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The Miscalculations Underlying Miller & Zywicki's Payday Loan Paper

posted by Adam Levitin

Earlier this month Professors Todd Zywicki and Thomas Miller, Jr. wrote an op-ed in the Wall Street Journal arguing against payday loan regulation, based on their new empirical paper. Miller & Zywicki wrote:

Our findings will startle the rule writers at the CFPB. Contrary to the research cited in the CFPB’s 2017 rule, which claimed that “loans are almost always made at the maximum rate permitted,” we found that neither fees paid nor loan amounts inexorably rose to maximum allowable levels when those allowable levels were reasonable.

The implication is that there must be price competition among payday lenders with supply and demand setting prices, vitiating the need for regulation.

The problem is that Miller and Zywicki have incorrectly calculated the maximum fees permitted in numerous states. They wrongly assume that the effective rate charged for the first $100 of credit also applies to higher amounts. In fact, in many states, there is either a tiered, decreasing rate or a rate plus a flat fee included in any loan. As a result, Miller & Zywicki calculate the maximum permitted fees as being substantially higher than they in fact are in every state in which they find lenders are not pricing up to the legal limit.

Once this error is corrected, Miller and Zywicki’s figures actually confirm a truth that has long been obvious to anyone who has ever looked at payday loan pricing: there is no price competition, as lenders virtually always price up to the legal limit.

If my (lengthy) analysis below the break is correct, Professors Miller and Zywicki ought to retract both their op-ed and their paper. This is the sort of error for which op-eds and research papers are properly retracted. While Professors Miller and Zywicki might be opposed to payday regulation on ideological grounds, they surely do not want to base their claims on erroneous calculations of state fee caps.

Miller & Zywicki’s claim in their paper's abstract is that “loan prices and loan amounts are generally not at state-mandated maximum levels.” In other words, payday loans are frequently being made at less than the legal maximum rate and for amounts smaller than the legal maximum. To support this claim, they utilize a database of payday loans made in thirty states in 2013 (the loans are either illegal or functionally impossible to make in other states). There are problems with their calculation of both the applicable fee caps on loans and on loan amounts, as discussed in turn below. Before proceeding, however, I want to give credit to the sharp-eyed researcher who first spotted an issue with the paper. I don't normally Fisk data tables, but upon digging into the paper, it appears that there are many other issues.

Fee Caps

In 2013, twenty states had a statutory fee cap on payday loans. Miller & Zywicki claim that “about 30 percent of the payday loans in states with a statutory Fee Cap are made at less than the statutory maximum fee per $100.” (p.5). They define loans a being made at less than the statutory maximum if the fees are less than 99% of the legal maximum. (One might well quibble with such a high threshold—I would urge Miller & Zywicki to show the data also using 95% and 90% cutoffs—but that's not the point here.)

Miller & Zywicki present their data in their discussion in terms of percentage of loans made in those twenty states, never weighting those states by number of loans or population other than to sometimes present the data excluding California. But a very different picture emerges in their data tables, where they break the data down by state. What is observable in Table 2, for example, is that in a large percentage of lenders in thirteen of the twenty states are pricing below the legal limit, but that in seven of the twenty states, however, lenders are virtually always pricing right up to the legal loan limit. Indeed, 100% of the Rhode Island loans were made right at the legal limit.

This seems quite puzzling: why would lenders price up to the cap in Nebraska, but not neighboring Iowa (which has a lower rate cap) or in Mississippi, but not neighboring Louisiana? Do market forces somehow magically work in Iowa, but not Nebraska? Strangely, there is no discussion anywhere in the paper about this very obvious discrepancy. Instead, despite a marked bimodal split among states, data is presented in the discussion on an aggregate basis and the state distributional puzzle is never discussed.

As it turns out, there is no puzzle to solve because there’s no actual discrepancy. Instead, there’s a pervasive data coding problem. Miller & Zywicki miscoded state payday law rate caps in every one of the thirteen states where they claim lenders are not pricing up to the legal limit. When state law is correctly coded, it’s clear that lenders are actually pricing up to the limit everywhere, which is what everyone already knew.

