Effect of agency costs on the optimal matching grant rate in a model of tax competition with benefit spillovers

The paper investigates how agency costs within jurisdictional governments interact with horizontal fiscal externalities—tax competition and benefit spillovers—to determine the optimal matching grant rate set by a benevolent central government. Agency problems, well documented in both corporate governance and political settings, imply that local governments incur agency costs (disutility of effort) when providing public goods, potentially leading to under-provision. The literature on tax competition (e.g., Zodrow and Mieszkowski, 1986) shows under-provision of local public goods financed by distortionary taxes, while intergovernmental transfers (matching grants) can correct such inefficiencies (Dahlby, 1996). Spillovers of local public goods typically exacerbate under-provision, though under certain conditions they may mitigate it (Ogawa, 2006; Kawachi and Ogawa, 2006). Few studies integrate agency costs with horizontal tax externalities; existing work suggests yardstick competition can raise financing costs and worsen under-provision. This paper asks: how do agency costs and benefit spillovers jointly shape the optimal matching grant in settings with and without tax competition, and can tax competition ever mitigate inefficiencies stemming from agency costs? The study builds a two-stage fiscal federalism model to derive optimal matching grants under closed-economy (no capital mobility) and open-economy (capital mobility and tax competition) scenarios, emphasizing the roles of agency costs and spillovers.

The introduction surveys core strands: (i) agency theory and political agency (Jensen and Meckling, 1976; Besley and Case, 1995; Seabright, 1996; Belleflamme and Hindriks, 2005; Wrede, 2001); (ii) fiscal externalities and intergovernmental grants (Dahlby, 1996; Dahlby and Wilson, 2003); (iii) tax competition and public good under-provision (Zodrow and Mieszkowski, 1986) and the potential disciplining effect of tax competition on Leviathan governments (Brülhart and Jametti, 2019); and (iv) spillover effects on public good provision (Boadway et al., 1989; Ogawa, 2006; Kawachi and Ogawa, 2006). It highlights the relative scarcity of studies combining agency costs with horizontal tax externalities, noting Nishigaki and Kato (2016) who show yardstick competition can increase financing costs and exacerbate under-provision. The present study contrasts by identifying conditions where tax competition may mitigate agency-cost-induced inefficiency, especially when agency costs are large.

The paper develops a two-stage model of a federation with n identical jurisdictions. Governments are partly self-interested; agency costs enter local government welfare as V[X(g)], with V′<0 and X′>0 capturing disutility of effort that rises with public good provision. Residents’ utility is U(G,x), with local public good G_i = g_i + β Σ_{j≠i} g_j, where β∈[0,1] measures benefit spillovers. The central government is benevolent and uses a uniform matching grant rate m to induce efficient local provision; it finances grants with a lump-sum national tax h subject to a hard budget constraint. Two environments are analyzed. 1) Closed economy (no capital mobility; lump-sum local finance): - Resident budget: x_i = y_i − z_i − h. Local budget: z_i + s_i = g_i with s_i = m g_i. Central constraint: nh = Σ s_i = Σ m g_i. - Stage game: Stage 1 central chooses (m,h). Stage 2 each local i chooses (z_i,g_i). - Local objective: W_i = V_i[X_i(g_i)] + U_i(G_i, x_i). The FOC at a symmetric equilibrium yields: V′X′ + U_G − (1−m)U_x = 0. The Pareto-optimality condition (maximizing Σ U_i subject to resource constraint) implies U_g + β U_G − U_x = 0, which in symmetric terms gives U_G[1 + β(n−1)] = U_x. - Equating the decentralized FOC to the planner’s condition delivers the optimal matching grant: m = [β(n−1)] / [1 + (n−1)β] − (V′X′)/U_x × [1 / (1 + (n−1)β)] (presented in-text as Eq. 11 with notation aligning to V′X′ and U_x). The key qualitative result: m rises with agency costs magnitude |V′X′| (since V′<0, X′>0). 2) Open economy with tax competition (capital mobility; capital taxation): - Production in each jurisdiction: y_i = f(k_i), with f_k > 0, f_{kk} < 0. Private capital is perfectly mobile: after-tax returns equalize, f_k(k_i) − t_i = r for all i; total capital fixed at K^P. - Resident budget: x_i = f(k_i) − f_k(k_i) k_i + r(k̄_i − k_i) − h (after using return equalization), where k̄_i is the resident’s capital endowment. - Local budget: t_i k_i + s_i = g_i, with s_i = m g_i. Central budget: Σ h = Σ m g_i. - Two-stage game: Stage 1 central chooses (m,h). Stage 2 each local i chooses (t_i, g_i) taking others as given. - Local objective: W_i = V_i[X_i(g_i)] + U_i(G_i, x_i). Define ε as the private capital demand elasticity with respect to the local capital tax: ε = −(∂k_i/∂t_i)(t_i/k_i). Under symmetry, the FOC system leads to a condition (Eq. 21) linking V′X′, U_G, U_x, β, and ε. - Comparing the decentralized condition to the planner’s condition yields the optimal matching grant rate (Eq. 22): m = {[β(n−1) + ε(1−β)] / [1 + β(n−1)]} × [V′X′(1−ε)/U_x]. - Differentiating with respect to ε gives (Eq. 23): ∂m/∂ε = {[1 + β(n−1) − β]/[1 + β(n−1)]} × (V′X′/U_x). The analysis focuses on the left side of the Laffer curve, 1 − ε > 0. Assumptions include identical jurisdictions, symmetric equilibrium, benevolent central government, hard budget constraint, and that SOCs hold.

