Making a Match

Plus! Diff Jobs; Instacart: Ahead of the IPO; Movie Clips and the Piracy Equilibrium; EVs and Public Choice Theory; Banks Retrench; China's Lost Decade?

Byrne Hobart Byrne Hobart

Making A Match

It's not uncommon for someone to turn academic research into a business. There are plenty of examples of people turning academic research into real businesses, like dividend futures, Moderna, Genentech and large swathes of the AI industry (even if we exclude cases where someone realizes that the PhD thesis they're working on has a pre-money valuation of $30m). But they're rarer in social science and economics. Sure, you might perform a study arguing that business owners irrationally do X instead of Y, but the natural rejoinder is that this study really shows that Y sounds good on paper and X is what you do when you have skin in the game.

One surprisingly complex example of economic research turning into a viable business with a real-world impact is the story of how med school students get matched to residencies. Every year, on Match Day, tens of thousands med school students find out where they'll be working over the next three to seven years. Last year, there were 48,000 applicants for 40,000 positions; 93.3% of positions were filled, and 81.1% of applicants found a match. These matches, and thus the next half-decade or so of students' lives, get determined by an algorithm. (One funny thing about modern discourse on "algorithms" is that it's used as a pejorative term, but really isn't. When someone joins a union, for example, they're demanding that their wages get set by an algorithm! hourly_pay = min(18 + (1.50 * years_of_experience), 25) is, in fact, just as much of an algorithm as the dynamic pricing of an Uber ride.)

This is a nontrivial problem, in three senses:

  1. The theoretical number of potential matches is 48,000^40,000, though that assumes that everyone gunning for a neurosurgery would be fine with ophthalmology and vice-versa. There's just an unavoidable layer of transaction costs required to get each side to narrow down their preferences enough that it's tractable to compare them.
  2. In any situation where people are asked to state preferences that the other side will incorporate into their decision, whether it's haggling, hiring, dating, an auction, or a plea bargain, there's an incentive for each side to fib a bit in order to improve their negotiating position. And in matching in particular, there's an incentive to jump the gun: if everyone else makes a decision on day T, there's much less competition on day T-1, but as soon as everyone realizes this, that day becomes the new Day T, and the process repeats. Programs also had an incentive to make "exploding offers," giving students a tight deadline in which to make their decision. If this happened before they’d interviewed widely, it would weaken their direct negotiating position and mean they were operating with less information. Meanwhile, the student—who is making the choice one time—had to make a quick decision against a counterparty who did this multiple times a year and had many years of experience.
  3. For med school matches, and others, there are additional quirks. Some programs want an even-numbered set of applicants: four or six are preferable to five if you want people to either work in pairs or to have twelve-hour shifts that provide 24-hour coverage. Some medical students are in relationships with each other, and want programs in the same location.

Medical students and residencies faced that middle problem in the 1940s: schools kept recruiting earlier, and students tried to game that system to get the best placements. Everyone knew it was inefficient for both sides to invest so much effort in rearranging who went where instead of spending that time studying or practicing medicine, but there wasn't a good way to break the logjam. Then, in 1950, a med school professor suggested a "clearinghouse" system, where everyone, students and programs, would submit a ranked list of their preferences all at once, and then get matched on that basis. This turned out to disincentivize students from making high-risk first choices, but a later tweak, "Deferred acceptance," mostly addressed this: students get an initial match, but can accept a better one.

This basic model—rank choices on both sides, and match—has been in place ever since. And it turns out to be similar to the model in this paper, "College Admissions and the Stability of Marriage," published in 1962. (The paper was published in The American Mathematical Monthly, but is extremely clear to the non-mathematical reader. There isn't a single formula, though the authors did insist on using Greek letters for variable names a handful of times.) The original implementation was manual, but became more automated over time. At one stage of the automation process, around 1970, the The National Resident Matching Program hired an engineer, Elliott Peranson, to implement it. A decade later, the rise of minicomputers led to an opportunity to reimplement the same system on cheaper and faster hardware, making it cost-effective for more matches, so Peranson formed National Matching Services (NMS), which continues to provide this service some 50 years later.

NMS's business is a bit like the classic open source model. It can't function if the algorithm itself is proprietary, since so much of the value comes from whether or not users trust it. But understanding an open technology well and being able to implement it means having a comparative advantage in offering adjacent services like application services, scheduling software, and analytics. So NMS is a sort of Mongodb of Matching, a for-profit entity whose model encourages it to care for and improve access to the commons. The optimal pricing for this ties into yet another Nobel-Memorial prize winner’s work: there’s a two-sided network, so there’s more than one stable arrangement regarding who pays. Usually the optimal arrangement is to subsidize the most price-sensitive side of the network, because its growth is an implicit subsidy to the other side.

