Impact of a Two-Rate Property Tax on Residential Densities

Most municipalities in the United States collect residential real estate property taxes based on a percentage of total assessed property value. These policies place equal value on land and structures, but the taxation of buildings or structures inflates the perceived cost of improvements, thereby discouraging site improvement and potentially reducing economic returns (26). Thus, the land owner can reduce their tax burden by developing projects that use relatively more land than structures. This behavior leads to lower than optimal residential densities (36)

In response to suboptimal residential densities, researchers have investigated reducing tax rates applied to structures and increasing tax rates on land using a “two-rate property tax” (TPT) as an alternative to placing equal weight on land and structure taxes¹4 demonstrated that TPTs might result in additional land improvements. Brueckner also showed that (1) land taxes, property improvement taxes, and property taxes had different effects on the speed and capital intensity of development and (2) that the precise effect depends on the complementarity or substitutability between capital and development time. 31 found that land tax increases accelerated commercial development in Pittsburgh, Pennsylvania, a city which had a TPT from 1913 to 2001. 33 revealed that 15 municipalities in Pennsylvania with TPTs between 1972 and 1994 had significantly higher levels of construction than 204 similar Pennsylvania municipalities with single-rate taxes. 24 concluded that a pre-development land tax also affected development density in Finland These retrospective analyses document the observed effects of municipal property taxes on residential development patterns, but ex-post analyses are context-specific which may limit their generality. Alternatively, ex ante analyses provide a framework for predicting the actions of agents in response to policies before policy implementation.

Our current research contribution applies a method for performing ex ante impact analyses of TPTs on residential density in municipalities. The methodology is theoretically consistent with the urban development literature related to the optimal residential location choice of consumers and the profitmaximizing behavior of housing service providers. We develop a conceptual framework for a housing market in spatial equilibrium following 13 and 16, among others. Based on this model we develop a method for quantifying the impacts of a TPT on residential density using a probabilistic two-step procedure to predict residential development patterns. We estimate the parcel development model/housing density model using individual parcel data collected in Nashville-Davidson County, Tennessee. The econometric method applies recent developments in estimating linear outcome equations with sample selection bias and spatial dependence. The two-step procedure first estimates development decisions using spatial probit regression. We use weighted least squares adjusted for spatial dependence to estimate the second-stage housing density equation.

Based on econometric estimates, ex ante in-sample and out-of-sample forecasts simulate changes in housing density to compare a “status quo” tax scheme (equal weight placed on land and structure values) to hypothetical TPT scenarios (different weights on land and structure values). The scenarios incrementally increase land tax rates relative to the tax rate on property improvements, holding total municipal property tax revenues unchanged from the observed, status quo aggregate revenue A non-parametric procedure compares the simulated distributions of development density, conditional on the hypothetical TPTs at different rates. The ex ante analysis finds that a TPT above a minimum level triggers an increase in residential density above suboptimal densities associated with the status quo property tax schedule.

Conceptual Framework for Modeling the Parcel Development Decision

We hypothesize that housing development is codetermined through neighborhood spillover effects based on findings from previous literature (e.g. 7; 8). The agent interaction models of 3 and 1 are useful for conceptualizing the transition of residential parcels from an undeveloped to a developed state. Two important assumptions are that the housing market is in equilibrium, yet the observed equilibrium may vary across the market (i.e. equilibrium may be local or neighborhoodspecific), and that the unobserved latent propensity to develop a parcel may be correlated with development decisions in nearby locations.

We extend 13 and 14 housing development models to represent local market equilibrium as the intersection between housing service providers (housing supply) and consumers (housing demand). For developers providing housing services, the indirect cost function is c_i(q_i,R_Hi,R_H,−i,w_i), where q_i is a house built on parcel i, R_Hi is the cost of building a house on parcel i, and w_i is a vector of other costs. We hypothesize that costs at location i are a function of costs at other locations (−i), so the development decision at parcel i is potentially influenced by development costs of neighboring parcels. The indirect utility that a house buyer receives at parcel i is v_i(R_Hi,R_H,−iy_i,p_i), where R_Hi and R_H,−i are previously defined, y_i is income, and p_i is a price vector of other goods. Market clearing at location i occurs at cost , where developers build houses at parcel i to meet consumer demand for houses at that location.

