رقابت مالیاتی ایالتی و محلی در مدل فضایی با مالیات فروش و مالیات بر املاک مسکونی

This paper presents a theoretical model with a uniformly populated line that is divided into local jurisdictions (and/or states). If one level of government imposes sales and residential property taxes, and if the spatial extent of each taxing jurisdiction is positive and finite, then (in Nash equilibrium) the sales tax rate is less than residential property tax rate, housing consumption is suboptimal, and the public good is underprovided in each jurisdiction. If a very large state (or country) is divided into local jurisdictions, and if both levels of government choose tax rates endogenously, then under some assumptions there is an efficient outcome.

This paper presents a spatial model in which there are many local jurisdictions along a uniformly populated line. It derives a Nash equilibrium in tax rates when local governments (or both state and local governments) choose sales-tax and residential-property-tax rates, and it compares the equilibrium and socially optimal amounts of local public goods and housing. Sales and property taxes are commonly used in the United States. A general sales tax is used by 45 of the 50 states.1 Sales taxes form 54% of state tax revenues (income taxes form 42%). Local general sales taxes are used in 34 states, and sales taxes make up 22% of local tax revenues in the United States as a whole. Although property taxes are unimportant at the state level, local property taxes (residential and business) make up 72% of local tax revenues. Several branches of the theoretical literature are relevant to national, state or local taxation choices, usually with only one level of government, but sometimes with more than one level of government, choosing tax rates. In most of the papers, a benevolent government of each jurisdiction chooses the tax rates that maximize the well-being of its own residents, and there is a Nash equilibrium in the tax rates chosen by different jurisdictions. One branch of the theoretical literature consists of “business-tax-competition” models.2 A number of regions produce output using labor and capital. Regions compete for mobile business capital. This creates a “horizontal taxation externality” (see Wildasin, 1989), since if one region increases its tax on business capital, it has a capital outflow, but all other regions benefit from capital inflows. Consequently, if only a (source-based) business capital tax can be used, then it is underused and the local public good is underprovided in each region. A business capital tax is the same as a business property tax in most models (since land is usually absent). Business-tax-competition papers such as Bucovetsky and Wilson, 1991 and Gordon, 1986, part of Wilson (1991), and Braid, 1996, Braid, 2000 and Braid, 2005 consider the choice by jurisdictions among more than one distortionary tax. The first three have source-based business capital taxes and residence-based wage taxes that are distortionary because of labor-leisure choice. The last three consider the tax choices of sub-metropolitan jurisdictions between business property taxes and source-based wage taxes that are distortionary because of interjurisdictional commuting.3 Some business-tax-competition papers, such as Keen and Kotsogiannis, 2002 and Keen and Kotsogiannis, 2004, have business capital taxation by both a national government and state governments. In addition to horizontal taxation externalities due to capital flow, there are vertical taxation externalities due to double taxation (by national and state governments) of the same tax base. Another branch of the literature consists of “residential-tax-competition” models. There is a horizontal taxation externality due to interjurisdictional migration of consumers. Some authors consider the choice between different taxes. For example, Hoyt (1991) and Krelove (1993) show that under some conditions a residential property tax may dominate a land tax. One residential tax competition model, by Nechyba (1997), considers tax choices made by both state and local governments. Based on a calibrated computable general equilibrium model, local governments (particularly school districts) will choose to use property taxes, while states will tend to use income taxes, if these are the two taxes that are available. A third branch of the literature consists of “sales-tax-competition” models, including the Leviathan models (in which governments maximize tax revenues) of Kanbur and Keen, 1993, Ohsawa, 1999 and Ohsawa, 2003 and Nielsen (2001), and the benevolent-government models (in which governments maximize the utilities of their residents) of Arnott and Grieson, 1981, Mintz and Tulkens, 1986 and Braid, 1993 and Trandel (1994).4 These models have a horizontal taxation externality due to the cross-border shopping that may occur if there is a differential in sales or commodity tax rates between adjacent jurisdictions.5 Most of these models are explicitly spatial, unlike the papers mentioned in previous paragraphs (except Braid, 2000). Only a single type of distortionary tax and a single level of government are considered.6 Lucas (2004) presents a sales-tax-competition model that has a federal structure, with one country that has two regions. There are two commodities, one of which is taxed by both national and regional governments. There is a horizontal taxation externality due to cross-border shopping for this commodity, and also a vertical taxation externality due to taxation by both national and regional governments. The other commodity is untaxed. There are federal and regional public goods. Efficiency results from federal government use of matching grants.7 Hoyt (2001) does not fit into any of the categories above. A country has a number of states. Leisure is untaxed, and labor is used to produce