Falling housing prices in Sydney and Melbourne in the third quarter cut nearly half a year off the time taken to save for a deposit as affordability improved last year, new analysis of official housing and weekly earnings figures shows.

Sydney’s $21,000 and Melbourne’s $20,000 fall in median house price in the September quarter cut 23 weeks off the time needed to raise a deposit in the NSW capital and 22 weeks in the Victorian capital, figures published by the Australian Institute for Progress, a conservative-aligned think tank, show.