Sovereign Defaults and Interest Rate Spread in the Presence of a Self-Control Problem

Conventional sovereign default models, with stochastic aggregate output as the only factor driving endogenous defaults, leave some main features of the Argentine economy unexplained: a large sovereign debt with respect to GDP (31%), and a large interest rate spread on average (10%) with high volatility. These models' predictive power is especially poor during economic booms. To capture these features, I introduce self-control preferences (Gul and Pesendorfer, 2001, 2004, 2005) into the standard setup. The sovereign suffers from the temptation to consume the entire wealth and save nothing for the future due to a lack of self-control, and thereby has an incentive to incur a higher level of debt than normal: the temptation is reduced by the larger repayment if the sovereign stays in the non-default regime. The larger repayment, however, comes at the cost of a higher probability of default. As a consequence, the international loan market charges a higher interest rate in compensation for the default risk. This richer model captures the main unexplained trends and successfully matches Argentine sovereign default history. In the presence of the self-control problem, consumption tax has a non-trivial welfare effect and can reduce sovereign default risk. In response to the concern (Barro, 1999) about observational equivalence between a lack of self-control and the presence of a low discount factor, I show that the latter cannot generate the observed interest rate spreads. To surmount the computational difficulties that arise from the introduction of self-control preferences, I develop an algorithm that builds on the genetic algorithm (Holland, 1975) and the tripartite method. Combined with the technique of state space segmentation to properly handle non-local approximations of the value function, I show that the new algorithm is significantly more precise, and at the same time more efficient, than the standard algorithms.

Welfare Implications of Consumption Tax for Sovereign Default

Sovereign default is prevalent in emerging markets. With excessive impatience, savings subsidies can be welfare improving by reducing over-consumption (Krusell, Kuruscu and Smith, 2009). This paper shows that a consumption tax scheme which is equivalent to savings subsidy can be welfare deteriorating when the capital market is imperfect, because of the existence of a feedback mechanism. For Argentina, the overall effect is slightly negative. The feedback mechanism is as follows: with consumption tax, the decreased likelihood of default leads to a decrease of interest rate at equilibrium, which induces over-consumption. It would offset part of the welfare gain obtained from imposing the consumption tax. Furthermore, the decrease in the level of sovereign loans would increase next period’s temptation. I quantitatively show that when the degree of self-control problem exceeds a certain level, the feedback mechanism dominates. The policy recommendation would be a consumption subsidy.

Increasing Borrowing Limit in the Presence of Self-Control Problem: Policy Implications for the U.S.

The U.S. has been increasing its borrowing limits over the last three decades. In a standard model, welfare improves if borrowing limit has been increased when a binding credit constraint is relaxed. This conclusion can be reversed if the decision maker has a self-control problem. To make this argument, I compare two cases where the decision maker has her credit constraint binding versus non-binding. I show that welfare decreases as the credit constraint is relaxed in the non-binding case. For the binding case, there are two effects. The increase in temptation to spend causes a decrease in welfare that offsets the welfare gain from relaxing a binding credit constraint. The overall effect can only be positive if the constraint relaxation is small, the cost of resisting the temptation is very small and if the decision maker’s discount factor is low relative to the market. This research has a number of policy implications: it implies that when shaping the credit market reforms, the knowledge of the agent’s time preference, self-control cost to resisting available resources across population and market equilibrium interest rate are crucial for determining the direction of the welfare changes resulting from expansionary credit policy or tightening credit policy.

In this paper, I develop genetic algorithm (GA) and tripartile method combined with the techniques of multiple sections and function transformation to solve value functions with self-control preferences. The algorithm is based on Hatchondo et al. (2010) who developed Chebyshev polynomials and cubic spline interpolation algorithms to solve the inefficiency problems of grid points’ technique. The Hatchondo et al (2010) procedure, while more efficient compared to discrete state space with evenly spaced greed points technique, is still unable to solve non-monotonous value function and has difficulties finding global maximum in order to approach the true value of the function. My algorithm provides high precision for value function computation enhances convergence speed and controls divergence during value function iteration and is more efficient than traditional algorithms. The algorithm has wide application: self-control value functions, value functions with low default output cost, low discount factors and high default risk