We hypothesize that a development decision reflects this transaction between housing service providers and residential consumers. Our empirical model applies the linear random profit maximization framework of 27, pp. 105–142) from the perspective of the housing-service provider, although a similar approach could be taken from the residential consumer's perspective using a random utility maximization model. Focusing on the “reservation rent” , the development decision depends on the difference between the reservation rent at parcel i and the market price of housing services, R_Hi:

(1)

where X_i are location and neighborhood-specific factors determining the housing and housing service provider's reservation rent, and the e_i's are random disturbances reflecting an imperfect relationship between the local attributes and rents. The reservation rent (i.e. the threshold at which parcel development occurs to meet housing demand) is generally unobserved, but market prices that represent housing values are recorded at a point in time (which could proxy R_Hi). In addition, it is likely that reservation rents and market prices are codetermined as functions of those revealed at other locations, suggesting the structural equations:

(2)

with (ρ,ρ^γ) determining the degree of correlation between reservation rents and market prices at other locations. If a housing service provider develops a parcel, the difference between the reservation price and the expected market price will be positive. The decision-making process with correlated outcomes belongs to a class of latent variable models with spatial lag autocorrelation (1):

(3)

Focusing on the reduced form system (the last term in equation (3)) is a common estimation strategy (25) because the reserved return is unobservable. In addition, the annual reservation rent is not observed for service providers who did not win development bids. However, because the development decisions are likely correlated, the usual maximum likelihood framework may not provide consistent estimates of the factors determining the parcel development outcome. We estimate the spatially-lagged latent variable development equation using a General Method of Moments (GMM) procedure suggested by 19, which is developed below. First, however, we provide a theoretical framework motivating an index for measuring the influence of a TPT on housing density, given the local factors determining parcel development.

Conceptual Framework for Modeling Residential Development Density

Our conceptual framework of demand for single family housing density extends 5, 13, and 16 respective interpretations of the Alonso-Mills-Muth residential location model. We modify the general model to demonstrate the potential role of a land value tax on housing density, and how such a tax operates through the consumer's housing bid rent function. The positive effect of the land value tax on development density is represented by the backward movement of the housing bid rent function which corresponds with more compact housing development. We develop the comparative statics of this system to illustrate the anticipated effects of a land value tax on housing density and to motivate the econometric model we use to evaluate a TPT on compact development We suppress the location-specific subscripts (i's) in what follows.

Consider a continuum of workers commuting distance r to work, earning income Y. Households consume an aggregate commodity called housing services, with the per unit price at distance r, R_H(r) Housing services include the land parcel and the finished area of the structure built on the lot. The utility (U) of each consumer depends on the consumption of a composite good (z) that excludes housing services and the quantity consumed of household services q (13, p. 41). Utility is a twice continuously differentiable, quasi-concave function strictly increasing in each good. Both q and z are essential goods, and every indifference curve has each axis as an asymptote. The housing service bundle is a normal good. The consumer's budget constraint is z+q⋅R_H(r)=Y −T(r), with Y −T(r) representing the net income remaining after commuting costs T(r).

The consumer's residential location decision is:

(4)

Profit-maximizing firms in the housing industry produce a housing service under constant returns to scale, with q=F(A,H), using lot area A and materials to produce a house of size H:

(5)

at each distance r, where R_A(r) is per unit land rent at r, and τ_A the land value tax rate. For now, we assume that tax rates on structures are constant and that building material costs are the same everywhere and normalized to 1.

We define land consumption per household and house size as (respectively) a≡A⋅[q/F(A,H)] and h≡H⋅[q/F(A,H)]. Rearranged, the housing production function in terms of inputs used to provide housing services is:

(6)

Under constant returns to scale technology, and assuming the housing industry is competitive, profit at distance r is zero: R_HF(A,H)−(1+τ_A)⋅R_A(r)A−H=0. Therefore,

(7)

The reduced form version of the consumer's residential location decision is then:

(8)

with the corresponding housing bid rent function being

(9)

where u is an equilibrium utility level, and Z(f(a,h),u) can be obtained by solving U(z,f(a,h))=u with respect to the composite good.