One part of that, and an essential part, was demonstrating that the algorithm used was, in fact, fair. There was a fierce debate about this in medical circles in the early 1990s, and a seminal contribution to the debate was this paper by, which Peranson wrote with the economist Alvin Roth. The paper looks at, among other things, whether changing the sequencing of matches, i.e. if you work through programs or candidates in a different order, do you get a different set of matches? The paper tested an alternative sequencing and found that out of over 22,000 applicants, exactly four would end up with different matches under a different sequencing system. (Roth ended up winning the Sveriges Riksbank Almost-Nobel along with Shapely, who coauthored the stability of marriage paper, in 2012.)

This is a null result. But it's an incredibly valuable one, because what it tells people on both sides of the match is that they're getting a match that's hard to improve on. (Publishing socially valuable null results is somewhat analogous to the practice of doing lots of research to justify an investment that's obviously cheap. If a company is growing 10% annually and you can buy shares at a 10% free cash flow yield, that's obviously, blatantly, a good decision—which, of course, means that you need to work very hard to think of all the reasons someone might be selling those shares to you, and validate that these are not good reasons.) It won't be perfect, but another part of the paper dives into an important feature: the lower the transaction cost for applying, the more potential stable sets of matches there are. But with high transaction costs, there are fewer equilibria and most changes make both sides worse off.

That's important as a theoretical matter, because it helps explain why residency matching can actually work. But it also has a practical application: the way the process works is that students reach out to programs and interview them, and that's how each side ends up on the others' target list. During the pandemic, these interviews switched to Zoom. And that cut a big deadweight travel cost from the process. And since that fixed cost is gone, Alchian-Allen tells us that the rest of the interview process will be shorter, too; if someone's already traveling across the country, a multi-day interview process is fine, but if they're on Zoom, shorter is better. Anecdotally, interviews range from a few hours to a full day. That means more potential interviews per candidate, and a theoretical increase in the number of matches. Two forces keep this from being a huge problem: improvements in teleworking software have not outstripped improvements in number-crunching hardware, so for now this has not led to any combinatorial explosion in potential stable matches. And, more importantly, most of the time saving was on the part of the applicants, not the programs, since the applicants were the ones traveling for interviews. The opportunity cost of interviews still constrains how many a given residency will do.

In a narrow sense, matching is a zero-sum game: being the runner-up candidate for a spot you wanted means somebody else got it. But there's definitely value to be created in good matching; it's more realistic to think there's a rank-ordering of the best students for a given program than a rank ordering of the best medical students, period, because different sub-skills are rewarded in different domains. (A terrible bedside manner is less of a liability if the patients are usually sedated, for example). And the special thing about matching is that it involves both choosing and being chosen, so every match has to satisfy two parties. If it's positive-sum to match the right people, that means that it's socially useful to a) have a good algorithm, and b) have a trusted algorithm

Looking at this system, a natural question arises: if there's a pretty fair model for matching talent to opportunities, why isn't it used more widely? It does get used in things other than medical school residencies, in fact; it gets used in the New Museum's incubator, public school admissions in New York City, and study abroad programs. But matching algorithms have some strict criteria: they work best when every match happens on a set timetable (so they're great for recruiting out of and into academic programs) and they need the highest-status institutions to join. That condition works best when the best-known institutions are all reasonably close in status, or at least think so.

One natural place where this could theoretically work is in private equity, where recruiting schedules have been notoriously creeping earlier ($, WSJ). The old process was that people would go work for a bank for two years, and late in their banking stint they'd start interviewing with the PE firms that would hire them next. But that keeps getting earlier to the point that the recruiting process for 2025 started in July of this year(!). PE firms could all get together and agree that it's ridiculous to hire people for jobs that require two years of experience at a time when the candidates have zero years of experience. ( In the bad old days, med school matching had the same issue. Apparently the old joke was "I've got to get into med school—my neurosurgery residency starts in six years!) But private equity executives think differently than doctors; they're all trying to get differentiated returns, and they like to be good at deal sourcing, so when you tell them to standardize something they consider a competitive advantage, they'll balk. And even if they did agree, the temptation to break the rules would be high. Perhaps as more firms work together on deals, they'll decide that coordinating other aspects of their business makes sense, too.

A big theme in economics is the quest to measure and maximize efficiency, where efficiency is specifically defined as the best allocation of resources. That itself is a big, complicated matching problem; arguably trillions of dollars of GDP are spent on matching (finance matches money to opportunities, advertising matches goods and services to their potential consumers, retail basically does this, too; the fact that Walmart carries a different set of products than Tiffany, and customers know what they're getting, is a testament to the value of a good match). Most of the time, this is a messy process with mistakes and deadweight loss on all sides. And, every once in a while, it works exactly the same way in the real world that it does in academic papers.

Thanks to Elliott and Jonah Peranson at National Matching Services for taking the time to talk to me about this history. And thanks to Jack Chong for flagging a tweet about them last year.

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Elsewhere

Instacart: Ahead of the IPO

Instacart has filed its latest prospectus update, raising its pricing range to $28-$30/share (i.e. a fully-diluted market capitalization, after the offer, of $9.9bn). One interesting update since the first filing is that their COO stepped down from the board of AppLovin. This could be a mere time-management exercise—one benefit of board membership is getting a sense of how much extra work being a public company entails!—but it might also be a prudent admission that an executive at one ad company might have a conflict of interest serving on the board of another.

