Enfoques de los determinantes sociales de la salud a escala de un país

Estimating the Sensitivity of Behavioral Parameters to the MID

Because consumers respond to tax incentives, I take into account two behavioral parameters with regard to the MID: how sensitive itemization is to the tax subsidy and how sensitive debt financing is to the tax subsidy. Using variation in the availability of the MID at the state level, I estimate the sensitivity of the percent of tax filers who itemize deductions (𝐼(𝑔)_𝑖) and of LTV ratios (𝜆(𝑔)𝑖) to the generosity (𝑔) of the MID. This is done with data from SOI and

AHS and follows a comparable method to that used in Hanson and Martin (2014) to estimate sensitivity of MID claims to MID generosity. I use both weighted least squares (WLS) and Instrumental Variables (IV) to estimate these relationships. The basic WLS specification for both variables is:

𝑌_𝑖 = 𝛼 + 𝛽₁𝑇𝑜𝑝𝑀𝑇𝑅_𝑖∗ 𝑀𝐼𝐷_𝑖 + 𝒁_𝒊′_{𝜷 + 𝜀 (19)}

When estimating the sensitivity of itemizing tax returns to the availability of the MID, 𝑌_𝑖 becomes the percent of tax filers who itemize returns in ZIP code 𝑖, 𝑇𝑜𝑝𝑀𝑇𝑅_𝑖 ∗ 𝑀𝐼𝐷_𝑖 is the state’s top marginal income tax rate interacted with an indicator equal to one if the state allows the mortgage interest deduction on state tax returns, and 𝒁_𝒊′is a set of controls including adjusted gross income, the percent of returns claiming dependents, the percent of filings that are joint, the amount of alternative minimum tax paid and the percent of filers who pay it in each ZIP code. The regression is weighted by the square root of the number of tax returns in each ZIP code. Standard errors reflect the White (1980) correction for heteroskedasticity. The coefficient of interest is 𝛽₁, which reflects the change in the percent of itemizers in a ZIP code resulting from a one percentage-point increase in the deductibility of mortgage interest.

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The second behavioral parameter I estimate is the sensitivity of LTV ratios to the

availability of the MID, in which case 𝑌_𝑖 becomes the LTV ratio of household 𝑖, 𝒁_𝒊′becomes a set of controls including the household’s salary and the number of minors living in the household. The regression is weighted by the AHS national weights, which reflect how representative each household is of the population using census controls. Standard errors are again corrected for heteroskedasticity. In this case, 𝛽1 reflects the change in LTV ratios resulting from a one

percentage-point increase in the deductibility of mortgage interest.

I also estimate the equations above using IV, whereby I instrument availability of the MID with an indicator variable equal to 1 if the state adopts the full itemization schedule from the federal tax code, and 0 if it deviates from the federal schedule. This instrument is designed to resolve endogeneity that may arise from unobserved political influence by homeowners seeking preferential tax subsidies in their state tax policy. Such targeted homeowner lobbying would most likely result in a state MID deduction that does not depend on adopting the full federal itemization schedule. The instrument therefore captures as compliers those states that do not provide preferential treatment to homeowners by way of an a la carte MID deduction.

A straightforward application of the instrument would be to fit 𝑀𝐼𝐷_𝑖, the indicator of MID deductibility, by regressing 𝑀𝐼𝐷𝑖 on 𝑈𝑠𝑒𝐹𝑒𝑑𝑖, the instrument described above. Because

my outcome of interest is not 𝑀𝐼𝐷_𝑖 but instead 𝑇𝑜𝑝𝑀𝑇𝑅_𝑖 ∗ 𝑀𝐼𝐷_𝑖, I construct an instrument to parallel this variable by interacting 𝑈𝑠𝑒𝐹𝑒𝑑_𝑖 with 𝑇𝑜𝑝𝑀𝑇𝑅_𝑖. This scales the instrument so that the fitted values of 𝑇𝑜𝑝𝑀𝑇𝑅_𝑖∗ 𝑀𝐼𝐷_𝑖 translate linearly to the second stage. The first stage, then, is:

𝑇𝑜𝑝𝑀𝑇𝑅_𝑖∗ 𝑀𝐼𝐷_𝑖 = 𝑎 + 𝑏₁𝑇𝑜𝑝𝑀𝑇𝑅_𝑖 ∗ 𝑈𝑠𝑒𝐹𝑒𝑑_𝑖 + 𝒁_𝒊′_{𝑩 + 𝜀 (20)}

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𝑌_𝑖 = 𝛼 + 𝛽₁𝑇𝑜𝑝𝑀𝑇𝑅̂_𝑖∗ 𝑀𝐼𝐷_𝑖 + 𝒁_𝒊′_{𝜷 + 𝜀 (21)}

Table 9Error! Reference source not found. shows the first-stage results of this regression for both the SOI and the AHS samples and their respective controls. The fit of the instrument is consistent across both SOI and AHS samples and is statistically significant at the one-percent level.

