Does easy credit (e.g. lower minimum down payment, lower interest rate) cause housing prices (purchase, rent) in that area to be more expensive? Intuitively, this seems to be the case, because the availability of credit means more people can be a potential buyer, which drives up demands, which should increase price. Has there been an empirical research that backed this up or refuted it?
Theoretically, multiperiod borrow and lend models I am familiar with suggest that an increase in ease of credit (increasing the credit supply) should increase demand. This in turn raises the price of housing. So I believe your intuition here is correct.
Empirically, I am only familiar with one paper analyzing this relationship, which finds the same thing.
...because of geographic diversification, treated banks expand credit: Housing demand increases, house prices rise, but to a lesser extent in areas with elastic housing supply, where the housing stock increases instead.
Credit Supply and the Price of Housing
Favara and Imbs (2014)