two taxed commodities. There are national and state public goods. There is a vertical taxation externality due to taxation of both commodities by national and state governments, or of both commodities by the national government and one by states, but no horizontal taxation externality (there is no capital flow, migration of residents, or cross-border shopping in the model). In this paper, I assume a spatial model with two goods (a numeraire good and housing), and two types of taxes (sales taxes and residential property taxes). There is a very large state (or country) on a line that is subdivided into many local jurisdictions. There is a horizontal taxation externality at the local level due to cross-border shopping. My paper examines the relative sizes of the sales and residential-property-tax rates and the efficiency of equilibrium. I assume benevolent government behavior. Potential cross-border shopping plays an important role in determining Nash equilibrium tax rates and public good levels even though no cross-border shopping actually occurs in the Nash equilibrium.8 One reason that my paper is significant is that it differs from existing models of sales-tax competition by considering two taxes, each of which is distortionary on its own.9 As a result of this difference, my analysis illuminates forces that were not well-understood previously in the important field of tax competition. I establish a number of results which are new to the literature, both when all taxation is by jurisdictions at a single level, and also when taxation is by jurisdictions at two levels. However, the results can be explained intuitively. There are three additional reasons that my paper is significant. First, in Section 8, I have a sales-tax externality at two levels of government. This contrasts with almost all papers in the literature, which do not have a horizontal taxation externality of any type (capital flow, migration of residents, or cross-border shopping) for the higher-level government.10 Second, the taxes I examine are commonly used in the United States and other countries, but there are differences between states in the US and between countries (see the second paragraph of this section, and Sections 9 and 10). Third, my model leads to comparative static results that could lead to interesting empirical work (see Section 10), and there are a number of interesting ways in which my paper could be extended theoretically (see Section 10). Section 2 presents the model and basic equations for cross-border shopping and the (very simple) housing market. Section 3 assumes endogenous local tax rates, exogenous higher-level tax rates, and exogenous higher-government transfers to local governments. It derives a set of equations that must be satisfied in Nash equilibrium. Section 4 derives the socially optimal solution, and the simple equations for the efficient levels of the local public goods and housing. Section 5 characterizes Nash equilibrium, assuming that only lower-level jurisdictions impose taxes and provide public goods. Jurisdictions can be interpreted as municipalities or counties within a very large state or country, or as states within a very large country. If the (lower-level) jurisdictions are very large, then the horizontal taxation externality due to potential cross-border shopping is of negligible importance, and thus the equilibrium sales-tax and residential-property-tax rates are equal, and the public good and housing are at their efficient levels. If jurisdictions are of negligible spatial extent, then the horizontal taxation externality is so strong that sales taxes are not viable. In this case, the sales tax rate is zero, but the residential property tax rate is positive. If jurisdictions are of finite but nonzero size, then the horizontal taxation externality has an effect, but sales taxes are still viable. In this case, therefore, the Nash equilibrium values of both tax rates are positive, but the residential-property-tax rate is the larger of the two. In all cases where jurisdictions are of finite size, the public good (in each jurisdiction) and housing consumption (by each consumer) are below their efficient levels. In Sections 6 and 7, tax rates are chosen endogenously by two levels of government, so there are vertical fiscal externalities. A very large state is divided into many local jurisdictions. If lump-sum transfers from the state to local jurisdictions are endogenous, then the sum of the state and local property tax rates equals the sum of the state and local sales tax rates, and the state and local public goods and housing consumption are all efficient. Intuitively, there is efficiency because the horizontal taxation externality due to potential cross-state-border shopping is of negligible importance (since the state is very large), and because endogenous lump-sum grants give the state the flexibility to deal with all of the externalities and still ensure that (i) the equality between tax rates stated above is satisfied and (ii) everything is efficient. However, with exogenous (or zero) lump-sum transfers, there is no longer efficiency in general. Section 8 considers the case where the line is divided into many states, and each state is divided into many local jurisdictions. States are only moderately large, so that there is a horizontal taxation externality at the state level (cross-state-border shopping cannot be ignored). Consequently, there is not efficiency (in the case for which I present results). Section 9 mentions some real world numbers in order to determine whether a key efficiency condition involving tax rates (from Section 4) is satisfied. Section 10 makes concluding remarks. It discusses the comparative static effects of an exogenous change in a state’s sales tax rate, and various limitations and possible extensions of the analysis.

