The effect of Ponzi schemes on crime: Evidence from the colombian case

This paper estimates the impact of a massive negative income shock led by the simultaneous crash down of several Ponzi schemes (also known as financial ``pyramids"") in Colombia on crime rates at the municipal level. Using novel data on the spatial incidence of the latest wave of Colombian pyramids and their crash down date, I estimate difference-in-differences models with both monthly and yearly frequency. I find that the negative income shock of the pyramids" crash down differentially exacerbates crime in affected municipalities compared to those with no presence of Ponzi schemes. This is true for minor offenses like commercial theft or residential burglary, but not for major crimes as murder or terrorism.

Economic shocks and crime: evidence from the crash of ponzi schemes

In November 2008, Colombian authorities dismantled a network of Ponzi schemes, making hundreds of thousands of investors lose tens of millions of dollars throughout the country. Using original data on the geographical incidence of the Ponzi schemes, this paper estimates the impact of their break down on crime. We find that the crash of Ponzi schemes differentially exacerbated crime in affected districts. Confirming the intuition of the standard economic model of crime, this effect is only present in places with relatively weak judicial and law enforcement institutions, and with little access to consumption smoothing mechanisms such as microcredit. In addition, we show that, with the exception of economically-motivated felonies such as robbery, violent crime is not affected by the negative shock.

Collateral avoids Ponzi schemes in incomplete markets

Without introducing neither debt constraints nor transversality conditions to avoid the possibility of Ponzi schemes, we show existence of equilibrium in an incomplete markets economy with a collateral structure.

On Ponzi schemes in infinite horizon collateralized economies with default penalties

Araujo, Páscoa and Torres-Martínez (2002) showed that, without imposing any debt constraint, Ponzi schemes are ruled out in infinite horizon economies with limited commitment when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2009) presented two examples in which they argued that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. Moreover, they claimed that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is restored. This paper questions the validity of the claims made in Páscoa and Seghir (2009). First, we show that it is not true that harsh default penalties lead to Ponzi schemes in the examples they have proposed. A competitive equilibrium with no trade can be supported due to unduly pessimistic expectations on asset deliveries. We subsequently refine the equilibrium concept in the spirit of Dubey, Geanakoplos and Shubik (2005) in order to rule out spurious inactivity on asset markets due to irrational expectations. Our second contribution is to provide a specific example of an economy with moderate default penalties in which Ponzi schemes reappear when overpessimistic beliefs on asset deliveries are ruled out. Our finding shows that, contrary to what is claimed by Páscoa and Seghir (2009), moderate default penalties do not always prevent agents to run a Ponzi scheme.

Caraterização e identificação de esquemas Ponzi: Casos Chales Ponzi, Bernard Madoff e Dona Branca

Mestrado em Auditoria

Collateral, default penalties and almost finite-time solvency

We argue that it is possible to adapt the approach of imposing restrictions on available plans through finitely effective debt constraints, introduced by Levine and Zame (1996), to encompass models with default and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002) and Páscoa and Seghir (2008) the concept of almost finite-time solvency. We show that the conditions imposed in these two papers to rule out Ponzi schemes implicitly restrict actions to be almost finite-time solvent. We define the notion of equilibrium with almost finite-time solvency and look on sufficient conditions for its existence. Assuming a mild assumption on default penalties, namely that agents are myopic with respect to default penalties, we prove that existence is guaranteed (and Ponzi schemes are ruled out) when actions are restricted to be almost finite-time solvent. The proof is very simple and intuitive. In particular, the main existence results in Araujo et al. (2002) and Páscoa and Seghir (2008) are simple corollaries of our existence result.

Competitive equilibria in infinite-horizon collateralized economies with default penalties

Araújo, Páscoa and Torres-Martinez (2002) have shown that, without imposing either debt constraints or transversality conditions, Ponzi schemes are ruled out in infinite horizon economies with default when collateral is the only mechanism that partially secures loans. Páscoa and Seghir (2008) subsequently show that Ponzi schemes may reappear if, additionally to the seizure of the collateral, there are sufficiently harsh default penalties assessed (directly in terms of utility) against the defaulters. They also claim that if default penalties are moderate then Ponzi schemes are ruled out and existence of a competitive equilibrium is ensured. The objective of this paper is two fold. First, contrary to what is claimed by Páscoa and Seghir (2008), we show that moderate default penalties do not always prevent agents to run a Ponzi scheme. Second, we provide an alternative condition on default penalties that is sufficient to rule out Ponzi schemes and ensure the existence of a competitive equilibrium.

Endogenous debt constraints in collateralized economies with default penalties

In infinite horizon financial markets economies, competitive equilibria fail to exist if one does not impose restrictions on agents' trades that rule out Ponzi schemes. When there is limited commitment and collateral repossession is the unique default punishment, Araujo, Páscoa and Torres-Martínez (2002) proved that Ponzi schemes are ruled out without imposing any exogenous/endogenous debt constraints on agents' trades. Recently Páscoa and Seghir (2009) have shown that this positive result is not robust to the presence of additional default punishments. They provide several examples showing that, in the absence of debt constraints, harsh default penalties may induce agents to run Ponzi schemes that jeopardize equilibrium existence. The objective of this paper is to close a theoretical gap in the literature by identifying endogenous borrowing constraints that rule out Ponzi schemes and ensure existence of equilibria in a model with limited commitment and (possible) default. We appropriately modify the definition of finitely effective debt constraints, introduced by Levine and Zame (1996) (see also Levine and Zame (2002)), to encompass models with limited commitment, default penalties and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002), Kubler and Schmedders (2003) and Páscoa and Seghir (2009) the concept of actions with finite equivalent payoffs. We show that, independently of the level of default penalties, restricting plans to have finite equivalent payoffs rules out Ponzi schemes and guarantees the existence of an equilibrium that is compatible with the minimal ability to borrow and lend that we expect in our model. An interesting feature of our debt constraints is that they give rise to budget sets that coincide with the standard budget sets of economies having a collateral structure but no penalties (as defined in Araujo, Páscoa and Torres-Martínez (2002)). This illustrates the hidden relation between finitely effective debt constraints and collateral requirements.