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International Tax and Public Finance

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11-04-2019

The welfare costs of Tiebout sorting with true public goods

Authors: Florian Kuhlmey, Beat Hintermann

Published in: International Tax and Public Finance | Issue 5/2019

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Abstract

We develop a model of Tiebout sorting based on decentralized income taxation, which allows for spillovers and imperfect rivalry in consumption of the publicly provided good. We identify three sources of welfare loss from decentralization: imperfect redistribution, interjurisdictional free-riding, and inefficient residential choice. Whereas the welfare loss from imperfect redistribution decreases and that from free-riding rises unambiguously as the publicly provided good becomes more pure, the welfare loss from the inefficient residential choice depends non-monotonically on spillovers and rivalry. The equilibrium can be characterized by relative crowding of either the rich or the poor municipality. Our results imply that the characteristics of the publicly provided good are an important determinant for the welfare costs of decentralization.

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According to Oates’ (1972) decentralization theorem, every publicly provided good or service should be provided by the lowest possible entity which contains all households affected by the public intervention (subsidiarity principle). Since this requires an impracticable plurality of entities, this perfect correspondence usually does not apply in practice. Kaplow (2006) offers an alternative view on what kind of public goods should be provided at what level of government, depending on the distributive incidence of such provision.

In capital tax competition models, the population is usually assumed to be fixed. For reviews of this literature, see Wilson (1999) and Wilson and Wildasin (2004).

Reviews of sorting models are provided by Ross and Yinger (1999), Epple and Nechyba (2004), Boadway and Tremblay (2012) and Bruelhart et al. (2015).

Although the majority of multi-jurisdiction models focus on property taxation, income taxes represent the most important source of revenue for municipalities worldwide (Bruelhart et al. 2015, p. 1138). Income taxes are used in several thousand municipalities in the USA (Henchman and Sapia 2011). For an analysis of income tax competition in Switzerland, see Feld and Kirchgaessner (2001).

Whereas Oddou (2016) allows for spillovers and abstracts from a housing market, Gravel and Oddou (2014) include a housing market but abstract from spillovers. In this paper, we abstain from investigating the necessary and sufficient conditions in a model that includes both a housing market and spillovers, and instead focus on the inefficiencies inherent in such a setup.

This literature is largely shaped by Dennis Epple and co-authors and includes, e.g., Epple and Zelenitz (1981), Epple and Romer (1991), Epple and Platt (1998), Epple et al. (2001), and focuses on the example of property taxes. Applications based on local income taxation include Hansen and Kessler (2001a, b) and Schmidheiny (2006b, 2006a). Calabrese et al. (2012) is the only paper in this literature that focuses on the welfare implications of decentralization.

Silva and Caplan (1997), Caplan et al. (2000) and Caplan and Silva (2011) extend these models by adding a federal government that can enforce interjurisdictional transfers. Because the example provided in these papers is often the environment, this literature has been referred to as “environmental federalism” by Oates (1999).

For the special case of positive spillovers that are proportional to a fixed capital stock, Ogawa and Wildasin (2009) show that local policy choices are efficient. However, if capital supply is elastic, the decrease in spillovers from other regions is smaller, making it optimal for regional governments to choose tax rates that are lower than what would be socially optimal (Eichner and Runkel 2012). Armbruster and Hintermann (2019) add a federal government and discuss the conditions under which the outcome is efficient.

Our Eqs. (1) and (2) representing the production and consumption levels of the publicly provided good have been inspired by Oddou (2016). The definitions of production $G_j$ and consumption $g_j$ imply that these variables have different units: While $G_j$ is equal to aggregate production in j and therefore measured in units of the publicly provided good, consumption $g_j$ describes the amount that every household in j can consume and is therefore measured in units of the publicly provided good per household.

Not all parameter combinations are equally meaningful. For example, it would make no sense to define the publicly provided good as perfectly rival in consumption ($\rho =1$), but simultaneously allow for interjurisdictional spillovers ($\sigma >0$) or neighbors to consume ($\nu >0$), because any outsiders could be easily excluded from consuming the good at home or by crossing borders. The combination ($\rho =\sigma =0$) would describe a club good for which households from outside the municipality can be excluded.

Instead of specifying $\nu $ and $\sigma $ as single parameters, we would define both as $J\times J$ matrices, with $\nu _{jj}=\sigma _{jj}=1$. $0\le \sigma _{ij}\le 1\;\;\forall \;i\ne j$ is then the degree of spillover from municipality i to j, and $0\le \nu _{ij}\le 1\;\;\forall \;i\ne j$ describes the extent to which households from municipality i have access to consume the publicly provided good in j. (2) would then read as $g_j=\sum _{i=1}^J\sigma _{ij}G_i / (\sum _{i=1}^J\nu _{ij}N_i )^{\rho }$. Since we rely on symmetric spillovers in our numerical application, we decided to keep the general model as simple as possible. Asymmetric spillovers could be used to reflect the spatial structure of a metropolitan area, whereas the assumption of symmetric spillovers renders the model essentially spaceless.