Miller & Zywicki’s argument that lenders are not pricing up to the legal limit is based on their construction of a fraction. In this fraction, the numerator is the observed fee amount, and the denominator is the maximum legally allowed fee:

[observed fee] / [maximum legal fee]

For thirteen of the twenty states that have statutory fee caps, Miller & Zywicki find that:

[observed fee] / [maximum legal fee] < 99%.

The problem is that Miller & Zywicki miscalculate their denominator. That's because they make a basic error in coding state payday laws. Miller & Zywicki calculate the maximum fees for what state payday law permits for a $100 loan and then appear to extrapolate from that figure to the fees permitted on larger loans.

I say "appear," as Miller & Zywicki never state this explicitly. Instead, they state their findings in terms of the percentage of loans that are priced at “less than the statutory maximum fee per $100." Implicit in this presentation, however, is the extrapolation from the fee per $100 to the fees permitted on the actual loans, which are substantially larger than $100.

The extrapolation method works for those states whose maximum fee is calculated as a simple flat percentage. In those cases, the fee on the first $100 is the same as on the second and third $100 of a loan, etc.

The extrapolation method, however, does not work for those states where the lender is required to charge a fixed amount state database fee in addition to the flat percentage rate. The database fee is only charged once no matter the loan size, so it makes the cost of the first $100 more expensive than the cost of the next $100. Similarly, the extrapolation method does not work in states that have a maximum fee calculated as a tiered, decreasing percentage of the loan amount. For both of these groups of states, extrapolating from the fees allowed on the first $100 results in an inflated denominator, which all but guarantees that the observed fees will be less than 99% of the maximum legally allowed fee.

A version of the calculation problem exists in every one of the 13 states where Miller & Zywicki claim that loans are generally being made for less than the legal maximum rate. In contrast, Miller & Zywicki correctly calculate the legal maximum rate for all seven states where 99%+ of loans are made at the maximum rate.

Lest this be too abstract, here are a pair of examples.

Example 1: Michigan

Consider Michigan, for example. Miller & Zywicki correctly determine the cost to borrow a $100 payday loan in Michigan is $15.45 (Table 1). Extrapolating from this, the maximum legal charge on the reported average Michigan loan size of $459 is $70.92. Miller & Zywicki report (Table C1) that 49.5% of Michigan payday loans are made at between 13% and 15% rates and 47.7% are made at between 11% and 13% rates. So that sounds as if nearly all Michigan payday loans are being made at something less than the 15.45% rate cap that Miller & Zywicki use.

The problem is that Michigan has a tiered, decreasing rate cap for payday loans, not a flat percentage cap. Michigan allows a charge of $15.45 for the first $100 borrowed, but only $14 for the second hundred, $13 for the third hundred, $12 for the fourth hundred, and $11 for the fifth hundred. That means that the actual maximum fee allowed in Michigan on a $459 loan is only $60.49, not $70.92. The implied blended rate cap using the correct $60.49 fee figure is 13.17%, not 15.45%. Using that correct rate cap, it would appear that virtually all Michigan payday loans are being made at something very close to the rate cap.

Example 2:  Wyoming

Miller & Zywicki report Wyoming as having a $30 cap per $100—in other words they are comparing Wyoming loans to a 30% cap.  The problem is that Wyoming's payday statute is more complicated. It provides that the fee is the greater of $30 or 20% per month.  The per month language means that the 20% figure has to be pro rated for loans shorter than a month. It translates into a 235% APR (=20/31*365—we have to use the longest possible month because it produces the lowest cap) for any loan where the lender charges more than $30. For a 14-day extension of credit, the 235% APR results in a fee equal to around 9% of the principal, so a lender will charge the APR instead of the flat $30 on any loan greater than around $333.

