Over at Economix, Ed Glaeser discusses whether Fannie and Freddie should be privatized, abolished, or kept in government hands. This brings to mind a quick thought experiment: if you’re planning on buying a house, would you be better buying before or after Freddie and Fannie go away? The conclusion I’ll come to is common sense, but it’s worth thinking through it through analytically.

The key issue is what abolishing the GSEs would do to capitalization rates, which are also called cap rates. This is the discount rate that converts a stream of income into an asset value. In the case of housing the cap rate converts the stream of rent, which is what homeowners consume,  into house prices. The price of a home is equal to the rent it could generate divided by the cap rate.

Like a discount rate, the cap rate varies by person, since the present value of a flow of housing services depends on, among other things, risk preferences, borrowing costs, and the time value of money. I haven’t seen recent data on this, but from from what I have seen, on average they tend to be in the general neighborhood of 8% for homeowners.

Whether a potential homebuyer will be better off in an post-GSE world depends on what happens to their own cap rate and everyone else’s cap rates. If borrowing costs are less important for you than for the average borrower, then your cap rate won’t be as affected when Freddie and Fannie are abolished and lending terms are more strict. This means your valuation of housing won’t go down as much. Borrowing costs could be low because of high savings, good credit, or a preference for cheap housing services relative to income.

On average, however, cap rates will go way up, as borrowing costs are important considerations for most buyers. If you need to have a 30% down payment, you’re willingness to pay for housing assets will decline greatly. This means house prices will fall. Likewise if mortgage rates increase.

So if you’re cap rate will be less affected by borrowing costs then housing may be more affordable for you in a post Fannie/Freddie world. Keep in mind that investors have cap rates as well, which means even if your cap rate goes up by less than the average homeowners’ you may be priced out of the market by investors who buy and rent housing.

I should emphasize that I’m looking at what happens along one dimension if Fannie and Freddie go away. This is not to suggest that the affects of abolishing them overnight would be modest or desirable. In fact, I believe it would be devastating and would probably make almost everyone worse off.