Low interest rates mean people can borrow more. If people have access to more money but supply is limited, then prices go up. This is the supply and demand equation, but I think it's good to test things we think we know. One issue we will find is that the US tend to sign mortgage loans with the interest rate fixed for 30 years, so interest rates changing don't impact existing owners except when they move. Here in NZ people tend to only get a fixed rate for a year or two, and no major bank offers one past 5 years. Here's one study "The Effect of Interest Rates and Mortgage Lending on House Prices".

The abstract states:

We find a surprisingly important role for short-term interest rates as a driver of house prices, especially outside the United States.

The "especially outside the US" part is why I mention the difference in US mortgages vs ours.

And in the actual paper, this is part of the conclusion:

Most empirical studies assume that short-term interest rates do not influence house price growth other than through the domestic cost of borrowing, ie by their influence on long-term interest rates. The findings in this paper suggest that this view might be mistaken: changes in short-term interest rates seem to have a strong and persistent impact on house price growth

Here's another that takes it a step further and says that purchasing power is the real driver, rather than interest rates in and of themselves.

Real income and the real interest rate have been widely considered as two important determinants of house prices. We find that the purchasing power for housing, which is based on the net present value of future income flows, is a more powerful concept. It is intuitive and realistic in nature for first time buyers who need substantial mortgage-financing. Based on aggregated yearly time series data for Belgium from 1973 to 2009, we find that nominal house prices are cointegrated with the purchasing power for housing.

A Google search on it pulls up a couple of studies, one from Germany, one from Australia appearing to show opposite results lol (also some commentary from the NZ Treasury, but not backed up from a quick scroll). It'd be interesting to know if someone's evaluated our ones.

https://www.google.com/search?q=buyer%20subsidies%20house%20prices%20effect%20study

So I guess it goes to my earlier point about feeling mixed about it. I'd suspect they have a far greater equalising effect when the market isnt so constrained that the subsidies can just can be capitalised into prices, so it might depend on the broader market a bit. And so pairing them with a massive state house building programme and allowing density with good public transport should go alongside. You know, all the stuff this government has cancelled, cut or rolled back ;)