Paige Marta Skiba of Vanderbilt has written Tax Rebates and the Cycle of Payday Borrowing. Here's the abstract:
I use evidence from a $300 tax rebate to test whether receipt of this cash infusion by payday borrowers affects the likelihood of borrowing, loan sizes, or default behavior. Results from fixed-effects models show that the rebate decreased the probability of taking out a payday loan in the short run. These impacts are most apparent among credit-constrained, infrequent borrowers. Those who take out loans around the time of the rebate borrow amounts similar to their normal borrowing behavior but are more likely to default. Overall, however, the effects are small and short-lived, suggesting a muted response to this cash windfall in payday borrowing and repayment.