An overview of the analysis and the results in my paper is found in the final several paragraphs of Section 1 (and in Proposition 1, Proposition 2, Proposition 3, Proposition 4, Proposition 5, Proposition 6 and Proposition 7 of Sections 4, 5, 7 and 8). In this section, I first present the results of a simple comparative static exercise, and I indicate how this result, and other comparative static results that might be derived, could lead to potentially interesting empirical work. Then I consider various limitations of my model that lead to a number of potentially worthwhile variations and extensions of the theoretical model in this paper. It is possible to consider the comparative statics of local tax rates, using the model of Section 3, with respect to exogenous changes in state tax rates. The simplest interesting case is when a state does not use property taxation (σ = 0) and its local governments cannot use sales taxes (t = 0).33 Totally differentiating (18), (19) and (24) with respect to an exogenous change in the state sales tax rate (s) leads to somewhat complicated equations. To derive results, it is necessary to assume more than g′(h) > 0, g″(h) < 0, m′(G) > 0 and m″(G) < 0. If I assume T = 0 (no transfers to local governments) and the functions (54) and (55) for g(h) and m(G), then it can be shown that an exogenous increase in s leads to increases in the local property tax rate (τ), per-capita housing consumption (h), and the local public good (G) in each local jurisdiction, and that an exogenous change in the state income tax rate, L, has no effects on these variables. It might be possible to test the theoretical predictions above, concerning the effects of differences in s and L across states on local property tax rates, using the 16 states that do not allow local sales taxation.34 It might also be possible to examine the effects of differences in s and L on local sales-tax and property-tax rates, using the 34 states that do allow at least some local sales taxation, although deriving theoretical comparative static results is harder in this case. The model used in this paper abstracts from certain features of the real world, suggesting possible extensions. First, in the real world, in the United States, general sales taxes that are imposed by states and local jurisdictions typically do not tax certain goods, most notably services and (non-restaurant) food. Footnote 13 suggests an alternative formulation which could be used to examine this, with two taxed goods (a numeraire good, z, and housing, h), only one of which (z) is subject to cross-border shopping, and one untaxed good (q). Efficiency might not require equal state-plus-local tax rates on the two taxed goods (as in (33) and Proposition 1). Second, in the US, 16 of the 50 states do not allow any local governments to impose general sales taxes, something considered to some extent in the second paragraph of this section (but only with an exogenous state sales tax rate), and five states do not have a state sales tax. Another feature of the real world is that different states, and different local jurisdictions within a state, are of different sizes. This is considered in some sales-tax-competition models in which governments use only a sales tax (some of these have Leviathan objective functions for governments, unlike my paper). Intuitively, this is a reason that large central cities (in states that allow local sales taxation) often have higher sales tax rates than the surrounding suburbs. Also, population density typically varies significantly within a state. In some states, a large fraction of the population is in a large metropolitan area, and the importance of actual or potential cross-state-border shopping varies significantly depending on whether this metropolitan area is in the middle of the state or at one of its boundaries, especially if a significant fraction of the metropolitan area is across the boundary in a neighboring state, as in (for example) New York City, Philadelphia, Washington DC, and to a lesser extent Chicago.35 My paper assumes two levels of government choosing tax rates endogenously in Sections 6, 7 and 8. Some countries have three levels of government (see footnote 30). In the United States, the federal government also imposes taxes, mostly income taxes (see footnote 30), and has certain policies which subsidize housing (see footnote 32). Also, in most US states, there are multiple types of local governments that impose taxes, including counties (typically the largest local jurisdictions), municipalities, townships and school districts. Finally, it is important to note that I have focused on the choice of sales-tax and property-tax rates by state and local governments (I have lump-sum state income taxes in some equations, but they are exogenous). In the real-world, countries and US states can choose their income tax rates, and at least some local governments use income taxes in 14 of the 50 US states.