Equation (8) is the maximum that land rent developers can extract from consumers, assuming the expected equilibrium of household utility is u, subject to the prevailing land value tax. In equilibrium the developer's profit is zero because the housing industry is competitive with constant returns to scale technology. The housing bid rent function for developers is then:

(10)

which represents the maximum rent per unit of land each developer could pay at distance r under the zero profit condition.

We find land use equilibrium conditions by rewriting housing industry behavior in terms of inputs and outputs per house:

(11)

at distance r with the corresponding bid rent function of the housing industry:

(12)

This equation is identical to equation (9) because f(⋅) exhibits constant returns to scale.

In equilibrium, Ψ(r;R_H(r))≡Ψ(r,u) (i.e. equation (11) = equation (8)), regardless of the tax burden on land value; the maximum amount of land rent each firm can bid must equal the amount a household can afford at distance r (Proof: 13, page 96). Solving the maximization problem of equation (7) yields the bid-max lot size function a(r,u) and the bid-max structure area h(r,u). These solutions to the maximization problem of equation (11) define the bid-max housing service function:

(13)

with q′>0, q′′<0 and a and hessential inputs for the housing service function. We depict the relationship in figure 1(a) with the isocost line:

(14)

which is tangent to the isoquant q(r,u) at the optimal lot size a*(r,u) and structure area h*(r,u) (point E). Clearly, as the finished house area-to-lot size ratio increases, the bid rent function must also increase such that the level of housing services remains constant; this relationship has important implications with respect to land value taxation and compact development.

We now examine how housing density measured as the structure-land area ratio h(r,u)/a(r,u) varies across the housing market with an added land tax (τ_A). Let R′=(1+τ_A)⋅R and Ψ′=(1+τ_A)Ψ(r,u). Using 13 duality results, we derive the comparative statics of this system from the conditional input demands of the housing service function. Let the conditional input demands [a(R′,q),h(R′,q)] solve the minimization problem:

(15)

In equilibrium then, land rent must adjust to correspond with the consumer's bid rent (14), Ψ(r,u)≡R(r). Because the housing service function has constant returns to scale, the ratio h(R′,q)/a(R′,q) is independent of output. This relationship defines the parcel-housing density equation as h(R′,q)/a(R′,q)=g(R′). First, it is apparent that as the land value tax increases, land rent and housing density also increase (i.e. ∂g(R′)/∂R′>0). Second, the bid rent function deceases moving outward from employment centers. By the envelope theorem and evaluating the bid rent function at equilibrium, ∂Ψ′/∂r<0.

It is evident in figure 1(a) that the house structure/lot size ratio increases as land rent becomes more expensive; dg(R′)/dR′>0 (development becomes more dense). Under the assumption that the same level of housing services must be maintained in equilibrium, the isocost line in figure 1(a) must also shift from Ψ(r,u) to Ψ′, with corresponding shifts in optimal tangency points from E to E′ and input demands (a^′*(r,u),h^′*(r,u)), which yields relatively smaller lots covered by more structure area. Thus, the structure area/land ratio increases as land value tax rates increase.

The correspondence between the reallocation of housing service inputs following an increase in land value and the location of this combination is nonlinear (figure 1(b)). This is a very general result of the Alonso-Muth-Mills model in that the equilibrium proportion of housing area/lot size decreases moving outward from a Central Business District (CBD), denoted by the shift from E to E′ in figure 1(b)). Overall, we expect that a higher tax on land value relative to a tax on improvements will increase the structure area/lot size ratio, thereby encouraging compact development.

In figure 1(c), r_f represents the urban fringe that would result in the absence of a land value tax. The opportunity cost of land is the agricultural land rent, R_G. The land value tax rate increases as the bid rent shifts from Ψ to Ψ′. The shift coincides with more compact housing development moving closer to the CBD, which corresponds with higher housing density inside the new urban fringe boundary r′_f.