The interaction of the flat fee and the APR means that it isn't actually possible to know if the lender is charging up to the fee cap in Wyoming unless one also knows the duration of the loan. This point eludes Miller & Zywicki entirely.

Nevertheless, their own data seem to indicate that lenders are pricing right up to the limit. A 14-day loan is the standard payday loan, as more people are paid on a biweekly basis than on any other pay frequency. We've seen that the fee limit for a two-week loan of average size in Wyoming ($491) is actually 9%, not the 30% given by Miller & Zywicki.  And lo and behold, Miller & Zywicki find that two-thirds of Wyoming lenders are charging between 9% and 11% for their loans (table C1), which would mean that they are pricing right up to the limit for 14-day loans.  Miller & Zywicki also report some lenders charging less than 9%, which is what you'd expect for 7-day loans, and some charging up to 19-21%, which is right at the limit of what they could charge for a 31-day loan (the maximum loan length in Wyoming). In other words, when with a proper reading of state payday loan fee statutes, Miller & Zywicki's data seems to show exactly the opposite of what they claim.

Example 3: Louisiana

The same problem exists for Louisiana. Miller & Zywicki report the fee cap in Louisiana being at $16.75 per $100 (plus a separate $10 per loan documentation fee—Table 1) and the maximum loan size as $350. That suggests an expected maximum fee of $58.63 for a $350 loan, but Miller & Zywicki report that the actual average fee is $46 and that the average loan size is only $282. Miller & Zywicki see this as evidence that lenders aren’t pricing up to the maximum amount or making loans in the maximum size. The problem is that Miller & Zywicki ignore that while Louisiana has a percentage fee cap for payday loans, it also has a hard cap of $45 in total charges on a payday loan. Extrapolating from the fees allowed for $100 misses this important feature of Louisiana law, which appears in the same sentence in the statute as the percentage fee provision, unlike the documentation fee. Once one gets the law right, it’s apparent that Miller & Zywicki’s data actually shows that lenders are pricing right up to the legal limit.

What about loan size? Louisiana lenders could make larger loans, but because of the $45 fee cap, if they made loan for any larger than $269, they would be charging a lower percentage than the maximum percentage allowed. Now $269 is still less than $282, but Louisiana law authorizes a $10 documentation charge, over and above from the $45 cap. If that charge is included in the loan amount, that puts the loan at $279, virtually the amount Miller & Zywicki report. In other words, once the legal coding mistake is corrected, Miller & Zywicki’s evidence is proving the very opposite of what they claim.

So what do we see then? It’s impossible to say with complete certainty given the aggregate data presented by Miller & Zywicki, but it it appears that if one uses the correct calculation of maximum loan fees, then in twenty of twenty states, rather than seven of twenty states, lenders are pricing right up to the legal maximum in almost all instances. Miller & Zywicki's claim that 30% of the loans are made at less than the statutory maximum fee is undoubtedly wrong. While Miller & Zywicki use the elocution of “less than the statutory maximum fee per $100” that is an inherently misleading metric. Miller & Zywicki’s data seems to confirm the common knowledge over everyone who has ever studied payday lenders—they price right up to the legal maximum.

Loan Amounts

Twenty-six states had a statutory cap on loan amount in 2013. In those states, Miller & Zywicki found that "52.3 percent of the loans were made for an amount within $50 of the cap.” In other words, nearly half the loans were made for a number substantially less than the cap.

Example: Mississippi

Miller & Zywicki appear to have similar coding problems regarding loan size. We’ve already seen that the Louisiana loan size is dictated by the total dollar cap on fees that Miller & Zywicki ignore. But it’s not the only sort of problem. Miller & Zywicki miss an important legal nuance in Mississippi. (Ironically, Miller teaches at Mississippi State University, and Zywicki started at Mississippi College School of Law.) While Mississippi is listed in the paper as having a maximum loan amount of “410/500,” Miller & Zywicki report that average loan size is only $207. So what’s going on?