This differs from models of property tax competition, in which the tax and the housing price are combined, such that municipalities differ in two dimensions only: the gross-of-tax housing price and the level of the publicly provided good. Note that $G_j$ is irrelevant for households’ relocation decisions, since what matters for utility is the consumption level $g_j$ and not municipality j’s contribution to the publicly provided good.

Note that Schmidheiny cannot establish conditions for the existence of an equilibrium but can show that if one exists, his conditions ensure that it is characterized by a segregation of households according to income.

The empirically more realistic case of an “imperfect sorting” of households requires that households differ with respect to income and additionally some preference parameter, as in Epple and Platt (1998). The model would then require that (5) holds for all values of the second source of heterogeneity, i.e., there is income segregation conditional on the value of the preference parameter (see Schmidheiny 2002, 2006b).

Loeper (2017) compares public consumption levels in a noncooperative setup with the case of Coasian cooperation. Abstracting from household mobility and tax competition, he finds that cooperation mitigates the free-riding incentives only if the demand for the publicly provided good is not too inelastic, irrespective of the size of the spillovers.

The assumption of voter myopia has no effect on the structure of the equilibrium, where no household has an incentive to move (and therefore no moving would be anticipated). However, the out-of-equilibrium processes differ with the assumption about voter sophistication, such that we end up in a different equilibrium depending on whether voters are myopic or far-sighted. Since our model does not allow us to say anything about the dynamics of the system, we maintain the hypothesis of perfect foresight for simplicity.

Our treatment of housing rents is the same as in Calabrese et al. (2012). Alternatively, one could, for example, assume that housing is collectively owned by the local population. While this would pose no problem for the first-best setting, it would require a redistribution scheme for (endogenous) housing profits in the decentralized model. Note that setting the welfare weight on the landlords to zero would lead to a complete expropriation of the landlords (the optimal transfer would be minus infinity). One could limit this by forcing $R=0$, but this would lead to a non-closed model that would not be suitable for normative analysis.

Note that the $\mathrm{MSV}_j(y)$ is generally nonzero, because the control variable $a_j(y)$ is at a corner solution for equilibria characterized by income segregation (either zero or one); the complementary slackness conditions have been omitted in (13) for notational convenience.

This set of efficiency and equilibrium conditions are valid for interior solutions. For the problem at hand, however, some parameter combinations would give rise to a corner solution. For example, if rivalry and spillovers are (very) low and if the housing supply elasticity is sufficiently high or the municipality sizes sufficiently heterogeneous, it might be optimal for the social planner to leave one municipality empty (just as we encountered for the decentralized case). In such cases, (13)–(18) would continue to hold for the occupied jurisdictions.

To avoid possible confusion, note that $\eta _j$ is not a measure for the housing price. The planner assigns people across jurisdictions. $\eta _j$ measures to what extent this assignment differs from the assignment that households themselves would choose.

We would like to stress that this is not an empirical application. A calibration of the model to actual data would require the use of an additional heterogeneity, other than income, because in practice pure sorting based on income is never observed.

To help the reader with the derivation of (29), note that (28) solves to $t_jY_j\equiv G_j^\mathrm{dec}=\left( N_j+\nu \sum _{i\ne j}N_i\right) ^{\rho }\beta _g+\frac{\alpha }{1-\alpha }\frac{Y_j}{y_j^m}\left( y_j^m(1-t_j)-p_j\beta _h-\beta _x\right) -\sigma \sum _{i\ne j}G_i$. Substitute $Y_j=N_jE[{y_j}]$ in the second term, bring $\frac{E[y_j]}{y_j^m}$ inside the bracket, and add and subtract $(p_j\beta _h+\beta _x)$ to obtain

$$\begin{aligned} \frac{\alpha }{1-\alpha }N_j\bigg (\underbrace{E[y_j](1-t_j)-(p_j\beta _h+\beta _x)}_{ = {Y_j^\mathrm{disp}}/N_j}\underbrace{+(p_j\beta _h+\beta _x)-E[{y_j}]/y_j^m \cdot (p_j\beta _h+\beta _x)}_{= -(E[{y_j}]-y_j^m)/y_j^m \cdot (p_j\beta _h+\beta _x)}\bigg ). \end{aligned}$$

Even in the case without spillovers, the supply of the publicly provided good depends indirectly on the other municipalities’ choices, which affect the population distribution and therefore determine $N_j$ and $Y_j$ along with the housing price $p_j$ and the median voter $y_j^m$.

