> Do you think people who own a house should be allowed to buy a 2nd one and push first time buyers out the market?
Just to address this, first, yes, I absolutely think people need to be able to buy a second house. There is also a natural impediment in place of investors buying up "too many" houses. The reason is, if there are more houses on the rental market than there is demand for rentals, it will drive rental rates down. Similarly, if there are not enough houses for sale to fill demand of all these investors as well as purchases for-self, it will drive house prices up. As those two things happen, the rate of return on an investment property will quickly become lower than that of other comparable investments, so people will not rationally keep buying investment properties until either prices go back down or more houses are built (which will also drive prices back down).
Obviously in the short term people don't always act rationally, but that situation can't logically persist indefinitely. (And while it does, renters get below-market rent, subsidized by owners. That was has been the case here in Canada for the past few years, and I happily rented for several of those years.) Long term though, investment owners will earn just enough return to make it worthwhile for them to provide the service of rental housing to people who want it. That's a good thing.
Now imagine if people couldn't buy second houses. It would be impossible to rent, because there would be no unoccupied homes. Yes, it would bring house prices down, but what if you were just starting out and didn't have the money to buy a home, even a cheap one? You would then have no options. I know you're not really advocating for outlawing second houses completely, but incentives for first-time buyers over investment buyers would have a similar effect to the lesser extent. You would be making first-time ownership cheaper, and renting more expensive.
Now, I don't think that some help for first time buyers is terrible policy. However, I think better policy would be to focus on helping young people in general. For instance, instead of a first time home buyers' credit, there could be a special reduced tax rate on the first $X (or £Y :P ) that a person earns after age 18. (Possibly varied on a means-tested basis.) That would help people get started, either saving up a down payment, or starting an investment portfolio, without skewing the housing and rental markets.
Of course I recognize that the problem with that plan is that many, or even most, people would waste that money instead of saving it. By tying it to house purchase, you force people to put it into an asset, and in turn, owning a home forces people to save (in the form of equity). However, we need to find a different solution to that problem, because we'll never be (or want to be) at the point where everyone is a home owner, and right now the people who most need that leg up early in life are the ones who aren't getting it. I don't know what the solution is, but there are certainly possibilities. For instance, a defined benefit state-backed pension plan can prevent people with no savings from being screwed in retirement. It could be made possible to borrow from one's state pension plan to buy a first home. In theory that should not skew prices vs rents as much as a straight tax break, because it's not free money. And it would be more equitable, because people who choose not to use it (or who aren't able to) will still get an equivalent benefit.