Bank Run Exposure in a Paycheck to Paycheck Economy with Liquidity Preference and Loss Aversion to Decline in Consumption

Abstract

According to recent Getting Paid in America Survey Results, about 69% of respondents receive their pay biweekly, and about 72% of those surveyed would find it difficult to meet financial obligations if their paycheck was delayed by one week. Additionally, about 96% of those surveyed received their pay by direct deposit. In that milieu, we introduce a simple consumption based behavioral asset pricing model, with consumption ratcheting, in a veritable paycheck to paycheck economy, which supports a dynamic bank run exposure process induced by bank clientele liquidity preference and loss aversion to decline in - which induce a run on the bank. A representative agent‘s fear, about whether transitory shocks to permanent income in the next period will adversely affect consumption, is resolved upon receipt of her paycheck. At which point, in order for markets to clear, our agent use revolving credit, i.e., credit card or overdrafts, to pay for consumption not covered by bad shocks to income. We show that endogenous loss aversion, induced by uncertainty over comparatively small probabilities of bad shocks to income, is enough to trigger a bank run - from which we characterize an abstract topological space for bank runs. For application, we compute endogenous probability of suspension of convertibility as a function of (1) the stopping time of a bank run, and (2) a comparatively small probability of bad shocks to - provided that loss aversion is outside taboo limits defined on our bank run topological space. Further, we show that even though cash reserve is linear in liquidity risk, its beta, i.e. bank run exposure, is highly nonlinear in bank clientele loss aversion to declines in and or consumption. In fact, our asymptotic theory shows that bank run exposure is in the class of Hidden Markov Models over latent states of bank clientele loss aversion to fluctuations in income. Econometrically, this implies, inter alia, that as a function of liquidity risk, fluctuations in the bank‘s cash reserves are underestimated. Consequently, the bank is faced with a pseudo underinvestment problem - it needs to hold higher cash reserves to meet increased fluctuations in demand for liquidity induced by loss aversion which crowds out its ability to make loans for some positive NPV projects. In which case, one of the bank‘s risk management problem is to control its bank run exposure process to a goal of optimal investment.