This paper uses a structural vector autoregression model to analyse the relationship between migration flows, housing construction and house prices in New Zealand. It shows that a net immigration flow equal to one percent of the population is associated with an approximately 10 percent increase in house prices. This size of this relationship, which has existed since the 1960s, is an order of magnitude larger than would be expected from the average change in the population and house prices in the long term. One explanation is that migration flows occur at times when locals are changing their demand for housing because of revised expectations about future income growth. A second explanation is that migrant flows have a destabilising effect on agents expectations about the fundamental value of houses. While the paper cannot satisfactorily distinguish between these two options, the results suggest that monetary policy can still be used to dampen the house price changes that occur at times when migration flows are unusually large.