In addition to changes in land tax policy, we conjecture that other site-specific and neighborhood factors influence the equilibrium between housing density and land rent. To accommodate these additional factors, such as house and property characteristics including structural attributes (e.g. brick siding, swimming pool, a garage), the structure/lot size ratio at location i is:

(16)

where X_i includes sitespecific and neighborhood attributes (e.g. house and property characteristics, school district quality, access to amenities, exposure to disamenities, and spatial boundaries).

The econometric model assumes equation (15) can be linearized by applying a first order Taylor approximation, noting that housing density is restricted between the (0,1) interval, which eventually has implications for estimation. The following section provides details of the variables we hypothesize as influencing compact development. The details of the spatial process model we use to estimate equation (15) and the forecasting algorithm are also discussed.

Data and Study Area

The study area for this research is Nashville-Davidson County, Tennessee. We used four primary GIS data sets: individual parcel data, boundary data, census-block group data, and environmental feature data. We report definitions of the variables used in the regressions and their detailed statistics in table 1.

We obtained individual parcel data as polygon shape files (i.e. sales price, lot size, residential space, structural information, and property tax) from the Metro Planning Department (MPD), Nashville-Davidson County, and the Davidson County Tax Assessor's Office. We also obtained boundary data (i.e. high school district, jurisdiction boundary, taxing district, and zoning district including minimum lot size) from MPD. We assigned data from 2000 censusblock groups (i.e. income, housing density, travel time to work, unemployment rate, and vacancy rate) to parcels located inside the census-block boundaries, and we used them as time-lagged socioeconomic variables. We extracted environmental feature data (i.e. municipal parks, golf courses, greenways, railroads, interstate highways, and water bodies) from the Environmental Systems Research Institute (ESRI) Data and Maps 2008.

We collected parcel development data for 2006 through 2007. At the beginning of 2006, the number of vacant parcels in Nashville-Davidson County was 35,928. Among these, 1,675 parcels were developed from 2006–2007 for single-family detached houses and 16,691 parcels were developed for other uses such as single-family attached houses and commercial and industrial land uses. We removed the 16,961 parcels developed for other purposes from the combined data set of 35,928 vacant parcels, yielding 19,237 parcels for use modeling the residential development of single-family detached houses. Of these, we defined 1,675 parcels as “developed” leaving 17,562 parcels defined as “undeveloped” We calculated the land value tax and property tax used in the development and density equations based on the assessed value of property (i.e. assessed value of land and structures) and the tax rates of Nashville-Davidson County from 2006–2007. We assigned different tax rates based on the location of parcels inside the general services district (GSD) and urban service district (USD) boundaries.

Estimating the Parcel Development and Residential Development Density Equations

A challenging aspect of estimating the development density model is potential sample selection bias introduced into the subset of parcels converted to residential use from 2006–2007. A second challenge is attending to the spatial structure of the residential market. Conversion and residential location decisions in the housing market may also be codetermined through neighborhood spillover effects In the first case, well-established econometric methods can attend to sample selection bias (6). In particular, 17 two-step and bivariate maximum likelihood models are frequently used to address such problems. In the second case, the feasible estimation of limited dependent variables with spatially-lagged outcomes using large datasets is relatively recent.

Limited dependent variable models are relatively well developed in the spatial econometric literature (e.g. 9; 19), but sample selection models have only appeared recently, receiving relatively little attention in applied studies. Exceptions include Bayesian spatial tobit models (22), and 12 and 28 sample selection models. 28 approach is computationally attractive and thus we adopt it for our analysis. 19 use a linear approximation of the probit model, circumventing the need to repeatedly invert large n-by-n matrices, a feature especially attractive given the sample size of 19,237 parcels analyzed in the first stage selection (or “development”) equation. By linearizing the first-stage selection model, we avoid computational issues that could arise from the repeated inversion of a large matrix. We then estimate the second-stage outcome equation (or “housing-density equation”) using an appropriate least squares estimator. Nonetheless, while this two-step procedure has some computational advantages, the full 19,237-by-19,237 matrix had to be inverted using the Schur complement method (38). The Schur method partitions a matrix into submatrices inverts them separately, and then reconstructs the full matrix through matrix algebra rules. The procedure produces identical results to typical matrix inversion procedures.

