Martingale properties of self-enforcing debt

Abstract

Not-too-tight (NTT) debt limits are endogenous restrictions on debt that prevent agents from defaulting and opting for a specified continuation utility, while allowing for maximal credit expansion (Alvarez and Jermann 2000). For an agent facing some fixed prices for the Arrow securities, we prove that discounted NTT debt limits must differ by a martingale. Discounted debt limits are submartingales/martingales under an interdiction to trade/borrow, and can be supermartingales under a temporary interdiction to trade. With high interest rates and borrowing limited by the agent's ability to repay debt out of his future endowments, nonpositive NTT debt limits are unique. With low interest rates, bubbles limited by the size of the total martingale components in debt limits can be sustained in equilibrium. Bubbles arise in response to debt limits more restrictive (at the prevailing interest rates) than the total amount of self-enforcing debt allowed by the underlying enforcement limitations.

On the sovereign debt paradox

“…Q.E.D Proposition 6.2 extends Proposition 3 in Bidian and Bejan (2015) in the same way Proposition 6.1 extends Proposition 3 in Hellwig and Lorenzoni (2009). Since these results follow from an arbitrage argument, we do not need to assume that preferences are additively separable with a strictly concave and differentiable Bernoulli function.…”

Borrowing in excess of natural ability to repay

“…Hellwig and Lorenzoni (2009) (see also Bidian and Bejan (2015)) went further and characterized an agent's repayment incentives without assuming a priori that his wealth is finite. They proved the following connection between debt sustainability and rational bubbles on debt limits.…”

Debt Limits and Credit Bubbles in General Equilibrium

“…The paper is related to the general equilibrium literature on risk sharing with limited commitment and endogenous borrowing constraints. A nonexhaustive list of contributions includes Kehoe and Levine (1993), Jermann (2000, 2001), Kehoe and Perri (2002), Kehoe and Perri (2004), Ábrahám andCárceles-Poveda (2006, 2010), Bloise and Reichlin (2011), Bloise et al (2013), Werner (2014), Martins-da-Rocha and Vailakis (2015), Bidian (2016), where default induces full exclusion from financial markets, and Bulow and Rogoff (1989), Gul and Pesendorfer (2004), Hellwig and Lorenzoni (2009), Werner (2014), Bidian and Bejan (2015) and Martins-da-Rocha and Vailakis (2017a,b), where defaulters are only excluded from future credit. To the best of our knowledge, our paper is the first that introduces the empirically relevant recourse feature of endowment losses from default into this general equilibrium environment.…”