Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Optimal Time-Consistent Taxation with Default

Academic journal article Federal Reserve Bank of Atlanta, Working Paper Series

Optimal Time-Consistent Taxation with Default

Article excerpt

1 Introduction

This paper studies the optimal time-consistent allocation of tax distortions and the optimal issuance of debt in an environment where government debt can be defaulted on. We consider a government that has to finance an exogenous stream of stochastic government expenditures and maximizes the utility of the representative household. The government can use distortionary labor taxes or issue non-contingent debt. The government can default on its debt subject to a default cost. Our setup is fully time-consistent; neither tax nor debt promises are honored.

Our analysis builds on the notion of Markov-perfect equilibrium (MPE) of Klein et al. (2008). Optimal policy is time-consistent in the payoff-relevant state variables, which for our case are government debt and government expenditures. Furthermore, we model default as in the work of Arellano (2008) and Aguiar and Gopinath (2006), that builds on the debt repudiation setup of Eaton and Gersovitz (1981). This setup allows to observe default in equilibrium.

In most of the sovereign default literature, government debt is assumed to be held only by foreigners whereas domestic households are hand-to-mouth consumers. However, Reinhart and Rogoff (2011) find that, on average, domestic debt accounts for nearly two-thirds of total public debt for a large group of countries. We consider a closed economy in which domestic households hold government debt. Thus, our model takes into account that default events often involve default on debt held by domestic households. This assumption is supported by the empirical literature. While domestic default events are more difficult to identify than external default events, Reinhart and Rogoff (2011) document 68 cases of overt default on domestic debt since 1800. Moreover, often even when default is only on external debt (which we do not model), a significant portion of the external debt is held by domestic investors (Sturzenegger and Zettelmeyer 2006). For these reasons it is of interest to understand the tradeoffs governments face when considering whether to default on domestic households.

Our purpose it to analyze optimal tax-smoothing and debt issuance in such an environment. The lack of state-contingent insurance markets hinders the ability of the government to smooth taxes. Default can in principle make debt partially state-contingent. In particular, the government affects both the pricing kernel of the agent and the payoff of government debt. Default risk is reflected in equilibrium prices and alters the optimal allocation of tax distortions over states and dates.

The government has an incentive to default when either government debt or government expenditures are high. By defaulting the government can avoid high distortionary taxation. However, default entails either direct costs in terms of output losses, or indirect costs, in terms of a limited functioning of the market of government debt after a default event. In particular, we follow Arellano (2008) and assume that the market for government debt pauses to function for a random number of periods after a default event.

Optimal policy is characterized in our model by a generalized Euler equation (GEE) that balances the dynamic costs and benefits that the government is facing. The average welfare loss that is incurred by an increase in debt issuance (since higher debt has to be accompanied with higher future taxes) has to be balanced with the benefits of relaxing the government budget and allowing less taxes today. Our GEE reflects the fact that interest rates increase when debt increases, due to a higher probability of default. However, higher debt can also lead to reduction in interest rates by increasing marginal utility. The increase in marginal utility is coming from the fact that future consumption decreases in the event of repayment. This second channel is particularly important in our setup because it reflects the interest rate manipulation through the pricing kernel that is essential for our time-consistent setup. …

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