Linear spatial probit model of the firststage development equation

19 provide details of the first-stage estimation procedure for the linearized logit and probit spatial lag models. 28 extended that model by constructing an inverse Mill's ratio (IMR) adjusted for correlation between locations. Using 19 and 28 notation the spatial lag model for limited dependent response variables is:

(17)

with . The scale of d is unidentifiable in discrete choice models, so is restricted to be a constant. In the case of the probit specification, , with the variances specified as the diagonal elements of Var(ε). Define S to be an n-by-n matrix with 1/σ_i on the diagonals, and let ω_ij be an element in the n-by-n matrix S(I−ρW)⁻¹. This arrangement suggests rewriting the reduced-form version of the latent variable in (16) as:

(18)

where , , and . The spatial probit model is estimated using the linearized general method of moments procedure suggested by 19.

Specification of the housing density equation

Housing density, or the proportion of the area of a parcel covered by a structure built in 2006, was only observed if a parcel was developed (d=1) in 2006. We apply 28 minimum distance procedure to estimate the density development equation using the standard normal cumulative density function to ensure continuity between the observed and predicted bounds of housing density. The expected ratio of house area to lot size is:

(19)

where Φ is the standard normal cumulative density function. Linearizing equation (18) and adding a disturbance term (u_i), an estimable equation for development density is:

(20)

where X_hdi=[R_i,τ_A,X_i] and Φ⁻¹ the inverse of the standard normal cumulative density function. The error terms of this equation are assumed to be correlated with the first-stage probit (parcel development) equation but not between observations; cov(u_i,ε_i)=σ_uε. In addition, equation (19) is only observed if the parcel was developed. Assuming that the error terms are normally distributed; (ω_ij is an element of S(I−ρW)⁻¹); cov(u_i,u_j)=0 for every i≠j. Moreover, assuming that the parcel was developed (d=1), the conditional expectation of the housing density equation is:

(21)

with ϕ the probability mass function of the standard normal distribution and “” denoting estimates from the first-stage development equation. The ratio of the probability mass function and the standard normal cumulative function is the inverse Mill's ratio (IMR), weighted by the diagonal elements of the n-by-n filter, S(I−ρW)⁻¹. We evaluate the IMR using the spatial probit estimates with the transformed explanatory variables, with the spatial structure of the housing market relayed through ω_ii.

Equation (20) suggests an estimable linear equation:

(22)

Weighted least squares (WLS) regression of z on the explanatory variables included in the housing density function entails the weights w_i=1/v_i, with v_i=[y_hdi⋅(1−y_hdi)]/[ϕ(y_hdi)]².

Determining Hypothetical TPT Rates and Forecasting Residential Development Density

We determine hypothetical tax rates on assessed land values using an optimization procedure. The key constraint in the mathematical program ensures that the sum of the tax revenue collected from all house locations following a hypothetical change in the tax rate is equal to the sum of the existing (“status quo”) property tax revenue. This constraint ensures that the hypothetical TPT scenario is tax revenueneutral compared to the existing property tax scheme. The justification for requiring tax revenue neutrality is that it may not be practical or politically feasible to raise or lower total municipal tax revenue.

Let , where M_i is the municipal government's revenue from property taxes on the assessed value (V) of lot area (A) and structures (S) at location i, and is the prevailing property tax rate. This equation depicts the existing property tax scheme (i.e. the baseline case) in which the tax rates on the assessed values of lot area and structures are identical (i.e ). The annual aggregate tax revenue for the county from land and associated structures is . Suppose a hypothetical TPT scenario placed more emphasis on the assessed value of land by decreasing the tax rate on structures by “α” percent. The revenue collected at property i is then , where α∈[0,1], with lower levels of α reflecting greater emphasis on taxing the assessed value of lot area relative to structures. When α decreases and remains at the existing tax rate () must increase for the hypothetical TPT to be revenueneutral.

