_“The creation of Debt should always be accompanied with the means of extinguishment.”_ — Alexander Hamilton, Report on Public Credit, 1790

# 1 Introduction

In many countries, revenue collection power is largely held by the central government, while spending responsibilities are disproportionately assigned to local governments.<sup>1</sup> Because of this asymmetry— known as “vertical fiscal imbalances,” local governments’ own revenue often falls short of their spending, and the gap is filled by intergovernmental transfers from the central government and local governments’ borrowing. Existing empirical findings suggest that widening vertical fiscal imbalances in a country are associated with worsening aggregate fiscal performance, such as faster public debt accumulation (see e.g., Rodden 2002, Eyraud and Lusinyan 2013). As an illustration, Panel A of Figure 1 shows the gaps in local government finances for three OECD countries, and Panel B shows that total (central and local) government debt tends to rise faster when vertical fiscal imbalances widen.<sup>2</sup> The theoretical literature on the soft budget constraint problem offers one channel for this relationship: rising vertical fiscal imbalances worsen local governments’ soft budget constraint problem and lead to rising local government debt (Boadway and Shah 2007, Chapter 5).<sup>3</sup> But because this literature uses mostly static or two-period models, it does not have anything to say about central government debt,<sup>4</sup> which accounts for the majority of government debt changes in the data.<sup>5</sup> Even less is known about the size of the effect of vertical fiscal imbalances on government debt accumulation.

In this paper, we quantify the effect of vertical fiscal imbalances on total government debt accumulation by developing an infinite-horizon model. The infinite-horizon is a valid choice because it allows us to consider central government debt alongside local government debt. The model delivers a novel result in the equilibrium: the central government over-transfers to local governments, to the extent that the marginal utility from local government spending is smaller than the marginal utility from central government spending. Applying the model to fiscal decentralization, wider vertical fiscal imbalances make local governments more reliant on transfers and exacerbate the soft budget

> 1We use “central government” to refer to the national government in a country, and use “local government” to collectively refer to the subnational government such as a regional, provincial, or municipal government.

> 2Appendix A includes plots for 25 other OECD countries and shows that changes in total government debt comove with vertical fiscal imbalances in a large set of countries over time.

> 3In their survey of the soft budget constraint concept, Kornai et al. (2003) define soft budget constraint as the phenomenon that arises when “one or more supporting organizations (S-organizations) are ready to cover all or part of the deficit” of an organization that has a budget constraint (a BC-organization). In our setting, local governments are the BC-organizations, and the central government is the S-organization.

> 4In a two-period model, central government debt is zero at the end of the second period by default. This means that even though it is possible to model central government borrowing between the first and second periods, a two-period model does not allow the accumulation of debt over time.

> 5For example, for G-7 countries, the change in central government debt-to-GDP ratio during 1995–2015 ranges from 35% (Canada) to 133% (Japan); the change in subnational government debt-to-GDP ratio is much smaller, ranging from 2% (United Kingdom) to 13% (Japan).

1