant deaths increased in July 2004, but the economists were unable to back up this finding with the more detailed data they have so far obtained from state health authorities.

"Getting the data out of the states and territories is like getting blood out of a stone. Only Western Australia gave us data for both births and deaths and it points to no demonstrable effect," Dr Leigh said.

When the bonus last jumped to $4000 in July 2006, about 680 births were delayed.

"We were struck by how big the 2006 effect was," Dr Leigh said. When the bonus jumps again to $5000 in July this year, the economists expect another bout of heavy babies. "The sudden jump creates an incentive to over cook your kids," he said.