Capozza, Hendershott and Green (1997) developed a model of
determining whether federal tax policy would be capitalized into house
prices. The foundation for their
analysis was an estimating of the user cost model of housing. In the user cost model, in equilibrium, the
costs of owning and renting the same house must be the same. This means that:
Rent = Value*(after tax cost of capital + property tax rate
+ maintenance rate – expected house price growth).
After tax cost of capital is a blend of return on equity and
the cost of debt, taking into account tax preferences. The equity return to homeowner is imputed
rent (i.e., the rent the homeowner pays herself). Because imputed rent is not taxed, it
receives a tax preference. The return to
debt—mortgage interest—also receives a tax preference in the tax code, at least
for homeowners who itemize their deductions (only about half of homeowners are
itemizers).
The effective property tax rate facing owners is the ad
valorem rate less the tax preference.
Expected house price growth and maintenance are difficult to observe,
but we will model them using a method described below.
We may rewrite the equation above to produce the foundation
for an estimating equation:
Rent/Price = R*(1ty)+PT*(1ty)+Mπ.
We estimate
R/P = α + β1*R*(1ty) + β2*)T(1ty) + MSAi + T + ε
Where R/P is the rent to price ratio, the α soaks up maintenance
costs, R is an interest rate, ty is the marginal tax rate for those taking the
mortage interest deduction, PT is the ad valorem property tax rate, MSAi are
MSA fixed effects, which proxies for price expectations, T is a time fixed
effect, and ε is a residual.
When Capozza, Green and Hendershott estimated an equation similar to
(X), they found B1 and B2 were not statistically different from one, which is
the prediction of the model. From this,
they concluded that taxes do get capitalized into house prices, and ran
simulations based on that conclusion.
The most recent data available in CGH was the 1990 census. The American Community Survey will allow us
to do a much more timely estimate.
Data
We use the most recentfive year American Community Survey to find
mean rents and mean house prices for 255 metropolitan areas in the United
States. The smallest sample we have
among these MSAs is 1912 observations over five years, so we have sufficiently
large samples to draw inferences about mean values and prices.
For the before tax cost of capital, we use the Freddie Mac 30year
fixed interest rate series. For average
marginal tax rates by state, we use the results produced by the NBER TAXSIM web
site, which gives the average marginal rate of those who use the mortgage
interest deduction and the average marginal rate of those who use the property
tax deduction. NBER TAXSIM gives
estimates by state and by year; for those MSAs in more than one state, we take
the population weighted average of the TAXSIM rates.
It is worth spending a little time discussing the TAXSIM data. It contains a number of surprising, including
the fact that the average total state and federal marginal tax rate for
California among those taking the deduction was only slightly higher than for
Texas. This is surprising because (1)
California has a state marginal top tax bracket of xx percent, while Texas has
no state income taxes and (2) nominal incomes in California are on average
higher than in Texas.
I conferred with Dan Feenberg, who runs the NBER model, to make sure I
was interpreting the data correctly, and be confirmed that I was. The following might explain why we see the
peculiar data phenomenon.
California relied very heavily on subprime lending, while Texas, owing
to its heavily regulated mortgage market, did not. Subprime lenders specifically targeted
minority borrower and lower income borrowers—they also originated loans for
borrowers who self reported their incomes.
Because California has a high state income tax, and because mortgages
were large, borrowers in low tax Federal brackets in California had an
incentive to itemize; those in Texas did not.
As we shall see below, we have difficulty finding a relationship
between the after tax cost of capital and house prices. We present our regression results below.
Regressions
We begin by presenting renttoprice ratios.
We will show four sets of regressions: simple linear regressions with
year fixed effects that are both population weighted and nonpopulation
weighted; linear regressions for each year individually, and panel regressions. Let us begin with a set of “base”
regressions, where the renttovalue ratio is explained by the after tax cost
of capital (atcc1) and the “aftertax” property tax rate (ptrate1).
Specifications (1) and (3) include dummy variables for years; (1) and
(2) treats each MSA as an equal observation, while (3) and (4) weight MSAs by
population.

