Agency problems, arising from differing objectives between principals and agents, are inherent in principal-agent relationships. This extends beyond firm ownership to political processes, where incumbent governments may prioritize self-interest over voter welfare. Existing literature analyzes agency problems in various contexts, including firm ownership (Jensen and Meckling, 1976), political agency (Besley and Case, 1995; Seabright, 1996; Belleflamme and Hindriks, 2005; Wrede, 2001), and fiscal externalities (Dahlby, 1996; Dahlby and Wilson, 2003; Brülhart and Jametti, 2019). The under-provision of local public goods due to tax competition (Zodrow and Mieszkowski, 1986) is often addressed by intergovernmental matching grants. While the literature generally views spillover effects as worsening under-provision (Boadway et al., 1989), Ogawa (2006) and Kawachi and Ogawa (2006) suggest that sufficient spillover might alleviate this. Nishigaki and Kato (2016) show that yardstick competition increases public good under-provision. This paper investigates how agency costs, tax competition, and benefit spillovers interact to influence the optimal matching grant rate, generalizing previous findings.

The literature extensively discusses agency problems and their impact on public good provision. Studies highlight how agency costs raise the marginal cost of public goods, leading to undersupply unless the marginal benefit is adjusted (Belleflamme and Hindriks, 2005; Besley and Case, 1995). However, few studies integrate agency problems with horizontal tax externalities. Nishigaki and Kato (2016) analyze yardstick competition in small jurisdictions, finding increased costs and under-provision. This study extends existing work by incorporating tax competition and benefit spillovers into a model that explicitly accounts for agency costs, examining how these factors interact to determine the optimal matching grant rate.

The study employs a two-stage game-theoretic model. Initially, a model with immobile private capital is presented. The model incorporates *n* identical jurisdictions, each with an immobile resident. Individual utility is represented by U(xᵢ, Gᵢ), where xᵢ is private consumption and Gᵢ is local public good consumption, defined as Gᵢ = gᵢ + β Σⱼ≠ᵢ gⱼ, where gᵢ is the jurisdiction's public good provision and β represents benefit spillovers. Jurisdictional governments are assumed to be partially self-interested, maximizing a welfare function Wᵢ = V[Xᵢ(gᵢ)] + U(Gᵢ, xᵢ), where V[Xᵢ(gᵢ)] represents agency costs. The model incorporates budget constraints for residents (xᵢ = yᵢ − zᵢ − h) and jurisdictional governments (zᵢ + sᵢ = gᵢ), with sᵢ being the matching grant (sᵢ = mgᵢ). The central government's budget constraint is Σsᵢ = nh = Σmgᵢ. The model is solved using the first-order conditions of the maximization problems. The Pareto-optimal condition is derived to determine the optimal matching grant rate. Subsequently, the model is extended to incorporate mobile private capital, where jurisdictional governments raise revenue through distortionary capital taxes. The production function is yᵢ = f(kᵢ), with perfect capital mobility equalizing after-tax returns across jurisdictions (fkp(kᵢ) − tᵢ = r). Budget constraints are modified to reflect capital taxation and the matching grant. The first-order conditions of the extended model are derived and analyzed to determine the relationship between the optimal matching grant rate (m) and the private capital demand elasticity (ε).

The analysis reveals a complex interplay between agency costs, benefit spillovers, and tax competition. In the initial model with immobile capital, the optimal matching grant rate (m) is given by equation (11): m = β(n − 1) / [1 + (n − 1)] (V'X'/U'x). This equation indicates that the optimal matching grant rate increases with agency costs (∂m/∂V'X' < 0). The extended model with mobile capital yields a different expression for the optimal matching grant rate (equation 22): m = [β(n-1) + ε(1 - β)] / [1 + β(n-1)] (V'X'(1 - ε)/Uₓ). The impact of the private capital demand elasticity (ε) on m depends on the level of agency costs and benefit spillovers. Proposition 1 summarizes the findings: (1) If agency costs are relatively small (1 + χ > 0) and β = 0, m increases with ε; (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 is ambiguous; (4) If χ = -1 and β = 0, there's no relationship; (5) If χ = -1 and β > 0, m decreases with ε; (6) If agency costs are sufficiently large (1 + χ < 0), m decreases with ε regardless of β. Tables 1 and 2 illustrate the relationships under various parameter values. The study shows that horizontal fiscal externalities can either worsen or mitigate the under-provision of public goods caused by agency costs, depending on the magnitude of agency costs and benefit spillovers.

The findings highlight the importance of considering agency costs when designing intergovernmental grant systems. The study demonstrates that the optimal matching grant rate is not solely determined by benefit spillovers and tax competition but is also significantly influenced by the level of agency costs. When agency costs are small and benefit spillovers are minimal, tax competition exacerbates the under-provision of public goods. However, when agency costs are substantial or benefit spillovers are high, tax competition can mitigate the inefficiencies arising from agency problems. This nuanced relationship underscores the need for policy interventions that are sensitive to the specific characteristics of the jurisdictions involved. The results extend previous research by explicitly modeling agency costs within a tax competition framework and demonstrating the complex interactions between agency costs, tax competition, and benefit spillovers in shaping optimal grant policies.

This paper demonstrates that the optimal matching grant rate is influenced by the interplay of agency costs, tax competition, and benefit spillovers. The relationship between the optimal grant rate and the private capital demand elasticity is contingent upon the level of agency costs and benefit spillovers. Future research should explore dynamic aspects, such as the ratchet effect, and incorporate a more sophisticated model of political agency, including the dynamics of re-election and a more general social welfare function. Empirical analysis is also needed to validate the theoretical findings.

The study relies on a theoretical model with simplifying assumptions, such as homogeneous jurisdictions and perfect capital mobility. The model abstracts from dynamic considerations, such as the ratchet effect, and uses a simplified representation of political agency. Further research incorporating these factors would enhance the model's realism and generalizability. Empirical validation of the theoretical findings is needed.