Well, I imagine you’d expect it to tend to cause rents to go up and house prices to go down if it shifts supply from the rental market to the sales market

Yes and no. Vast majority of rents are largely set by what it takes for an investor to pay the mortgage on the property, whether constructed or purchased. Property values crashing out due to no more institutional investors dumping cash into the market will have a downward pressure on rents overall, eventually.