Decentralization with porous borders: public production in a federation with tax competition and spillovers

Abstracting from inter-regional spillovers, decentralization can enhance or hinder efficiency depending on the context. Arzaghi and Henderson (2005) measure the determinants and the demand for decentralization in different contexts. From a political economy point of view, the principal (voters) can control the performance of the agent (government) better if the latter is local, which can lead to a better government performance and increased happiness (Voigt and Blume 2012).

Spillovers can consist of public goods produced in one jurisdiction “spilling out” to other jurisdictions (e.g., flood protection measures that also protect jurisdictions located downriver), or the population of other jurisdictions “spilling into” a jurisdiction to consume a public good (e.g., visiting a subsidized opera house or sports stadium).

See Wilson and Wildasin (2004), Fuest et al. (2005) and Keen and Konrad (2013) for comprehensive surveys on capital taxation.

There are economic and political arguments for an inability to commit on behalf of the central government. If the central government is benevolent and interested in maximizing total welfare, it might change from its pre-specified policy if inefficiencies from local policy decisions are too large (Wildasin 1999). Political motives include reputation effects and the incentives to win votes by giving transfers to poorer regions (see Oates 2005).

Some of the literature labels the lack of commitment inability as a “soft budget constraint” (see Qian and Roland 1998; Goodspeed 2002; Kornai et al. 2003). A soft budget constraint implies that the central government is expected to increase subsidies in response to regional government taxes as it allocates these grants in order to equalize marginal utilities of public good consumption across the federation. See Kornai et al. (2003) for a more in-depth discussion of soft budget constraints.

Bondarev et al. (2017) examine the choice between different types of public goods, some of which may convey negative externalities to other regions; however, they abstract from tax competition and thus from fiscal externalities.

For an analysis focusing on both spillovers and congestion, see Kuhlmey and Hintermann (2019).

Capital is interpreted as physical capital (i.e., factories) and not as financial investments, which would require a different type of model (in which the level of regional production would not depend on the level of capital). Generally speaking, capital is interpreted as anything generating real output that is mobile across regions; see Keen and Konrad (2013) for a discussion. We further refrain from modeling mobility costs of capital.

An alternative interpretation of \(L_i\) would be land. The relevant assumption about this factor is immobility across regions and that it does not serve as a regional tax base.

This means that the marginal rate of transformation between the private and the public good is equal to one.

Whether the individual transfers add to zero or some other value is immaterial, as long as this value is fixed. The crucial point is that \(\sum _i ds_i=0\) such that increasing the transfer to one region requires a reduction in the transfers for other regions; for a more general treatment with positive (but fixed) transfers, see Breuille et al. (2010).

With a perfectly competitive product market, condition (7) is always satisfied with identity. To see this, substitute (1) and (2) into the LHS of (7), and substitute (3), (4) and (12) into the RHS, to get \(\sum _N w_i + t_i k_i + R k_i = \sum _N w_i + t_i k_i R \bar{k}_i\). Since the sum of the employed capital (\(k_i\)) has to equal the sum of available capital (\(\bar{k}_i\)), the equilibrium condition (7) is always satisfied and can be ignored. Wilson (1987) modifies the model and analyzes trade in two goods; for a modification with trade costs, see Becker and Runkel (2012).

With a fixed capital supply (zero elasticity of supply), impacts of taxes are entirely felt by the aggregated suppliers of capital (= all households) as R will respond to changes in t. Papers relaxing the assumption of fixed capital supply include Ogawa and Wildasin (2009) and Eichner and Runkel (2012).

It is never a dominant strategy for region i to raise its tax until \(R = 0\), and we abstract from the possibility that capital could be in excess supply, as in Bucovetsky (1991).

If regions are not symmetric, the presence of a federal government affects the equilibrium outcome due to the (nonzero) transfer that will co-determine consumption and production. However, the functional forms of the optimality conditions would remain the same. In the social optimum, this is due to the fact that our benevolent federal government simply takes the place of the social planner in Bjorvatn and Schjelderup (2002). For the Nash equilibrium, any federal transfer is considered as given by the regional governments and thus drops out of the first-order conditions.

Because we focus on interior solutions, we abstract from the complementary slackness conditions. The second-order conditions are negative and therefore consistent with a welfare maximum.

