Collateral Avoids Ponzi Schemes in Incomplete Markets

Abstract

Without introducing either debt constraints or transversality conditions to avoid the possibility of Ponzi schemes, we show the existence of equilibrium in an infinite horizon incomplete markets economy with a collateral structure.

Patents as collateral

“…On date 0, each entrepreneur k receives an initial dividend d 0;k that he spends on consumption and has an initial endowment of n 0;k of valuable blueprints. 4 The aggregate number of patents on date 0 is denoted N 0 and aggregate dividends D 0 . Utility is given as the expected present value V 0 of dividends d t 0.…”

“…However, the growth rate cannot exceed 1 + 1 q , else consumption is zero. As debt is always fully backed by a correct evaluation of the value of available collateral at all future periods, lenders avoid repayment problems related to Ponzi …nance (see also Araujo et al (2002)). It is not necessary to add an alternative no-Ponzi …nance condition such that, in an equilibrium, the growth rate has to be lower than the interest rate, nor to assume overlapping and growing generations.…”

Harsh default penalties lead to Ponzi schemes: A counterexample

“…In an environment without commitment, Araujo, Páscoa and Torres-Martínez (2002) showed that Ponzi schemes are ruled out (and therefore equilibria always exist) if agents are forced to hold collateral when they take debt positions. Páscoa and Seghir (2009) subsequently presented two examples to show that if, in addition to collateral repossession, agents suffer harsh utility penalties when they default, then Ponzi schemes may reappear and equilibria fail to exist.…”

Conventional and Unconventional Monetary Policy with Endogenous Collateral Constraints

“…There is, however, one important respect in which we shall assume that financial markets are not frictionless in the sense of Arrow and Debreu, and this is important for the consequences of "unconventional" monetary policy: we shall assume, as in Geanakoplos (1997) and Araújo et al (2002), that all privately issued financial claims (as opposed to physical assets or government liabilities) must be collateralized. While the collateral requirements in our model represent a friction, in the sense that some 1 Many of the novel policies introduced by the Federal Reserve during the acute phase of the global financial crisis were of this kind; Bernanke (2009) characterized the Fed's policies during this period as "credit easing," to distinguish them from the "quantitative easing" of the Bank of Japan during the period 2001-2006 (which instead mainly involved open-market purchases of highly liquid securities, mostly Japanese government bonds).…”