EconMatch

We help candidates and departments find the best possible match
Candidates Employers

Can participating in the match negatively affect candidates?

Participating in the match can only help you. Here at EconMatch, we have been extremely thoughtful to make sure that candidates cannot be made worse off by participating. For instance, a user might be concerned that employers will learn how a candidate ranked them from the result of the match. We've implemented a differential-privacy scheme that prevents employers from being able to infer anything about candidates that weren't recommended.

We accomplish this by only providing to employers their top five matches while withholding the names of a random 20%. Recommended matches are very good for candidates: they are likely the best places a candidate could hope to receive an offer. At the same time, if a candidate is not recommended, the hiring committee cannot infer that the candidate was not interested in the position. Thus, participation helps you when recommended and doesn't reveal your preferences when you aren't.

Can participating in the match negatively affect employers?

We use everyone's preferences to “play out” the market so that each employer knows which candidates are the best ones likely to accept an offer. If incredulous, employers can always ignore our recommendation. We think, however, that focusing flyouts and offers to recommended candidates can simultaneously improve both hiring quality and yield.

What is the optimal strategy when ranking?

To be recommended to your most preferred, attainable employers, it is the dominant strategy for candidates to tell the truth (Dubins and Freedman 1981). In the case where some employers on a candidate’s list could consider the candidate for more than one opening (e.g. two openings in the same field), truth-telling is still likely a dominant strategy for candidates (Hatfield and Milgrom 2005), and it is at least weakly dominant (Dubins and Freedman 1981; Roth 1982; Kojima and Pathak 2009; Rees-Jones 2018). It’s smart, not to mention easier, to state your preferences as they are.

As the market gets large, it is also in the interest of employers to state their preferences honestly (Immorlica and Mahdian 2005; Kojima and Pathak 2009; Azevedo and Budish 2017). This is especially true when employers don’t know much about the preference rankings of candidates and competing employers; without such information, it is difficult for employers to identify profitable strategic manipulations (Roth and Rothblum 1999). Even with complete information about others’ preferences, the set of employers that can possibly benefit from misrepresenting their preferences vanishes as the market gets large (Roth and Peranson 1999; Immorlica and Mahdian 2005). As Roth and Peranson conclude, “the opportunities for strategic manipulation are surprisingly small.”

As an example of how unlikely it is that strategic play can improve your match outcomes, in the resident match that implements a modified deferred-acceptance algorithm, fewer than 1 in 250 employers could possibly improve their match by misreporting their preferences. Even fewer, just 1 in 2,000 candidates, could improve their match by misreporting (Roth and Peranson 1999). It may sound familiar, but honesty is the best policy.

Are my rankings confidential?

Yes, completely. Departments will only see our handful of recommendations, not your rankings and not your personal information. More broadly: we will not, under any circumstances, share your data with anyone.

What market failure is this solving?

EconMatch solves a coordination failure arising from incomplete information. This coordination failure comes from two sources. In part, it reflects the difficulty of candidates to credibly signal their interest in various employers. Second, it reflects the enormous difficulty of employers to discern who is attainable: when an employer considers a candidate, they not only has to evaluate which candidates they like, but also which candidates are likely to receive other offers they would prefer. This herculean task—predicting the preferences of candidates and the preferences of other employers—involves many mistakes which leave advantageous matches unrealized (Coles et al. 2010).

What are the benefits of solving this problem?

Centralized matching markets, like those for medical residency, resolve this coordination failure by eliciting preference rankings from both sides of the market and “playing out” those preferences to find stable matches between candidates and employers using what is now known as the Gale-Shapley deferred-acceptance algorithm (DAA) (Gale and Shapley 1962; Roth 1984). The resulting matches are stable and perform better than decentralized matches (Roth 1990, 1991; Davis 2017), and they improve the welfare of both sides of the market, being weakly Pareto efficient (Abdulkadiroglu, Pathak, and Roth 2009).

Why did you make EconMatch?

