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).