To derive (30), substitute the partial derivatives of the indirect utility function (described in Table 5) into (21), use that $t_j=0$ in first-best, that the aggregate disposable income in j, $Y_j^\mathrm{disp}$, is given by $N_j\int _y\left( y+r(y)-T_j-p_j\beta _j-\beta _x\right) a_j(y)f(y)\text {d}y$, and solve this expression for $g_j$. To calculate the corresponding efficient production of the publicly provided good, solve (2) for $G_j$ and plug in the previous expression for $g_j$.

Since municipalities differ along three dimensions, there are three different possible trade-offs that may emerge: (1) higher level of public provision in exchange for a higher housing price and higher taxes; (2) a lower housing price in exchange for higher taxes and a lower level of public provision; and (3) lower taxes in exchange for a higher housing price and a lower level of public provision. Our findings for the publicly provided private good are consistent with the results in Schmidheiny (2006b), but as is evident from Fig. 2, this is not a general result.

Consider combinations of $\sigma =0$ and $\rho <1$, which correspond to the surface in front and to the right in Fig. 1. If rivalry in consumption is low enough (in our case approximately 0.65), households choose to reside in only one municipality, leaving the other empty.

This implies that the distribution of households boils down to a one-dimensional decision for the planner: By determining the border household, all poorer (richer) households are located in municipality 1 (2). Formally, $a_1(y)=1\;\forall \; y<y^\mathrm{border}$ and $a_2(y)=1\;\forall \; y>y^\mathrm{border}$, whereas all other values of a are zero.

Given our parameter choices, this results in $\omega _R=0.444$. Note that given our parameters, the housing rents are relatively small, such that the results are not very sensitive to the choice of $\omega _R$.

Formally, $\mathrm{CV}(y)$ solves $V^\mathrm{SB}(p^\mathrm{SB}_j,t^\mathrm{SB}_j,g^\mathrm{SB}_j;[y+\mathrm{CV}(y)])=V^\mathrm{FB}(p^\mathrm{FB}_j,T_j^\mathrm{FB},t_j^\mathrm{FB},g_j^\mathrm{FB};y)$.

For the calibrated model of Kuhlmey (2017), which is an adjusted version of the current model, it is assumed that the “set of spillover-generating expenditure categories consist of health, culture and leisure, security, environment, and traffic.” Using this categorization, the suburban municipalities in the metropolitan area around Zurich (Switzerland) spend around 25% of their budget on goods or services associated with a high degree of spillovers.

The corresponding case of a publicly provided private good is shown in Table 6 and Fig. 13 in the Appendix. This has been the focus of the previous literature.

In principle, one could separate this step into one step where lump-sum taxes are ruled out but head taxes are still allowed, and a second step where head taxes are removed from the set of available policy instruments. However, given that income is fixed in our model, income taxation does not entail a deadweight loss in terms of factor supply and is thus not qualitatively different from a specific combination of a lump-sum tax with a linear income tax. For this reason, we chose to combine the removal of r(y) and $T_j$ into a single “redistribution” step.

Alternatively, one could try to isolate the inefficiency from voting by comparing the first-best situation, where all decisions are made by a social planner, with a model where the decisions are made by a central median voter. However, this is complicated by the presence of spillovers and congestion. A uniform public consumption, which could serve as a benchmark for the decentralized outcome, is only consistent with zero or perfect spillovers. If spillovers are imperfect, the location of the central median voter would matter.

The relative welfare losses due to the inter-municipal free-riding and the JCE are qualitatively similar when measured with the SWF or the CV. However, not having access to individualized transfers (the difference between first-best and step I in Fig. 6) has a much larger welfare effect in terms of the CV than in terms of the value of the SWF. The underlying reason is that the CV for a given change in utility depends on a household’s income level. The non-monotonicity of the solid line in the bottom panel in Fig. 6 is due to different households being expropriated by the social planner, due to very different population distributions at low levels of $\sigma $.

We stress that this is the welfare loss from the JCE (which is one number and positive by construction), not the JCE itself (which depends on the municipality and the income level of the involved household, and which can be positive or negative).

Recall that these are equilibrium outcomes, such that by “faster” we mean a higher correlation between $\sigma $ and the income of the equilibrium border household at low levels of spillovers.

The different trade-offs between utility and money for households of different income levels is the reason why the aggregate compensating variation turns negative for decentralization steps I and II. The respective level of the SWF, which is the relevant measure from the perspective of the social planner, is higher at each step of decentralization than in the fully decentralized equilibrium.

To arrive at (A8), set up the system of equations of (A7) for $J=2,3,\ldots $ and solve it manually. This reveals the general formula.

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Title: The welfare costs of Tiebout sorting with true public goods
Authors: Florian Kuhlmey
Beat Hintermann
Publication date: 11-04-2019
Publisher: Springer US
Published in: International Tax and Public Finance / Issue 5/2019
Print ISSN: 0927-5940
Electronic ISSN: 1573-6970
DOI: https://doi.org/10.1007/s10797-019-09534-z

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