The simulation requires the choice of a functional form for 𝐼(𝑔)_𝑗 and 𝜆(𝑔)_𝑗. I use the linear form:

𝐼(𝑔)𝑗 = 𝛼𝑗 + 𝛽𝑖𝑡𝑒𝑚𝑖𝑧𝑒∗ 𝑔𝑗 (22)

where in each market 𝑗, the percent of itemizers in the market who would itemize without any subsidy is given by 𝛼_𝑗, the generosity of the subsidy is given by 𝑔_𝑗, and the slope 𝛽_{𝑖𝑡𝑒𝑚𝑖𝑧𝑒} is the coefficient 𝛽₁ in equations 19 and 21 when 𝑌_𝑖 is percent of itemizers. For instance, if ten percent of tax filers in market 𝑗 would itemize deductions without any subsidy, and the policy under consideration is a twenty percent mortgage interest deduction for itemizing tax filers, then the function predicts the proportion of itemizing tax filers as:

𝐼(𝑔)_𝑗 = 0.10 + 𝛽_{𝑖𝑡𝑒𝑚𝑖𝑧𝑒}∗ 0.20 (23)

Similarly, the LTV function is:

𝜆(𝑔)𝑗 = 𝛾𝑗+ 𝛽𝐿𝑇𝑉∗ 𝑔𝑗 (24)

where 𝛾_𝑗 is the average LTV ratio that would obtain in a market without any subsidy, and the slope 𝛽_𝐿𝑇𝑉 is the coefficient 𝛽₁ in equations 19 and 21 when 𝑌_𝑖 is the LTV ratio.

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Table 9. First Stage Results of Instrumental Variables Specification

IRS AHS

Variables: No Controls Controls No Controls Controls

Instrument (𝑇𝑜𝑝𝑀𝑇𝑅 ∗ 𝑈𝑠𝑒𝐹𝑒𝑑) 0.919*** 0.911*** 0.962*** 0.962*** (0.00302) (0.00384) (0.00306) (0.00306) Average Adjusted Gross Income (in

$1,000s)

-0.00634*** (0.000629)

Household Salary (in $1,000s) 0.000211

(0.000136) Percent of households claiming dependents 0.000600

(0.000514)

Number of minors in household 0.00951

(0.0104)

Percent of households filing jointly 0.0207***

(0.00104) Average Alternative Minimum Tax Paid (in

$1,000s)

0.0882*** (0.0109) Percent of households paying Alternative

Minimum Tax -0.942** (0.449) Constant 0.643*** -0.120* 0.338*** 0.321*** (0.0239) (0.0672) (0.0274) (0.0273) Observations 26,622 26,622 22,661 22,661 F-Test 92,941 56,113 98,774 99,159

Note: The fitted variable is the state income tax rate interacted with an indicator equal to one if the state allows the mortgage interest deduction (MID) on state tax returns. The first two columns contain observations from ZIP codes in the IRS Statistics of Income (SOI) in 2011, and the fitted values are used in table 10. The second two columns contain observations from households in the American Housing Survey (AHS) in 2011, and the fitted values are used in table 11. Regressions are weighted by the square root of the number of tax returns in each ZIP code. Robust standard errors in parentheses. *** p<.01 ** p<.05 * p<.1

52 Estimating Parameters in the User Cost Model

The user cost model in equation 15 can be used in a number of ways. In section 3 I complete the right-hand side with real-world proxies for each parameter and then vary one or more of the parameters to obtain a percent change in the user cost associated with parameter changes. This use makes two key assumptions: 1) that the user cost reflects the true opportunity cost to consumers (i.e. it is correctly specified) and 2) that the selected proxies for each

parameter are representative of the true values. The second assumption seems particularly tenuous for the parameter 𝜋, or expected price appreciation. How does one know what

consumers use to form beliefs about future home prices? Additionally, there is no clear proxy signaling the degree to which homeowners view property tax as a benefit tax, a belief

characterized by the parameter 𝜅. Because of these shortcomings I briefly explore an econometric test of the user cost model that provides a data-driven estimate for these two parameters.

