## Friday, October 19, 2012

### I try to find a relationship between the after tax cost of a mortgage and house prices, and can't.

Some years ago, I wrote a paper with Pat Hendershott and Dennis Capozza looking at the impact of tax policy on house prices.  We ran the following regressions using a panel of cities across three census years:

Rent/Price = alpha + Beta1*ATCC + Beta2*NPT + Beta3*E[g] + e

where Rent/Price was the average rent to average housing price for an MSA, ATCC was the after tax cost of capital, NPT is the net average property tax rate after deductions, E[g] is expected house price growth net of depreciation, and e is an error term.  This is just the user cost model: Beta1 and Beta2 should equal one (and they did) and Beta3 should equal -1 (and it didn't, but we never got a decent measure of expected house price growth, and so it is not surprising that it didn't work).  Our results implied that removing tax advantages for housing would push rents up or drive prices down, or, most likely, both.

I have been redoing this exercise using American Community Survey Data from 2006-2010.  I get the following scatter plot, where each dot is an MSA at a different time:

The x -axis, the after tax cost of capital, is a function of two things: the mortgage rate for each period, and the effective rate at which mortgage interest is deducted (which is taken from the NBER TAXSIM model, Table 2).  Do you see a relationship between the after tax cost of capital and house price to income ratios? I don't.  Here is a regression with MSA and year fixed effects:

Fixed-effects (within) regression               Number of obs      =      1275
Group variable: msa                             Number of groups   =       255

R-sq:  within  = 0.4535                         Obs per group: min =         5
between = 0.1258                                        avg =       5.0
overall = 0.1387                                        max =         5

F(6,1014)          =    140.25
corr(u_i, Xb)  = -0.6549                        Prob > F           =    0.0000

rvratio1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
atcc1 |   .1972777   .1165485     1.69   0.091    -.0314262    .4259817
ptrate1 |   3.075967   .1451177    21.20   0.000     2.791202    3.360733

The coefficient on the after tax cost of capital is much smaller than one, and is not different from zero at the 95 percent confidence level.  But even if we take this coefficient at face value, it suggests that capitalization effects now are about 1/5 of what they were when Pat, Dennis and I wrote our paper.  I am curious about feedback (I should also note that the coefficient floats around depending on specification, and sometimes has the wrong sign).

David Barker said...

There is some correlation between land use policies and state income tax rates - states with restrictive land use policies (CA, OR, VT) also tend to have high tax rates. Many highly urbanized states (NY, NJ) also have high tax rates. Many states with less restrictive land use policies (TX, NV) have low income tax rates, and many rural states also have low tax rates.

Urbanization and land use policy effects go in the same direction as your ATCC effect, because expected appreciation should be higher, raising prices for any given current rent. (expected appreciation should be higher because both restricted land use and urbanization reduce the elasticity of land supply)

Leaving these things out ought to strengthen your effect, but since your measured effect is weak, it seems likely to be close to zero.

It could be that the effect of tax rates is nonlinear. Small state differences might be ignored by home buyers, but big federal changes that get more attention might have an effect.

But if it is is true that the effect is small, does it mean that the allocative efficiency costs of the mortgage interest deduction are larger than you suggest in Capozza, Green and Hendershott (1996)?

rjs said...

no varible for disposable personal income?

JPC said...

How about monthly mortgage cost and interest rates? in 1998, \$1300 at 8% bought a \$130k house, in 2003, \$1300 at 4% bought a \$260k house. (All approixmate values). My theory is that the low interest rates, being held low for so long, caused the bubble.

john said...

You could look at house prices relative to expected lifetime income. Figuring that is really easy right now since there's almost no discount rate. And no income growth.

My own amateur look at it indicates we're paying multiples more for residential land in most markets now compared to lifetime income than we did 15 years ago before the bubble. And it's far worse if you net out other unavoidable large lifetime purchases such as healthcare, education, retirement (lol).

Unknown said...

I can see tax policy to help with home ownership for first time buyers, but how about something that encourages home equity? Say a homeowner’s savings plan allowing up to \$5k tax deduction per year for \$25k? And then up to \$5k per year principal reduction for the first 5 years of home ownership. Then people are encouraged to “own” their home in that they actually have equity and increase their equity.

It has a benefit that if people then find they have financial problems they are better able to navigate them.

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uwwoman said...

What's going on in the middle of the graph? I would expect after tax cost of capital to be nearly continuous, but there's an empty space there. It could just be an artifact from your data set using categories rather than precise numbers, but if not, something doesn't look right.

Richard Green said...

I think the discontinuity comes from the bush tax cuts.