The theory of tax capitalization posits that variations in taxes are reflected in the value of an asset. In the property tax relief context, decreasing a home's property tax liability by $1 a year, all other things equal, would result in a home price increase equal to the sum of the present value of $1 a year over the benefit period (Sirmans, Gatzlaff, and Macpherson, 2008; Hilber, 2017). The economic theory underlying capitalization maintains that individuals make spending decisions subject to their budget constraint. The reservation price for housing is the maximum someone is willing to pay for a home. As housing operating costs decline, our reservation price for housing increases, all other things equal.
Unlike property tax incentives for land development, which must be capitalized to be effective, any capitalization of property tax relief serves only to drive prices higher, thus not only undermining the intent of the relief but also creating a self-perpetuating cycle. That is, tax relief lowers tax liabilities which in turn increases property values through higher reservation prices, which in turns necessitates more tax relief. Since every state offers some form of property tax relief, according to the Significant Features of the Property Tax (2018), the implication that tax capitalization undermines the intent of tax relief policy is potentially far-reaching. This argument, though, is not new, as others have commented on the unintended policy consequences created by capitalization. (1) However, reviews of the property tax capitalization literature, which have been done most recently by Sirmans et al. (2008) and Hilber (2017), reveal a curiosity: a lack of discussion about the equity implications of property tax capitalization. Tax equity is often the policy outcome citizens are most concerned about, as Schwartz (1998) and Sheffrin (2013) note, compared to other outcomes such as tax efficiency. Equity concerns arise in the property tax capitalization context because some property owners will benefit more or less than others from a change in tax levels owing to variations across space in the economic conditions that predict the degree of capitalization. (2) The implication of this is that uniform tax relief within a jurisdiction will not be experienced uniformly by residents, leading some to enjoy a capital gain and others a capital loss.
This article makes a twofold contribution to our understanding of capitalization of property tax relief. The first contribution is that it provides a detailed discussion of some circumstances in which inequities may arise and four are explored: the timing of relief policy announcement and implementation, differences in housing market characteristics within a jurisdiction, choice of relief delivery mode, and the homeownership status of beneficiaries. For the first and third inequity sources, existing research and theory are drawn upon to support the presented arguments. For the second and fourth, novel data analysis is offered. A focus is on residential property in order to simplify the discussion. (3) The second contribution is that it offers policy recommendations to help mitigate the inequities, to the extent they are undesirable. An emphasis is placed on mitigating inequities rather than eliminating inequities because elimination can only be accomplished by legislating all tax relief policies away, which is not realistic.
This study is the first part of a multi-phase project to better understand the policy design implications of property tax relief. Property tax relief serves as the initial focus because of advances in recent empirical research (Moulton, Waller, and Wentland, 2018), the ubiquity of property tax relief programs, and the importance of tax capitalization as a predictor for economic outcomes (Yinger et al, 1988). In addition, this study makes no assumptions about a community's taste for redistribution, and as such does not take a stand on what constitutes desirable or undesirable inequities. Instead, the intention is simply to describe inequities, their source, provide some evidence they exist, and offer mitigating strategies. It is hoped that the arguments and evidence presented encourage discussion not only about their merits but also about better policy designs that might mitigate undesirable differential treatment than those suggested here. (4)
The remainder of the paper is organized as follows. In the next section, the theory of property tax capitalization is reviewed and an overview of relief programs in the US is offered. The subsequent four sections then discuss the aforementioned sources of inequities along with policy recommendations to mitigate their occurrence. The paper closes with a brief summary and suggestions for future research.
