"The restrictions have meant young people are taking longer to get into their first home so there's more people out there wanting to rent."
Rising costs for landlords were another factor, he said.
Mr Davidson expected rents to continue to gradually increase as more people returned home from Australia or migrated from Auckland looking for more reasonable priced homes.
Nationally, weekly rents rose nine per cent year-on-year to a median rent of $420 a week.
Head of Trade Me Property Nigel Jeffries said the rental market was "sparking into action" after a stable and relatively quiet 2014. "The nine per cent year-on-year increase in January is the largest single month rise we've recorded over the past five years. Median weekly rents clicked up $20 per week between December and January to a record high of $420 per week. That's grim news for tenants."
The increases were due to landlords wanting better returns on their investments, Mr Jeffries said.
"It was more a question of when, not if, landlords were going to start recovering some level of yield. It looks like that signal has flowed into the market this month and started to sting tenants in the pocket."
Rents for five-bedroom homes were up 7.7 per cent year-on-year to a record of $700 per week. Rents for medium-sized homes were also strong, Mr Jeffries said.
Only Gisborne and the West Coast recorded falls in median weekly rent.NZME.