The amount that M_i changes is site-specific because changes. We simulate the hypothetical TPT scenarios using four levels of α*=[0.25,0.50,0.75,0.95], using an optimization procedure to find parcel-specific values of at a given α*. For each level of α, the optimization problem finds a new level of τ_A that satisfies the tax revenue neutrality constraint. Thus, the optimization problem is conditional on the selected values of α*.

Nashville-Davidson County has two tax rates. In the GSD, the prevailing tax is 4.04% of the assessed value of land and structure, which is 25% of the appraised value of land and structure determined based on market value. In the USD the prevailing tax rate is 4.69%. Given equation (19), these levels generated assessed tax rates on land value of τ_A=[4.91%,4.62%,4.33%,4.10%] in the GSD In the USD, the simulated land value tax rates were τ_A=[5.70%,5.36%,5.03%,4.76%]. While the GSD covers the entire study area, the USD is an area originating from the old boundaries of the city extending into suburban areas that were annexed into the USD to receive urban services and includes those areas that incur another tax rate in addition to the basic GSD rate. The jurisdictions designate the boundaries of the USD as a means for phasing in capital improvements as determined by the location and density of allowed and existing development. Note that the ratios of the districts' τ_A relative to their respective base tax rates are identical, reflecting the neutrality of the TPT as expressed in the optimization problem.

To simulate the effect of a TPT on housing densities, we rescaled tax revenue at the ith location by the new tax rates on land () and structures . Given the consistent parameter estimates of the first-stage development (equation (16)) and second-stage residential development density (equation (20)) equations, we forecasted deviations from the equilibrium (e.g. “status quo”) residential development density by replacing the observed tax rate at location iwith the simulated value holding other location factors constant.

We recalculated the IMR given these shocks, followed by generating the predicted values of housing density estimated by the second-stage regression. To assess the effects on housing development density of increasing the land value tax rate relative to the tax rate on improvements, we compared the empirical distributions of the simulated housing densities with the empirical distribution of the baseline scenario. Rearranging equation (21):

(23)

with the under bar indicating that the property tax was adjusted (increased) by replacing the original land value tax with the simulated level in the matrix of covariates. We compared differences between the distributions using a Kolmogorov-Smirnoff (KS) test within the respective service districts with respect to the differences in the prevailing baseline property tax rates.

Simulation of a land tax increase on housing density

A clear pattern emerged between the land value tax and the house-to-parcel density in the GSD and USD zones. In the GSD zone, a 0.06% point increase (land tax rate increase associated with α=0.25) in the land value tax rate from the base rate of 4.04% did not significantly increase the house-to-parcel ratio from the baseline scenario. Similarly, in the USD zone, a 0.07% point increase in the land value tax rate from the base rate of 4.69% did not significantly increase the house-to-parcel ratio from the baseline scenario (figure 2). However, at higher simulated land tax rates, the house-parcel area density significantly increased at all levels of the distribution. The average difference between the house-parcel ratios in the base case and highest simulated levels was about 20%. Thus, it appears that the expectations derived from the theoretical model developed above are consistent with the in-sample results; a TPT encourages higher house-to-parcel area ratios.

In general, the ordering of the out-of-sample simulated empirical ratios was consistent with the empirical densities associated with the observed house-to-parcel ratios, yet the shape of the distributions and the average difference between the housing-parcel ratios in the base case and the out-of-sample simulated case are remarkably different (figure 3). The KS tests demonstrate that the out-of-sample simulated empirical densities with a 0.06% point increase and a 0.07% point increase in the land value tax rate from the base rate for parcels in the GSD and USD zones, respectively, were not significantly different from those of baseline scenarios at the 5% level. As with the in-sample results, at higher simulated land tax rates, house-parcel area ratios significantly increased.

The consistent ordering of the out-of-sample simulated empirical densities passed the sensitivity test showing whether the TPT consistently increases house-to-parcel area ratios regardless of the parcels' development status. This finding suggests that with the higher TPT level, house buyers and developers of both undeveloped and developed parcels sharing similar observable characteristics and neighborhood proximity may prefer higher house-parcel area ratios. However, the different shapes of the distributions between the in-sample and out-of-sample results reflect differences in the degree of reaction with the same level of increases in the TPT between the developed and undeveloped parcels. Specifically, the average difference between the housing-parcel ratios in the base case and the highest simulated levels was about 3% for the out-of-sample result which is about 17% lower than the in-sample result.