OVERVIEW OF TAX CAPITALIZATION AND PROPERTY TAX RELIEF PROGRAMS IN THE US
Property tax capitalization is a widespread phenomenon--Hamilton (1976) famously opined that "capitalization is everywhere"--and it can be illustrated algebraically. The theory takes as a starting point the assumption that a property's value is equivalent to the benefits it provides minus property taxes owed, both discounted over some period of time at a rate that accounts for inflation. Using the notation of Yinger et al. (1988), the expression for the value of a home receiving permanent relief is:
 V = R/r - T/r
where V is the property value, R is the stream of value of housing benefits, T is a stream of property tax payments, and r is a real discount rate. Tax relief is typically implied since T reflects tax liability net of any credits and exemptions such that T= [tau](A-E)-C where [tau] is the statutory tax rate, A is the assessed value, E is the value of any exemptions, and C is the value of any property tax credits. Substituting the property tax liability components into the previous equation yields:
 V = R/r - ([tau](A -E)-C )/r
If tax relief is delivered over a definite period of time, then the value of the asset reflects the cumulative discounted stream of tax savings over the period:
 V = (R-[tau]A+[tau]E + C )/[(1 + r).sup.n]
where n is the number of periods (usually measured in years) a property receives tax relief. To simplify, allow an asterisk to denote discounted values, and comparing two otherwise identical homes, A and B, where the former receives a tax credit (C > 0) and the other does not (C = 0):
 [V.sub.A] - [V.sub.B] = [(R* - [tau]A* + [tau]E* + C*).sub.A] - [(R* - [tau]A* + [tau]E*).sub.B]
 [DELTA]V = [C*.sub.A]
which says that the difference in home value between A and B is equal to the difference in the sum of the discounted tax relief, which is the discounted present value stream of the benefit for property A in this case. The rate at which C is reflected in V is theorized to be unity in competitive markets with fully informed and rational buyers. To the extent these assumptions fail to hold, the value of C will "show up" in home values to some other degree:
 [DELTA]V = [beta][C*.sub.A]
where [beta] measures the rate at which a $1 reduction in property tax liability increases a home's value. If [beta] = 1, then a $1 annual increase in property tax savings results in a cumulative discounted $1 increase in home value, and the relief is said to be fully capitalized. If 0 1, $1 of relief results in a home price increase greater than the cumulative discounted value of the stream of relief, or overcapitalization.
The literature on property tax capitalization has sought to measure its degree on average, but the theory of tax capitalization predicts variation in the degree of capitalization within a jurisdiction by characteristics of market participants (their rationality and information) and by characteristics of the market itself (relative elasticity of housing supply and demand). To the extent these characteristics vary within a jurisdiction, different eligible residents will benefit differently from the same amount of statutory relief. That different people benefit from property tax relief adoption dissimilarly because of property tax capitalization is a potential equity issue to the extent the differential treatment is undesirable.
Thus far, property tax relief has been discussed here in a general way without identifying characteristics of actual relief programs. The most important for the present discussion is benefit delivery mode, and Equation 2 implies that relief is delivered as either an exemption or as a credit. This is not obvious given the variety of relief programs used by jurisdictions in the US. Based on the most recent data from the Significant Features of the Property Tax (2018), there were 294 active relief programs in the US in calendar year 2017. Table 1 tabulates the number of states with such programs organized by the most common relief mode name. Half of active programs were exemptions offering reductions in taxable assessed value with the remaining distributed between assessment freezes, circuit breakers, credits, and deferrals.
However, these common categories mask important similarities between the programs. Assessment freezes, for instance, are really just exemptions but rather than an exact amount being exempted, the difference between an assessment minimum and a property's taxable assessed value is exempted. Circuit breakers, meanwhile, can be delivered as either a credit or exemption. Deferrals are unique in that the mode of delivery is irrelevant. Whether property taxes are nullified due to a reduction in assessed value or a credit does not change the fact no property taxes are owed. Thus, upon further consideration, from a tax capitalization standpoint there are only two ways relief can be delivered--as a reduction in assessed value or as a reduction in liability. (5)
The volume of active property tax relief programs suggests that inequities may be widespread. Moreover, as it will be argued later, the mode of property tax relief delivery...
CAPITALIZATION OF PROPERTY TAX RELIEF: SOME EQUITY IMPLICATIONS AND RELEVANCE TO POLICY DESIGN.
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