## Sunday, October 21, 2012

### 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.

David Barker said...

Maybe the problem is that the situation is so different for high, medium and low income buyers.

From the ACS can you estimate quintiles of prices and rents, and use different costs of capital for them based on different tax brackets?

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