A payday loan is sometimes called a “deferred deposit advance”, and some states regulate the size of the post-dated check that is given the the payday lender, rather than the size of the loan. The check is for the sum of the loan amount plus the loan fee. Mississippi caps the check size at $500, but at the maximum fee rate is really a maximum $410 loan and a $90 fee. So Miller & Zywicki’s data is technically correct. But they miss something important about the specifics of Mississippi payday lending, What Miller & Zywicki miss is that Mississippi imposes a 30 day term on deferred deposit of checks of more than $250 and allows a two week term for smaller loans. A Mississippi Attorney General opinion letter provides that two simultaneously made $250 loans from the same lender are not treated as a $500 loan, so both can be for two weeks, enabling more lending that might be apparent from a facial reading of the statute. Smaller loans are subject to a slightly different rate cap, but the short of it is that with a deferred deposit of a $250 check, the maximum actual loan is $208—virtually the same amount that Miller & Zywicki find as the average loan amount in Mississippi.

What This All Means

Let me be clear: the type of error demonstrated here is not a minor quibble or passing technical detail. It is about the reliability of the basic input to Miller & Zywicki’s study. If Miller & Zywicki are wrong on the coding of the law, then all of their claims are wrong or at least unsupported by data. It does not matter what sort of fancy statistical analysis one does if the underlying data are incorrectly coded.

Now let me be the first to say that calculating usury caps is not always an easy thing (and do not rely on anything on the internet other than from about rate caps for any product), and particularly for payday loans. Students who have used my Consumer Finance textbook have to work through some problems calculating maximum loan fees and amounts precisely because it is tricky, and at times there has been legal uncertainty in some states about how fee limits apply. So, I think it is entirely possible to make a good faith mistake in this area. I am troubled, however, by the lack of discussion in the paper of the most obvious distinction in patterns on a state-based level, especially given the authors’ apparent awareness of state-based distinctions on all kinds of other issues throughout the paper.

Perhaps I am wrong, and Professors Miller and Zywicki can explain to me why. If not, I hope that Professors Miller and Zywicki will correct their paper and retract their op-ed.


Miller & Zywicki respond to the critique in the podcast (start around 15 minutes in). TL;DR version is that they don't have a response to the criticism, but instead point out that I don't say anything about two of their paper's other findings: the states with low loan amount caps see more loans per borrower and that in states without fee caps the fees cluster.

Specifically, they aren't disputing my findings, but are "working through it" or something like that. It's not a concession, but I don't know what else they can say but "whoopsie."

Their main move is to try to redirect to their other findings, which they think show that the market regulates itself.

I haven't dug into their data on these points, but I'll offer two observations. First, even if fees are clustering in states without caps, that is susceptible to another interpretation, namely that there isn't price competition protecting borrowers, but that there's a natural risk limit--once lenders raise the prices too high, the default losses offset the gains. In other words, there's some natural credit rationing.

Second, regarding their total dollar demand findings, the empirical point sounds correct to me. It comports with what Pew found in Colorado--demand did not fall when rates were regulated. The problem is that Miller and Zywicki are assuming that they can use level of demand to imply price sensitivity. In a normal market, that's correct. But that assumption may not hold true for borrowers who are desperate to obtain funds. It's sort of a distress market. Many borrowers with poor credit do not appear to be price sensitive for short-term funding. These borrowers need a certain number of dollars. They might have some reserve price (e.g., kidney, first born child), but they don't shop around because they don't have a lot of sure-fire options and they don't seem to care about the cost differences below their reserve price--they are just glad that they are able to get credit from someone and fast. Basically, they have a vertical demand curve that has a sudden discontinuity at the reserve price. With a vertical demand curve, the price is determined by whatever the supply level is--there's not counterbalancing supply and demand forces regulating the market. If that's an accurate description of many payday borrowers, then the aggregate dollar amount of an individual's borrowing is irrelevant to showing competitive forces in the market.

In short, I don't think their study is showing what they think it shows.

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