The natural hiring process often results in unstable matches, which comes with significant costs to candidates and employers (Roth 1990, 1991). The hiring process can be simpler, and less stressful, while producing better outcomes with a very simple adaptation.

Why? As candidates, we have difficulty persuading employers we’re truly interested in them; and sometimes, we don’t have the time to perform an elaborate dance to demonstrate interest to each of the many places we would like to call home. This leads candidates and employers to depend more on informal networks for signals of interest, narrowing the effective field of search substantially, especially for young faculty.

As employers, the challenge is compounded: we can’t tell which candidates are gettable, in part because their signals (or lack of signals) are not very informative. Even if employers could elicit truthful preferences from each candidate under consideration, they would have difficulty predicting whether the candidate’s preferred employers would prefer the candidate. We developed EconMatch to address both fundamental issues. The resulting matches not only contain information about candidate preferences, but also the preferences of other employers.

Why hasn’t anyone used a normal residency-style matching program for economics before?

The benefits of a match assignment process like the National Resident Matching Program (NRMP) are many, but, unfortunately, these benefits are not widely realized in the labor market because they require a widespread ex ante commitment to the outcome of the centralized match. Our solution marries the flexibility of traditional markets and the wise pairing of centralized markets by adapting DAA into a recommender system that generates for employers a ranked list of candidates in the order of expected match quality.

What if not everyone uses EconMatch?

The recommendation employers receive gets better as more people use the tool. That is, as we incorporate more information (more candidate and employer preferences), the resulting recommendations are unambiguously better. We think, however, that the cost-benefit of using the tool, even if not everyone adopts it immediately, are quite high. For an employer, it should take no more than 10 minutes to register an account and input her preferences for candidates since we have pre-filled their openings with all their candidates that are using EconMatch. We’ve done all that we can to make using the tool simple, quick, and easy.

The benefits, however, can be quite significant. The employer will learn a great deal about those candidates who participate: The department receives a rank-ordered list of the top five participants. From the process, they learn which participants are the best-attainable, and which are not. Learning about the attainability of a significant fraction of candidates from a 10-minute process seems like a good tradeoff.

What’s the big picture here?

In the labor market, candidates (employers) attempt to match with the best willing employer (candidate). It would be a mistake for the average employer to devote their flyouts to only the most accomplished candidates since those candidates are likely to secure a better (that is, preferred) offer. Employers, therefore, often bypass strong candidates for those they think will accept an offer, though they have limited information on the preferences of the other market participants. This strategic interaction gives rise to a coordination failure in which employers and candidates, who would be well-suited, fail to match.

A few matching markets, like the one for residency programs, adopted a centralized matching process that allows candidates and employers to rank-order each other. The gains of such a solution may be particularly large in settings where preferences are idiosyncratic, since accommodating one person's unique preferences is less likely to come at the expense of another's. Though efficient, this solution is not widely used because candidates and employers must commit (ex ante) to accept the outcome of an algorithm. While submitting to a match could be theoretically better for both parties, the coordination requirements of the centralized technical solution may be too great.

We developed a recommender system by modifying the Gale-Shapley deferred-acceptance algorithm to generate a ranked list for employers which reflect the ordered likelihood of a good match with each candidate based on the candidates' preferences, the employers' preferences, and the preferences of other employers. This allows employers and candidates to be guided to the best, attainable match likely to maximize the welfare of both sides of the market.

How the does the algorithm work to generate recommendations?

The Gale-Shapley deferred-acceptance algorithm (DAA) is a canonical algorithm, based on the problem of a village Yenta. Consider the local matchmaker's difficulty of pairing single men and women. Her intent is to create married pairs for which there is no preference for divorce or infidelity. This is accomplished if every man (woman) prefers his wife (her husband) to the women (men) that prefer him (her) to their husbands (to their wives), a boggling logistical puzzle.