In addition to differences between the developed and undeveloped parcels, other reasons may explain why the out-of-sample simulated distributions poorly fit the in-sample simulation results. The underestimated distributions may be an artifact of the imputed data used to proxy the unobserved attributes of the parcels. The relatively low predictive power of the first-stage probit could also affect the predictive power of the second-stage density equation through the spatially adjusted inverse Mill's ratio.

Despite the relatively poor correlation between the simulated out-of-sample and in-sample distributions, the findings of both simulations consistently suggest that the TPT is effective with respect to increasing housing density under the land value tax rates of 4.33%, 4.62%, and 4.91% in the GSD zone and 5.03%, 5.36%, and 5.79% in the USD zone (compared to the baseline distribution). This was not the case under the 4.10% and 4.69% rates in the GSD and USD zones, respectively. These findings imply that the increase in land value tax must be higher than a minimum level (i.e. minimums of between 4.10%–4.33% and 4.76%–5.03% in the GSD and USD zones, respectively) to increase house-parcel areas ratios.

Conclusions

Our research analyzed the impact of a two-rate property tax (TPT) on residential densities, measured by the finished house area-to-parcel size ratio using data from Nashville-Davidson County, Tennessee between 2006 and 2007. We applied recent developments in the spatial econometric modeling literature to attend to sample selection issues and define spatial neighborhoods using a data-driven procedure. Based on the empirical results, we conducted a counterfactual experiment to assess, ex ante, the impact of a TPT. We found that a TPT above a minimum level triggers increases in residential densities above the suboptimal densities associated with the conventional property tax system The empirical approach developed in this study may have broad implications for many U.S. municipalities because it can be used to evaluate the potential impacts of TPTs on residential densities in all but a few U.S. municipalities that currently have a conventional property tax structure (e.g. the same tax rate for land and structures). Our research extends TPT impact analyses by simulating development patterns, given the unique characteristics of a municipality's housing market under ex ante counterfactual property tax structures.

It is important to recognize two critical assumptions that condition the results: (i) the TPT simulations are valid only to the extent that the landuse equilibrium condition is fulfilled under the baseline case; and (ii) house buyers and developers react to the implementation of a TPT through changes in the total dollar amount of property tax owed. Other challenges remain in extending our methods. First, although the TPT is revenue-neutral, the distribution of winners and losers is undetermined. Changes in the tax burden caused by TPT implementation produce changes in net income after taxes; after-tax net income may increase, decrease, or remain the same depending on the site-specific weights on land and structures. These changes in after-tax net income may allow further evaluation of changes in consumer welfare following equilibrium shocks induced by a TPT, which could help determine winners and losers.

Second, this research focused on changes in housing density under a TPT at the site-specific level and dealt only with how individual decisionmaking was affected by a hypothetical tax scheme. We have not addressed the cumulative effects of those individual decisions on area-wide development patterns. Because an overall area-wide development pattern driven by individual choices across locations is important for land use planning, aspects that require further attention are the links between individual decision-making in response to a hypothetical TPT, and changes in spatial development patterns at the area-wide level.

Third, instead of using the mean values of developed parcels to proxy the unobserved attributes of undeveloped parcels, the poor out-of-sample estimates could be improved by using the attributes of the closest parcels developed prior to 2006 to proxy the unobserved attributes of the undeveloped parcels from 2006–2007. Bettermatching pairs may also result from using alternative matching procedures to generate out-of-sample observations for ex ante analysis. Although the Mahalanobis procedure is robust, a parameterized matching algorithm may be more efficient. Developing matching procedures that attend to spatially correlated observations would be a promising step in this direction.

Acknowledgements

Senior authorship is shared by the researchers. Authors are listed alphabetically. This research was funded by the Lincoln Institute of Land Policy. Views expressed are the authors' alone, and do not necessarily correspond to those of the University of Tennessee or Kyungpook National University.