More detail on the MID and House Prices (long and wonky)

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*(1-ty)+PT*(1-ty)+M-π.

We estimate

R/P = α + β1*R*(1-ty) + β2*)T(1-ty) + 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 recent-five 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 30-year 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 rent-to-price ratios.  

We will show four sets of regressions: simple linear regressions with year fixed effects that are both population weighted and non-population weighted; linear regressions for each year individually, and panel regressions.  Let us begin with a set of “base” regressions, where the rent-to-value ratio is explained by the after tax cost of capital (atcc1) and the “after-tax” 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 after-tax 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.  

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).

Sherman Maisel on how Fannie Mae "left" the government in 1968

Go to 3:55

Southwest CEO Gary Kelly understands price elasticity

I am at the ULI conference in Denver, and reading the local magazine, which features an interview with Gary Kelly. His quote on why Southwest doesn't charge for baggage: "it takes the loss of one customer to offset about ten bag fees."

I enjoy it when an executive talks about demand curves.

A gentle rebuke to Paul Krugman--she was referring to Oakland, not Los Angeles

Tomorrow I am teaching a book I admire--Paul Krugman's Development, Geography and Economic Theory.  The book contains three Olin Lectures that are beautifully written, accessible and insightful.  But on page 58, he quotes Gertrude Stein as having said that Los Angeles had "no there there."  

She actually was referring to her home town.  Specifically, she wrote:

What was the use of my having come from Oakland it was not natural to have come from there yes write about it if I like or anything if I like but not there, there is no there there.

I am not sure Oakland deserves the insult either, but still, LA gets enough abuse as it is.

Rub ́en Herna ́ndez-Murillo, Andra C. Ghent, and Michael T. Owyang show that the Community Reinvestment Act did not induce subprime lending.

They look at lending originations and loan performance on either side of the CRA thresholds.  If CRA encouraged subprime lending, one should see a discontinuity at the thresholds, but there is none.

These are originations for 2-28 subprime loans.  Under CRA, lenders received credit for originating and funding loans in census tracts whose median incomes were below 80 percent of area median income.  If the CRA was inducing lending, we should see a jump in lending to the left of the 80 percent cut-off--there isn't (either visually or econometrically).  They find the same result when looking at pricing and default.   

Was Paul Ryan a math major?

Ryan says it is too complicated to explain his budget numbers. Imaginary numbers are indeed complex.