In all other cases it is estimated as ordinary least squares
Because in many cases the transition from one legal regime to another disrupts loans made very close to the time of the change, making them atypical of loans either before or after, all regressions are estimated removing loans made within 30 days of the change itself
where is an outcome of interest such as amount borrowed, and are in dollars, and are in days, and the other five law variables are binary. Because the main source of variation is differences in laws across states we cannot add state fixed effects, but we can at least partially account for cross-state differences with , a vector of macroeconomic variables including monthly unemployment at the state level provided by the Bureau of Labor Statistics and monthly house prices at the zip code level provided by CoreLogic. is a set of time dummies for every month in the data, is a state-specific error term, and is the idiosyncratic error term.
For regressions in which is delinquency or repeat borrowing, both of which are binary, the regression is estimated as a probit with marginal effects reported. All standard errors are clustered at the state level. For regressions in which is indebtedness three months later, the relevant law is the law in force three months later. For this reason, whenever this dependent variable is used the laws are coded to reflect the law in force at the time of the outcome, rather than the time of origination.
where is a dummy variable equal to 1 if the loan was originated after the law change, is a dummy variable equal to 1 if the loan was originated in the state that changed its law, is the time running variable, and is a set of month dummies 
meant to capture seasonal factors. , , , and are the same as before. In this setting the coefficient captures the discontinuous jump at the time of the law change in the state that changed the law, with and capturing linear trends on either side of the discontinuity and capturing jumps that happen in other states at the time of the change. Again, when is delinquency or repeat borrowing the regression is estimated as a probit, and when is repeat borrowing the laws are coded to correspond to the time of the outcome rather than the time of origination.
South Carolina provides an interesting case because it had not one law change but two. The state amended its law on , raising the maximum loan size to $550, creating an extended repayment option, instituting a 1-day cooling-off period between loans (2-day after the eighth loan in the calendar year) and prohibiting customers from taking more than one loan at a time. However, in order to allow time for the establishment of a statewide database the simultaneous lending and cooling-off provisions did not take effect until . This delay of part of the law makes it potentially possible to separate the effects of the simultaneous lending prohibition and cooling-off period from the effects of the size limit and extended repayment option, and necessitates a slightly different specification:
where is a binary variable equal to 1 after the first law change, and is a binary variable equal to 1 after the second law change. Now and capture the effects of the first and second laws changes, respectively.
4 . 1 Using Cross-State Variation
Table 4 presents the results of regressions employing cross-state regulatory variation. Each column corresponds to a separate regression of the form given in Equation (1). These regressions help us understand the contributions of various regulatory components.