Bjorvatn and Schjelderup (2002) and Koethenbuerger (2004) use a quasi-linear utility function defined by \(U_{i}(c_{i}, G_{i})= c_{i} + \mathrm{ln}\left( [t_{i} k_{i} + s_{i}] + \beta \sum _{m\ne i}^n \left[ t_{m} k_{m} + s_{m}\right] \right) \). Using this in (14) and solving leads to the Pareto-optimal tax \(t^\mathrm{PO} = 1/k\), which is independent of \(\beta \) and n. However, this is due to the fact that the marginal utility of income is constant with quasi-linear preferences, which is obviously a special case.

Akai and Sato (2008) provide a comparison of expenditure and tax optimization in a decentralized leadership game. Our setting, as well as that in Koethenbuerger (2004), Breuille et al. (2010) and Silva (2016) relate to their scenario B, in which \(t_i\) is decided ex ante and \(g_i\) adjusts ex post. They find that a decentralized leadership system in which taxes are the strategic choice variable leads to revenue sharing due to local government’s free-riding on tax collection efforts of others, in line with Koethenbuerger (2004) and our own results. In contrast, when \(g_i\) is the choice variable, cost sharing of expenditures leads to excessive expansion, i.e., over-provision. The intuition is that choosing \(g_i\) leads to cost sharing of own expenditure with all other local governments (hence a common pool problem). Ex post per capita transfers to regional governments are increasing in its expenditure and decreasing when other regions spend more. As the ex post tax burden of each regional government depends only on the economy-wide resource constraint, not on its own ex ante spending decisions. Akai and Sato (2008) demonstrate that this fosters overspending ex ante. See Wildasin (1988) for a further discussion on how the choice of strategic variable can influence the Nash equilibrium. In this paper, we focus on regions setting \(t_i\).

We would like to note that the equalization of public consumption is not the goal but a by-product of utility maximization. Transfers are chosen with the aim to maximize social welfare, and under symmetry, equalized public consumption is implied.

In symmetry, taxes are equal and consequently capital such that \(s^\mathrm{NE}\) is zero.

We refer to Bloch and Zenginobuz  (2015, Proposition 3). The equilibrium tax rate in their model depends nonlinearly on the spillover parameter, as is the case here. Furthermore, the equilibrium tax rate decreases if mobility increases, which is conceptually similar to the tax in the Nash equilibrium defined by (22)–(23). Here, the tax decreases if capital is “more mobile”, meaning that \(|f''|\) is smaller (the more linear the production function, the greater is the elasticity of regional capital demand with respect to the tax rate, \(\epsilon \)).

If spillovers were asymmetric in the sense that \(\beta _{ij}\ne \beta _{ji}\) and/or \(\beta _{ij}\ne \beta _{im}\), for \(i \ne j\), \(i\ne m\), the spillover parameters would not cancel. In this case, the best-response function would depend on the region in question, and on the associated vector of spillover parameters.

With a self-financing transfer system and symmetry, it must be that \(s_i=0 \, \forall \, i\) in equilibrium. In order to supply the efficient amount of the public good, the regions have to set the tax rate to \(t^\mathrm{PO}\).

Given that all federal inputs are fixed in this model, this could be substituted by a federal tax on capital or labor without loss of generality.

For \(\beta =1\), both sides of the reaction functions are zero, and again, as with a net transfer system (4.1.1), any federal transfer will lead to the same outcome since all regions consume the “pure” public good.

Conversely, we can state that with ex ante identical regions, any non-symmetric outcome will not be efficient as the federal government can only tailor \(s_i\) to individual regions, but not T. This means that the MRS cannot be equalized across regions if regional tax rates differ. However, non-symmetric tax rates by ex ante identical regions will not constitute a Nash equilibrium in the first stage of the game and thus can be ruled out.

For simplicity, we have modeled the grant as a lump-sum transfer above. In the Nash equilibrium, regional governments take the money amount of the transfer as given, regardless of how this amount is determined. In the decentralized leadership setting, the grant is chosen such that public consumption is equalized across regions (\(G_i=G_j\)). Again, the form of the grant is immaterial.

Ogawa (2006) uses a region-specific tax \(T_i\), but one that is not self-financing and therefore does not correspond to the income-redistributing net transfer considered above (note that he does not discuss the issue of commitment). The result is the same under symmetry, as all regions pay the same tax, but the outcome would differ with asymmetric regions. Since both the population and the total amount of capital are held fixed, T could also be specified as a tax on labor, or as a residence-based tax on capital \(\bar{k_i}\).