Can Mathematical Modeling Help Create Payday Lending Regulations?

Daria Roithmayr of USC, Justin Chin, a USC law student, and Bruce Levin, an Emory biology professor, have written Cat and Mouse: A Dynamic Analysis of Predatory Payday Lending.  Here's the abstract:

Legal actors and the regulators who pursue them often engage in a co-evolutionary game of cat and mouse, as each innovates to out-compete the other. Predatory payday lenders are a prime example of this co-evolutionary arms race. Lenders have discovered increasingly creative ways to escape state regulation, like partnering with Indian tribes to claim immunity from state jurisdiction. In turn, regulators continually adapt their regulation to retarget the latest innovation. A regulator trying to keep pace with legal actors faces a tradeoff: adapting more frequently reduces the prohibited behavior, but increases wasteful innovation for both regulator and lenders, as each innovates in response to the other. In this paper, we draw from dynamic mathematical models of drug resistance to map this process and to advise regulators on how to optimize their regulatory approach. We construct a simple mathematical model using coupled differential equations to describe the arms race of innovation between regulatory strategy and the strategy of the regulated, in the context of payday lending. We conduct numerical approximations, to analyze the evolutionary pathways of regulator and lender strategy over time, and to map the tradeoff between the benefit from reducing predatory lending and the harm from having to return again and again to the drawing board to generate new regulation. We show that, contrary to intuition, a regulator should delay responding to an innovative payday lender strategy: we calculate an optimal response time that balances the need to respond slowly in order to minimize triggering repeated innovation, and the need to respond quickly to minimize the number of predatory payday lenders. We also show that a regulator that is unable to adapt quickly should weaken the strength of its innovation, in order to minimize further innovation by predatory lenders.

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