(1)

(2)

(3)

(4)


Unweighted

Unweighted

Weighted

Weighted

atcc1

0.190^{***}

0.266

0.226^{***}

1.191^{***}


(3.60)

(1.30)

(4.12)

(4.73)






ptrate1

0.965^{***}

0.954^{***}

1.018^{***}

0.985^{***}


(13.75)

(13.58)

(13.0)

(12.7)






y1


0.00584^{*}


0.0195^{***}



(2.02)


(5.59)






y2


0.00708^{*}


0.0196^{***}



(2.53)


(5.79)






y3


0.00636^{**}


0.0161^{***}



(2.68)


(5.66)






y4


0.00227^{*}


0.00500^{***}



(1.99)


(4.06)






_cons

0.0488^{***}

0.0325^{***}

0.0430^{***}

0.00917


(19.02)

(4.21)

(15.7)

(0.97)

N

1275

1275

1275

1275

t statistics in parentheses
·
p < 0.05, ^{**} p <
0.01, ^{***} p < 0.001
In equilibrium, the signs on both coefficients should be
positive, and the magnitude of the coefficient should be one. The property tax coefficient works quite
nicely across all four specifications—it is statistically different from zero
at the 99.9 percent level of confidence, and is quite close to zero. The coefficients on aftertax cost of capital
are another matter, however. They are in
two instances negative, and in one instance not different from zero. The predicted result only occurs in specification
(4). While one might argue that this is
the best specification, it also would amount to cherry picking to rely on it
when the three others are so different.
It is thus worth investigating other regression techniques.
We next turn to panel techniques, where we allow the
intercept of the regression to vary with MSA; this could reflect differences in
expectations about house prices from one MSA to the next. Now our after tax cost of capital is either
not different from zero, or has the wrong sign.
Interestingly, property taxes now become even more important, and their
magnitude is too large—it suggests full capitalization and then some. This also does not comport with economic
theory.

(1)

(2)

(3)

(4)


rvratio1

rvratio1

rvratio1

rvratio1

atcc1

0.0618^{**}

0.143

0.144^{***}

0.128


(3.07)

(1.25)

(7.48)

(1.09)






ptrate

2.632^{***}

2.713^{***}

1.720^{***}

1.782^{***}


(21.14)

(22.30)

(18.54)

(19.33)






y1


0.00191


0.00290



(1.23)


(1.83)






y2


0.00326^{*}


0.00422^{**}



(2.17)


(2.75)






y3


0.00361^{**}


0.00418^{**}



(2.88)


(3.26)






y4


0.00128^{**}


0.00151^{**}



(2.77)


(3.17)






_cons

0.0227^{***}

0.0145^{**}

0.0366^{***}

0.0260^{***}


(11.10)

(3.17)

(20.95)

(5.67)

N

1275

1275

1275

1275

t statistics in parentheses
^{*} p < 0.05, ^{**} p
< 0.01, ^{***} p < 0.001
Finally, we run regressions separately for each year (both
weighted and unweighted).
Unweighted

(2006)

(2007)

(2008)

(2009)

(2010)


rvratio1

rvratio1

rvratio1

rvratio1

rvratio1

atcc1

0.319

0.992^{*}

0.951

2.090^{***}

1.529^{*}


(0.87)

(2.20)

(1.91)

(4.18)

(2.42)







ptrate1

1.322^{***}

1.288^{***}

1.006^{***}

0.679^{***}

0.590^{***}


(7.61)

(7.95)

(6.62)

(4.87)

(4.02)







_cons

0.0532^{**}

0.0859^{***}

0.00737

0.0415^{*}

0.0113


(2.85)

(3.83)

(0.31)

(2.03)

(0.48)

N

255

255

255

255

255

t statistics in parentheses
^{*} p < 0.05, ^{**} p
< 0.01, ^{***} p < 0.001
Weighted by Population

(2006)

(2007)

(2008)

(2009)

(2010)


rvratio1

rvratio1

rvratio1

rvratio1

rvratio1

atcc1

0.355

0.967

2.045^{***}

4.137^{***}

4.145^{***}


(0.81)

(1.79)

(3.34)

(6.70)

(5.38)







ptrate1

1.423^{***}

1.343^{***}

0.998^{***}

0.643^{***}

0.604^{***}


(7.62)

(7.76)

(5.88)

(4.11)

(3.80)







_cons

0.00997

0.0769^{**}

0.0666^{*}

0.131^{***}

0.116^{***}


(0.45)

(2.84)

(2.25)

(5.18)

(4.01)

N

255

255

255

255

255

t statistics in parentheses
^{*} p < 0.05, ^{**} p
< 0.01, ^{***} p < 0.001
To say the coefficient on the after tax cost of capital are
unstable is an understatement. The
series of regressions listed above suggest that we cannot currently reliably
estimate the impact of changing the tax treatment of mortgage interest on house
prices.