The Gale-Shapley DAA solves this problem. Each single man (woman) indicates his (her) preference for potential mates by ranking them. In the first stage, the men propose to their first choice and the women review their offers and conditionally accept their most preferred mate. Men who did not match in their first proposal approach their second-choice, even if that person has conditionally accepted another man's proposal. If the woman prefers the new proposal, she can decline her previous proposal and conditionally accept the new suitor. This process iterates with unattached men sequentially proposing until everyone is engaged or has exhausted their list of mates they prefer over remaining single (Gale and Shapley 1962).

The algorithm has a few interesting properties. First, the resulting pairs are stable—that is, no one would prefer a potential spouse who also prefers them to their partner. Second, the algorithm is strategy proof for the proposing party. It is also strategy proof for the receiving party as the market becomes large because the set of possible stable matches becomes smaller and smaller. This means that men and women will find it in their interest to reveal their true preferences to maximize the utility they receive from the resulting match. This algorithm can also be used in labor markets to help facilitate the optimal matching of employers and applicants, rather than husbands and wives.

To help accommodate the fact that departments and candidates have evolving preferences as they learn more about one another in stages, we modify the algorithm to provide a ranked-list of matches in order of likely match quality rather than a single set of pairs. The first-best match is the pair generated by the traditional DAA. We then remove from each preference list the party they matched with and re-run the DAA to generate the best match should the first fail for any reason. After which, we remove the first and second matched party from each person's ranked list and re-run the DAA. In this way, we generate an ordered list of potential matches that represent the “best matches” while allowing preferences to evolve as employers and candidates absorb new information.

References

Abdulkadiroğlu, Atila, Parag A. Pathak, and Alvin E. Roth. “Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match.” American Economic Review 99, no. 5 (2009): 1954-78.

Azevedo, Eduardo M., and Eric Budish. “Strategy-proofness in the large.” No. w23771. National Bureau of Economic Research, 2017.

Coles, Peter, John Cawley, Phillip B. Levine, Muriel Niederle, Alvin E. Roth, and John J. Siegfried. “The job market for new economists: A market design perspective.” Journal of Economic Perspectives 24, no. 4 (2010): 187-206.

Davis, Jonathan MV. “The short and long run impacts of centralized clearinghouses: Evidence from matching teach for America teachers to schools.” No. pda791. Job Market Papers, 2017.

Dubins, Lester E., and David A. Freedman. “Machiavelli and the Gale-Shapley algorithm.” The American Mathematical Monthly 88, no. 7 (1981): 485-494.

Gale, David, and Lloyd S. Shapley. “College admissions and the stability of marriage.” The American Mathematical Monthly 69, no. 1 (1962): 9-15.

Hatfield, John William, and Paul R. Milgrom. “Matching with contracts.” American Economic Review 95, no. 4 (2005): 913-935.

Immorlica, Nicole, and Mohammad Mahdian. “Marriage, honesty, and stability.” In Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 53-62. Society for Industrial and Applied Mathematics, 2005.

Kojima, Fuhito, and Parag A. Pathak. “Incentives and stability in large two-sided matching markets.” American Economic Review 99, no. 3 (2009): 608-27.

Rees-Jones, Alex. “Suboptimal behavior in strategy-proof mechanisms: Evidence from the residency match.” Games and Economic Behavior 108 (2018): 317-330.

Roth, Alvin E. “New physicians: a natural experiment in market organization.” Science 250, no. 4987 (1990): 1524-1528.

Roth, Alvin E. “The economics of matching: Stability and incentives.” Mathematics of operations research 7, no. 4 (1982): 617-628.

Roth, Alvin E. “The evolution of the labor market for medical interns and residents: a case study in game theory.” Journal of political Economy 92, no. 6 (1984): 991-1016.

Roth, Alvin E., and Elliott Peranson. “The redesign of the matching market for American physicians: Some engineering aspects of economic design.” American economic review 89, no. 4 (1999): 748-780.

Roth, Alvin E., and Uriel G. Rothblum. “Truncation strategies in matching markets—in search of advice for participants.” Econometrica 67, no. 1 (1999): 21-43.

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