In order to test the validity of parameters on the left-hand side, I substitute a real-world proxy for imputed rents: actual market rents, 𝑅_𝑎. I then conduct regression analysis of the model with (𝑅_𝑃𝑎) = 𝑈𝐶𝑎 as the dependent variable. Specifically, I use median rental housing prices per

square foot and median home values per square foot for 𝑅 and 𝑃 respectively.39

I examine two specifications using WLS. In both cases the unit of observation 𝑖 is the ZIP code. The first specification is:

𝑈𝐶𝑎,𝑖 = 𝛼𝑖+ 𝛽𝜏𝑃𝜏𝑃,𝑖+ 𝛽ΠΠ𝑖 + 𝒁𝒊′𝜷 + 𝜖𝑖 (25)

39 _{Using rents and home values normalized per square foot reduces the problem that renters and homeowners select} different units due to heterogeneous preferences, income constraints etc. to the extent that these preferences manifest themselves in quantity differences. Data is not available to control for differences in unit quality.

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where 𝑈𝐶_𝑎,𝑖is the ratio of market rents to market prices (per square foot) in market 𝑖, 𝜏_𝑃,𝑖 and Π_𝑖 are property tax rate and the 13-year average annual price appreciation in market 𝑖 respectively, and 𝒁_𝒊′ is a vector of all other user cost parameters that vary over geography. The coefficients of interest are 𝛽_𝜏𝑃 which is related to 𝜅 in the user cost model as (1 − 𝜏_𝑖𝑛𝑐 − 𝜅) = 𝛽_𝜏𝑃, and 𝛽_Π, which can be viewed as a weight placed on the selected proxy of expected price appreciation in order to construct 𝜋 (i.e. 𝛽Π∗ Π = 𝜋).40

This specification leaves out important features of the user cost model: namely, the interactions across continuous variables as seen in equation 11(11), and interactions with the percent of itemizers in equation 12(12). In a second specification, I regress 𝑈𝐶_𝑎,𝑖 on each space- varying parameter as well as on the percent of itemizers; each parameter in 𝑈𝐶_{𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑} is included again without such an interaction:

𝑈𝐶_𝑎,𝑖 = 𝛼_𝑖+ 𝛽_𝜏𝑃1𝜏_𝑃,𝑖+ 𝛽_Π1Π_𝑖+ 𝛽_𝜏𝑃2𝜏_{𝑖𝑛𝑐,𝑖}∗ 𝜏_𝑃,𝑖+ 𝛽_𝜏𝑃3𝐼_𝑖∗ 𝜏_{𝑖𝑛𝑐,𝑖}∗ 𝜏_𝑃,𝑖+ 𝛽_Π2𝐼_𝑖 ∗ Π𝑖+ 𝒁𝒊′𝜷 + 𝜖𝑖

(26)

where 𝒁_𝒋′ contains all variables and interactions that are not of interest. This equation creates a more complicated derivation of the partial effect of property taxes on the user cost (given before as simply 𝛽_𝜏𝑃). It is now not a single regression coefficient, but a function of the MTR and the percent of itemizers:

𝜕𝑈𝐶𝑎

𝜕𝜏_𝑃

⁄ = 𝛽_𝜏𝑃1+ 𝛽_𝜏𝑃2∗ 𝜏_{𝑖𝑛𝑐,𝑖}+ 𝛽_𝜏𝑃3𝐼_𝑖 ∗ 𝜏_{𝑖𝑛𝑐,𝑖} (27) Likewise, the partial effect of anticipated home price inflation on the user cost is no longer 𝛽_Π but is now given as:

40 _{Note that the user cost in equation 11 includes parameters that are assumed to be fixed across space: namely the} tax rate on long-term capital gains (𝜏_𝑦), the risk-free rate of return (𝑟_𝑇) and the risk premium of homeownership (𝛽). These parameters will accrue to the constant in the regression.

54 𝜕𝑈𝐶_𝑎

𝜕𝛱

⁄ = 𝛽Π1+ 𝛽Π2∗ 𝐼𝑖 (28)

I compute these partial effects at the sample means of the MTR and the percent of itemizing tax filers in order to obtain single values of 𝜅 and 𝜋 to use in the simulation.