- In the closed-economy baseline with spillovers, the optimal matching grant rate m that decentralization requires to achieve the planner’s allocation increases with agency costs (since V′<0, X′>0 implies ∂m/∂(V′X′) < 0 in sign-convention terms). This extends Boadway et al. (1989) and Ogawa (2006) by incorporating agency costs. - With tax competition (mobile capital), the optimal matching grant rate is m = {[β(n−1) + ε(1−β)] / [1 + β(n−1)]} × [V′X′(1−ε)/U_x] (Eq. 22), where ε is the capital demand elasticity with respect to the capital tax. On the left side of the Laffer curve (1 − ε > 0), m increases in the magnitude of agency costs even with horizontal externalities. - The sensitivity of m to tax competition intensity (ε) is ∂m/∂ε = {[1 + β(n−1) − β]/[1 + β(n−1)]} × (V′X′/U_x) (Eq. 23). The sign and magnitude depend on β (spillovers), ε, and agency costs via V′X′/U_x. - Proposition (assuming 1 − ε > 0): 1) If agency costs are relatively small (1 + χ > 0) and β = 0, m increases with ε (more intense tax competition raises m). 2) If agency costs are relatively small and β = 1, m decreases with ε. 3) If agency costs are relatively small and 0 < β < 1, the relationship between m and ε is ambiguous. 4) If χ = −1 and β = 0, m is unrelated to ε. 5) If χ = −1 and β > 0, m decreases with ε (especially when β = 1). 6) If agency costs are sufficiently large (1 + χ < 0), m decreases with ε regardless of β. - Interpretation: Horizontal fiscal externalities (tax competition and spillovers) typically cause under-provision of local public goods, but can mitigate under-provision stemming from agency costs. If agency costs are small and spillovers are zero, externalities worsen under-provision; m should rise. If agency costs are large or spillovers are perfect, tax competition can ease agency-cost inefficiency; m should fall. When spillovers are imperfect and agency costs small, effects are ambiguous. - Policy implication: With larger agency costs, even in the presence of horizontal externalities, central matching grants should be higher; however, when agency costs are sufficiently large, horizontal externalities mitigate agency-cost inefficiency and m can be appropriately reduced compared to the no-competition case.

The research question concerns how inevitable agency costs within local governments alter the standard tax competition prescriptions for optimal intergovernmental matching grants, especially in the presence of benefit spillovers. The models show that agency costs shift the decentralized FOCs by adding a term V′X′, increasing the marginal cost of providing local public goods. In a closed economy, matching grants can correct both spillovers and agency-cost distortions; the optimal rate rises with the severity of agency costs. Introducing tax competition adds an additional distortion via capital mobility (ε), which raises the marginal cost of public funds. This intensifies under-provision but simultaneously reduces agencies’ excess rents (lower effort disutility), so net welfare depends on the balance between resident welfare loss and agency-cost reduction. The derived expressions (Eqs. 22–23) formalize this trade-off: depending on spillovers and agency cost magnitude, more intense tax competition can call for higher or lower matching rates. The findings thus refine fiscal federalism guidance: grants should be tailored not only to spillovers and tax-base elasticities but also to political-agency distortions, implying context-dependent policies. This contributes to the literature by identifying conditions under which tax competition may be welfare-improving as a second-best remedy for agency problems.

The study demonstrates that when agency costs are incorporated, the optimal matching grant rate depends critically on both benefit spillovers and the intensity of tax competition. With zero spillovers, whether m rises or falls with capital-tax elasticity hinges on the size of agency costs; tax competition can alleviate agency-cost-induced inefficiency only if the disutility of effort is sufficiently large. With spillovers, results become ambiguous and depend on parameter values. Policy-wise, higher agency costs warrant higher matching grants, but horizontal fiscal externalities can partially correct agency-cost inefficiencies when agency costs are large, justifying lower grants relative to the no-competition benchmark. Future research should incorporate dynamic considerations (e.g., ratchet effects), explicit electoral re-election mechanisms in the political agency process, more general objective functions, and empirical validation.

- Dynamic aspects are abstracted from; ratchet effects and intertemporal commitment issues are not modeled. - The political agency process is simplified: re-election probabilities and incumbents’ strategic behavior are omitted; results’ robustness to explicit electoral mechanisms remains to be tested. - Identical jurisdictions and symmetric equilibrium are assumed; heterogeneity is not analyzed. - The central government is assumed benevolent with a hard budget constraint financed by lump-sum taxes; alternative financing and soft budget constraints are not considered. - Second-order conditions are assumed to hold without detailed verification. - Potential yardstick evaluation/incentive contracts that could restore efficiency under full information are explicitly neglected. - No empirical analysis is provided; results await empirical verification.