## Monday, December 29, 2014

### The limits of knowledge in economics, Part V

How much does it cost you to live in your house?  If you are a renter, the answer to that question is fairly straightforward (although if your rent includes a gym membership and heat, it is not clearcut what the simple cost of occupying your place is).

But suppose you are an owner.  What is it costing you every month or every year to live in your house?  The truth is, you don't know with a great deal of precision, and neither does anyone else.

There are two ways to look at the issue.  One is to look at something called owner's equivalent rent. In principle, one could determine owner's equivalent by offering her house for rent, and seeing what it would fetch in the rental market.  Needless to say, owners don't do this very often.  Another way to calculate owner's equivalent rent is to find a perfect comparable for an owned house in the renter market, and impute the rent for the owner.  In the next episode of this series, we will discuss the problems with doing that.  It should be fairly obvious that they are large.

The alternative to owner's equivalent rent is user cost, which seeks to compute the cost of owning to those who live in their own houses.  [Pat Hendershott is the guru of user cost.  See a typical paper of his here]. The formula for the user cost of housing is

uct = Vt[((1-m)rt + mit)(1-ty) + τp(1-ty) + d - π

where uct is user cost at time t, Vt is the value of the house at time t, m is the loan-to-value ratiort is the opportunity cost of equity, it is the mortgage interest rate, ty is the marginal income tax rate, τp is the property tax rate, d is depreciation and π is expected house price appreciation.  This formula calculates the after-tax cash-flow cost of owning (including the opportunity cost of equity), adds depreciation and subtracts expected appreciation.

Of all these elements (and this formula doesn't incorporate everything, but it is close enough), the only thing we know with near certainty is the marginal income tax rate: once one calculates reported taxable income, one can know the marginal tax, which is set by statute, with certainty.

Everything else?  Up in in the air.  On a year-to-year basis, we don't know the value of our houses with certainty.  We don't know with certainty the opportunity cost of equity. While we know the coupon rate of a mortgage, we don't always know its total cost until we extinguish it, because mortgages with fees and points (and sometimes, even prepayment penalties) are amortized over time, and the life of a mortgage is generally considerably shorter than its term, as households refinance their mortgages or sell their houses.  We don't know property taxes until an assessor determines assessed value, which is usually at least a little different from market value.  Depreciation is difficult to measure.  Finally, we are pretty lousy at forecasting the values of our houses.

But let's say we are good at forecasting house prices, and you think the value of your house is going to increase by \$5,000 over the next year.  Is this the same as being handed a check for \$5,000?  No, because you still need to live somewhere.  If your house goes up by \$5,000 in value, so to does your neighbor's.  The only way to cash in on your \$5,000 is to downsize.  Pocketing the \$5,000 and downsizing may leave you better off, but not as well off as just having \$5,000.  So the user cost formula does not exactly get user cost right.