The study's associate director, Waikato-based public health physician Dr Polly Atatoa Carr, said moves were for a mix of positive and negative reasons.
"There are some people moving rentals because it's a desired move, such as they wanted a bigger property, but there will be others who will be moving because they are pushed to move," she said.
"I was certainly expecting that children would be moving around quite a lot. I have worked in health service delivery and I know how hard it is to get immunisation follow-up here in the Waikato with sharemilkers, for example."
Plunket clinical advisory manager Karen Magrath said Plunket nurses saw children moving more often.
"This can create challenges," she said. "We know that children do better when their families are connected to their local community."
Early Childhood Council chief executive Peter Reynolds said moves were often disruptive for children in childcare.
"It breaks relationships the child and the family will have established with the teacher and with other children in the centre."
Across the whole sample, 45 per cent of children moved at least once in their first two years, including 17 per cent who moved at least twice and 2 per cent who moved at least four times. A few families moved up to eight times.
Apart from private renting, the other main factors driving moves were overcrowding, living with relatives and friends, and partnerships breaking up or forming.
Uprooted family keep connections with their old suburb
Ether Fonoia moved house three times in his first five years - but his parents have kept on driving him and his two brothers to schools and preschools in the area where they lived when he was born.
Ether, 6, is part of a group of "leading lights" for the Growing Up in NZ study, born in the year before the main group of children.
When he was born, the second of three boys, his family lived in a two-bedroom private rental in Papatoetoe. They had to move out in 2010 when the house was sold to a new owner who wanted to renovate. They found a new rental home close by, but only a year later that house was sold too.
The new owner took over the garage for storage. The rent went up.
"We were paying a high rent and there was no garage," said his mother, Nina Fonoia.
They moved to Mangere, to a house owned by relatives who were moving. They could not afford to buy it when the relatives sold, so they moved again last year to another private rental nearby which is just behind their local Mormon Church.
Mrs Fonoia works at a money transfer agency in Otahuhu. Her husband, Mila Fonoia, had to stop work as a carpenter after an accident in 2010, but he still drives the three children back to their home suburb - to Papatoetoe North Primary and Papatoetoe Kindergarten - every day.
Read the full study here: tinyurl.com/growupinnz.