Payday loans are one of the most expensive forms of credit in the world. Borrowers typically pay non annualized finance charges of 18% for loans lasting two weeks. These terms imply an annualized cost of payday loan liquidity of +.+2#& + 5 1,3/&. Truth in Lending regulations result in posted Annual Percentage Rates (APRs) for two week long loans of 18% ,0 5 .02&. Since finance charges generally do not depend on loan length, month%long and week long payday loans respectively carry annualized liquidity costs of +.+2"# + 5 0,3& and +.+2%# + 5 /.01./&.

Despite these high interest rates, ten million distinct American households borrowed on payday loans in 2002 and the industryis growth rate exceeds 15% annually (Robinson and Wheeler 2003). Consumption models offer three main complementary explanations for such a phenomenon. First, consumers may have very high discount rates, particularly in the short term (Phelps and Pollak 1968, Laibson 1997b, Frederick, Loewenstein and OiDonoghue 2002). Second, consumers may experience shocks that cause large, unanticipated variation in the marginal utility of consumption (Deaton 1991, Carroll 1992). Third, consumers may have overoptimistically rosy forecasts of the future, in regard to either their own time preferences (Akerlof 1991, OiDonoghue and Rabin 1999a) or the probability of favorable shocks (Brunnermeier and Parker 2005, Browning and Tobacman 2007).

This paper evaluates the contributions of these candidate explanations by nesting them in a single structural model, and estimating that model using detailed measurements from a unique administrative panel data set of 100,000 borrowers and 800,000 payday loans. Provided by a financial services firm that offers payday loans, the data include complete histories of loan initiations, repayments, and defaults from the time this firm began offering payday loans in January 2000 through August 2004. Rich demographic information is also available. Means of borrowing probabilities, loan sizes, and default probabilities, conditional on the amount of time elapsed since each customeris first loan, identify the structural modelis parameters.

Results of estimation using the Method of Simulated Moments indicate that uncertainty and time consistent discounting go partway toward accounting for the observed phenomena. In this benchmark case we estimate two week discount rates of 21% and default costs of about $300. At the estimated parameter values borrowing occurs, and the average borrowing rate over a year roughly matches the empirical observations. However, average empirical loan sizes exceed simulated loan sizes by more than 10%: the simulated consumers smooth consumption as they ramp up their loan sizes too gradually in anticipation of default. In addition, simulated default rates at the estimated parameter values are 50% higher than the empirical rates. Simulated sophisticated quasi hyperbolic discounters have higher short term discount rates and hence borrow more aggressively, providing a better match of loan magnitude data.

However, sophisticated quasi hyperbolic discounters also exhibit preferences for commitment. In this setting default acts as a form of commitment, as defaulters are excluded from future access to payday loans. Real consumer sifailure to take rapid advantage of this form of commitment results in evidence against sophisticated quasi hyperbolic discounting. At the estimated parameter values, sophisticated quasi hyperbolics have default rates twice as high as the empirical values. The last model we study, naive quasi hyperbolic discounting, helps to account simultaneously for initial borrowing, moderate default rates, and delayed defaults. Naive quasi hyperbolics incorrectly predict that future selves will absorb the default costs, depressing overall default rates toward the empirical values. In some specifications we cannot reject the hypothesis of perfect naivete, in which quasi hyperbolic consumers believe that future selves will exactly implement the current selfis preferences.

This paper complements a rapidly growing literature on payday loans. Distinguished contributions by Caskey (1991, 1994, 2001, 2005) drew attention to the topic and studied jfringe bankingkmore generally. Flannery and Samolyk (2005) used store level data from two payday lenders to study profitability of the payday lending industry; and Skiba and Tobacman (2007b) complement that profitability work using asset return and micro level data. Surveys of payday borrowers have been conducted by Elliehausen and Lawrence (2001) and Io Data (2002). State Departments of Finance have analyzed the industry as well. Stegman and Faris (2003) and Stegman (2007) review regulatory considerations and policy proposals. Morse (2006), Melzer (2007), and Skiba and Tobacman (2007a) estimate causal effects of access to payday loans. Consumer advocates and the industry lobby have also produced numerous (separate) studies.

Section 2 introduces the data and presents the key empirical facts. We devote Section 3 to the model and its predictions. Section 4 reviews the Method of Simulated Moments estimation procedure. We report and interpret the estimation results in Section 5. Section 6 discusses possible extensions, and in Section 7 we conclude.

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