4 . 2 Using Variation from Law Changes
The next column’s dependent variable is total loan size. Unsuprisingly, maximum size caps matter, with an estimated increase of $41 per $100 increase in the size cap. However, this is well below the one-to-one correspondence we would see if size caps are binding. Maximum loan term and rollover prohibitions also come in as significant, though the connection is less clear.
Only one variable significantly affects loan term, and that is minimum loan term. The coefficient just misses the 5% significance mark (p=0.052 ) and implies a 10-day increase in the minimum will raise lengths by 2.6 days on average. This effect is likely non-linear and concentrated among states with longer minimum loan terms. Notably, the estimate for maximum term is insignificant and economically small, suggesting it rarely if ever binds.
Price caps and size caps are the only types of regulation that are significantly predictive of delinquency, with coefficients implying that a $10 increase in the cap on a $300 loan increases delinquency by 0.6 percentage points, and a $100 increase in the size cap increases delinquency by 0.4 percentage points. These effects are moderate relative to an overall delinquency rate of 4.3%, and the mechanism by which they might affect the rate is not certain.
One possibility is that larger and more expensive loans are simply more difficult to pay off, leading to delinquency
Four types of regulation appear predictive of repeat borrowing: price caps, maximum term limits, rollover prohibitions, and cooling-off periods. It is easy to see why there might be a connection between rollover prohibitions and cooling-off periods–both are specifically designed to limit repeat borrowing, and indeed both coefficients are significant and negative. Though much of the debate over rollover prohibitions focuses on the ability of lenders and borrowers to circumvent them, it is possible that on the margin such prohibitions still make rollovers a bit less convenient, with consequences for overall repeat borrowing.
It is less straightforward to see the link between price caps and repeat borrowing. The coefficient implies a significant 3 percentage point decrease in the repeat borrowing rate for each $10 increase in the cap. One possibility is that this is a simple price effect: cheaper loans are more attractive to prospective customers and so they choose to use them more often. Another possibility is that, assuming higher price caps lead to greater delinquency, delinquent borrowers are less likely to be allowed to borrow in the future, leading to less repeat borrowing. However, the estimated effect of price caps on repeat borrowing is larger than the estimated effect on delinquency, suggesting this cannot be the sole mechanism.
Given that this form of regulation appears to have no effect on loan term itself, its putative target, it is difficult to imagine a channel by which it would affect repeat borrowing
Next we examine states that changed their laws in order to see whether the results obtained from the pooled regressions of the previous section are supported or contradicted in a setting with fewer confounding factors. Table 5 presents analyses of the six states in the data with law changes. Each cell of the table represents a separate regression using the specification in Equation (2), except for the South Carolina cells which use the specification in Equation (3). For reference, Figures 4,5,6,7,8, and 9 present raw means over time for fees, amount borrowed, loan term, lending volume, delinquency, and 
repeat borrowing for each state whose laws changed. 9
The pooled regressions suggested a fairly tight connection between price caps and price, and this relationship appears at least as strong in the law-change regressions. As noted in the law matrix in Tables 2 and 3, price caps went up in Ohio and Rhode Island, while Tennessee and Virginia both loosened theirs. All four states saw price changes in the direction of the price cap changes, and the sizes of the price changes closely track the size of the cap changes: $1.03, 96 cents, 56 cents, and $1.16 changes per $1 change in the cap, respectively. The remaining states did not adjust their price caps, and their prices did not change. These results support the conclusion that actual prices adhere closely to price caps.