The big debate over Instacart is their growth. It was definitely a Covid story at one point (the point where it was raising at a $39bn valuation), and absolute order growth has slowed. But if you take their chart of Covid and non-Covid-related purchases, and strip out Covid, you get a growth rate in orders for the first half of this year that’s +9% Y/Y instead of +0.5% Y/Y. That’s still a big deceleration from before, but note that the “Covid-related” criterion is for products strictly related to the pandemic, not for demand induced by the pandemic-era shift towards online ordering. So Instacart’s order volume shows the decelerating-growth pattern one would expect from a high-growth company that reaches scale and from a company that benefited from a one-time shift in consumer behavior that partially reverted.

Revenue growth is higher, both because they've gotten more efficient at managing deliveries (increasing their order fee revenue) and because ad targeting gets better with scale. Earnings are noisy because of a tax benefit last year, but if you take their pretax income and just put a 21% tax rate on it, Instacart's trailing net income for the last four quarters would be $356m. That puts their earnings multiple at 27x. Which is not cheap, of course, but not the kind of valuation growth investors blink at.

(The Diff did a deep dive on Instacart's S-1 last month.)

Movie Clips and the Piracy Equilibrium

Piracy is as old as the existence of media that's expensive to create and cheap to duplicate, and media economics have always been defined by this relationship. (This means that the story of media is cyclical over incredibly long periods; both Taylor Swift and Homer made their big money from live performances.) Typically, there's a level of piracy that's tolerable, or even beneficial—people pirating desktop software in the 90s were also reinforcing software standards that would pay off as authentication got better and more products moved to subscription SaaS in the 2000s. In movies, short clips probably improve ticket sales, rental revenue, and streaming usage. But the rise of better algorithmic feeds like TikTok's mean that people can easily stream entire feature films in short chunks ($, WSJ). If someone has watched the first fifteen minutes of Barbie, the algorithm knows exactly what they want to see next. This is a fun edge case, and naturally won't last; YouTube, too, used to be a repository of pirated content until they cracked down. It's a good reminder for media businesses that even if they own valuable IP, the nature of distribution can rapidly change in ways that erode or increase that value.

EVs and Public Choice Theory

In the very long run, many technological shifts are inevitable: if there's a way to get more output from constant inputs, whoever adopts it first ends up owning their entire market or forcing incumbents to catch up. But the pace at which this happens, especially for technologies that have complex supply chains and network effects around consumption, is partly a matter of policy. For example: one reason auto unions are striking right now is that they're concerned that EV manufacturing is more efficient than ICE vehicle manufacturing, which means fewer jobs. And the EV supply chain, with its heavy dependence on batteries, was built at a time when unions were less popular, so the unionization level of the supply chain is also under threat.

Containerization presents a nice precedent for how to resolve this: a union represents the interests of union members, who are specific people with a specific career span. But a corporation is immortal unless something kills it. So companies tend to have lower discount rates than unions, and can offer deals where current union members do very well but there are fewer union jobs after those members retire. That's how US ports got more automated (while the remaining union jobs pay extremely well). One interesting side effect of this is that the more ambitious a car company is about its EV plans, the better a given wage package for the union looks, because going electric reduces their future dependence on unions. But that means the industry can easily fall into a trap, where their labor costs make it hard to afford risky capital expenditures, and the lack of a long-term plan to grow out of their current problems also means they're more fixated on cutting labor costs, even at the risk of strikes, in the present.

Banks Retrench

Higher rates have forced banks to reconsider their full-service model, mostly because of the squeeze on profits ($, FT). This is a paradoxical effect: the simplest model of a bank is that it provides a suite of services that allow it to borrow what is legally short-term, and at short-term interest rates, but what is practically long-term, and then to invest the proceeds into higher-rate but less-liquid assets and collect a spread. That is still a rates bet, albeit an esoteric one, whereas more elaborate banking models (credit cards, wealth management) tend to expose them to a different set of macro factors. But it's hard to run a multi-year campaign of diversification when you're also worried about quarterly earnings misses or day-to-day funding shortfalls. So the paradoxical effect of worse performance in the rates-sensitive part of the business is that that's where companies are investing more of their efforts today.

China's Lost Decade?

The Economist has a good piece digging into Chinese macroeconomic statistics a bit ($) to disentangle two effects: a broad economic slowdown that could push them into a Japan-in-the-90s style low-growth environment, and sector-specific problems in real estate and a shadow banking sector. They argue that the latter predominates, and that the rest of China's economy is still biased towards growth. One reason China doesn't face the same problem is that state-owned enterprises are essentially part of fiscal policy; the Chinese government can avoid running deficits by directing state-owned enterprises to borrow for capital expenditures (what shows up as a cost on the government's budget is a capital expenditure when done by a company, even if exactly the same amount is spent on exactly the same project).